CN112556981B - Suspension tunnel water elastic response holographic truncation simulation method and system - Google Patents
Suspension tunnel water elastic response holographic truncation simulation method and system Download PDFInfo
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Abstract
The invention provides a holographic truncation simulation method and system for water-elastic response of a suspended tunnel, and relates to the technical field of suspended tunnels, wherein the method comprises the following steps: determining a holographic truncation geometric scale, a wave field truncation boundary and a longitudinal truncation point position of the suspended tunnel in an initial simulation domain of the suspended tunnel based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model; determining a target control signal of an truncation execution structure (a pool wave generator and a six-degree-of-freedom motion platform in a physical domain) based on a holographic truncation geometric scale and the wave propagation and structure dynamic response coupling calculation numerical model; and performing holographic cooperative truncation control on the pool wave maker and the six-degree-of-freedom motion platform based on the target control signal so as to perform holographic truncation simulation on the hydro-elastic response of the suspended tunnel. The invention can ensure the authenticity and the accuracy of the complex wave hydrodynamic load action and can realize the simulation of the whole dynamic response and the local motion stress deformation water elastic response of the suspension tunnel.
Description
Technical Field
The invention relates to the technical field of suspension tunnels, in particular to a suspension tunnel hydro-elastic response holographic truncation simulation method and system.
Background
The suspended tunnel is a large underwater tunnel which is constructed by using buoyancy of water and suspended in the water, and is a subversive cross-sea channel technology for realizing crossing of deep-sea fjonds in the future by humans after crossing a sea bridge and a submarine tunnel. Compared with the traditional ultra-large floating structure, the suspended tunnel structure system is more complex in composition, the span can extend dozens of kilometers or even hundreds of kilometers, the range of water crossing is wider, the spatial difference of environmental loads such as submarine conditions and wave water current along the line is larger, the system composition is quite complex, and under the complex marine environmental load, the motion stress deformation response of the whole and local structure, the outside and inside of the structure, namely the 'hydro-elastic response problem' of interaction between hydrodynamic force and an elastic structure system, is inevitable.
The existing main method is to adopt numerical simulation or physical model test alone, however, the numerical simulation method easily causes that a calculation model is difficult to consider the propagation simulation of large-range complex waves and the accurate calculation of the overall and local motion and stress deformation parameters of a complex structure; and the physical model test method is difficult to accurately simulate the constraint action, the end constraint and the actual rigidity of the adjacent structural sections of the suspension tunnel. And the underwater real water elasticity dynamic and stress conditions of the super-long width suspension tunnel structure cannot be accurately and effectively simulated due to the limitation of the range of an experimental site, the performance of equipment, a scale and the like, the limited tunnel range can only be covered, the flexibility of transformation and modification is insufficient, the cost is huge, time and labor are wasted, and the underwater real water elasticity dynamic and stress conditions of the super-long width suspension tunnel structure cannot be accurately and effectively simulated.
Disclosure of Invention
The invention aims to provide a holographic truncation simulation method and system for suspension tunnel hydro-elastic response, which can ensure the authenticity and accuracy of the complex wave hydrodynamic load effect and can realize the accurate simulation of the whole dynamic response and the local motion stress deformation hydro-elastic response of the suspension tunnel.
In a first aspect, the invention provides a suspended tunnel hydro-elastic response holographic truncation simulation method, which comprises the following steps: acquiring a holographic truncation geometric scale, a wave field truncation boundary and a suspension tunnel longitudinal truncation point position of an initial analog domain of a suspension tunnel; determining a target control signal of an interception execution structure based on a holographic interception geometric scale and a pre-established wave propagation and structure dynamic response coupling calculation numerical model; the truncation execution structure comprises a pool wave generator and a six-degree-of-freedom motion platform in a physical domain; the physical domain is a model space determined by an initial simulation domain based on a holographic truncation geometric scale, a wave field truncation boundary and a suspension tunnel longitudinal truncation point; and performing holographic cooperative truncation control on the pool wave generator and the six-degree-of-freedom motion platform based on the target control signal so as to perform holographic truncation simulation on the hydro-elastic response of the suspended tunnel.
In an alternative embodiment, the step of establishing the wave propagation and structural dynamic response coupling calculation numerical model established in advance comprises: determining wave field parameters within a specified distance of the suspended tunnel structure through a preselected wave numerical model and a target environment condition; the target environmental conditions include seafloor terrain conditions and wave conditions; determining hydrodynamic force borne by the tube body and the anchor cable of the suspension tunnel according to wave field parameters in a specified distance of the suspension tunnel structure; and determining the motion, deformation and anchor cable tension of the pipe body-anchor cable system under the action of waves based on the hydrodynamic force borne by the pipe body and the anchor cable of the suspension tunnel so as to determine a wave propagation and structural dynamic response coupling calculation numerical model.
In an alternative embodiment, the step of determining the movement, deformation and anchor line tension of the tube and anchor line system under the action of the waves based on the hydrodynamic forces to which the tube and anchor line of the suspended tunnel are subjected comprises: constructing a stress-motion-deformation coupling model of the pipe body under the action of waves on the basis of hydrodynamic force borne by the pipe body and the anchor cable of the suspension tunnel and a pre-selected elastic beam theory; calculating the motion and deformation of the pipe body under the action of waves based on a modal superposition method and a force-motion-deformation coupling model of the pipe body under the action of waves; and establishing a numerical model of the anchor cable system by a concentrated mass method, performing iterative calculation on the motion and deformation of the pipe body and the anchor cable system, and determining the motion, deformation and anchor cable tension of the pipe body-anchor cable system.
In an optional embodiment, the step of determining the holographic truncation geometric scale of the initial analog domain of the suspended tunnel based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model, and determining the truncation boundary of the wave field and the longitudinal truncation point position of the suspended tunnel includes: pre-selecting an initial holographic truncation geometric scale, an initial wave field truncation boundary and an initial suspension tunnel longitudinal truncation point position; the holographic truncation geometric scale is the ratio of the geometric dimension of the suspended tunnel prototype to the geometric dimension of the model; determining prototype wave elements and the maximum motion quantity of a prototype structure based on a wave propagation and structural dynamic response coupling calculation numerical model established in advance and the overall dynamic response of the levitation tunnel; the prototype wave element at least comprises the maximum wave height and the corresponding maximum frequency of the prototype wave; maximum movement of prototype structure maximum movement amplitude and corresponding maximum frequency of the prototype structure; calculating to obtain model wave elements and model motion elements based on the initial holographic truncation geometric scale, the prototype wave elements and the maximum motion amount of the prototype structure; judging whether the model wave elements and the model motion elements meet all preset constraint conditions or not; if so, determining the initial holographic truncation geometric scale, the initial wave field truncation boundary and the initial suspension tunnel longitudinal truncation point position as the corresponding holographic truncation geometric scale, the wave field truncation boundary and the suspension tunnel longitudinal truncation point position.
In an alternative embodiment, the preset constraints include: (1) whether the model wave elements meet the maximum wave making capacity of the pool wave making machine or not; the model wave element comprises a model maximum wave height and a corresponding maximum frequency; (2) whether the model motion elements meet the maximum motion capability of the six-degree-of-freedom motion platform or not; the model motion elements comprise the maximum motion amplitude and the corresponding maximum frequency of the model structure; (3) whether the change amplitude of the terrain along the wave field truncation boundary meets the specified gradient requirement or not; (4) and whether the model length in the specified range of the longitudinal cutoff point position of the suspension tunnel exceeds the effective range of the physical domain test pool or not.
In an optional embodiment, the target control signal comprises a wave-making control signal and a six-degree-of-freedom motion platform power control signal; the step of determining a target control signal for truncating an executing structure based on a pre-established wave propagation and structure dynamic response coupling calculation numerical model comprises the following steps: extracting numerical dynamic information at the holographic truncation boundary based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model; the numerical power information comprises first numerical power information and second numerical power information; determining a wave generation control signal of the pool wave generator based on the first numerical power information; and determining a power control signal of the six-freedom-degree motion platform based on the second numerical power information.
In an alternative embodiment, the method further comprises: establishing a wave propagation truncation model according to a first similarity criterion based on the holographic truncation geometric scale and the specified wave parameters; wherein the designated wave parameters at least comprise wave height, period, wave direction and water depth; the first similarity criterion comprises a geometric similarity criterion and a gravity similarity criterion; establishing a suspended tunnel hydro-elastic response truncation physical model according to a second similarity criterion based on the holographic truncation geometric scale and the specified structural parameters; wherein the specified structural parameters include at least the length, diameter, density, modulus of elasticity, and stiffness of the model; the second similarity criteria include geometric similarity, gravitational similarity, and elastic similarity criteria.
In an optional embodiment, the step of performing holographic collaborative truncation control on the pool wave maker and the six-degree-of-freedom motion platform based on the target control signal comprises: inputting the wave-making control signal into a pool wave-making machine, and carrying out a wave-making test in a physical domain based on a wave propagation truncation model; inputting a power control signal to a six-degree-of-freedom motion platform, and performing motion control on a suspension tunnel longitudinal truncation point of a physical domain based on a suspension tunnel hydro-elastic response truncation physical model; the water pool wave making machine is in real-time data communication with the six-degree-of-freedom motion platform; and monitoring and compensating synchronous errors of the pool wave generator and the six-degree-of-freedom motion platform to perform holographic cooperative truncation control on the pool wave generator and the six-degree-of-freedom motion platform.
In a second aspect, the present invention provides a suspended tunnel hydro-elastic response holographic truncation simulation system, which is configured to execute the hydro-elastic response holographic truncation simulation method according to any one of the foregoing embodiments.
In a third aspect, the present invention provides an electronic device comprising a processor and a memory; the memory is stored with a computer program which, when executed by the processor, performs the suspended tunnel hydro-elastic response holographic truncation simulation method according to any one of the preceding embodiments.
The invention provides a holographic truncation simulation method and a holographic truncation simulation system for suspension tunnel hydro-elastic response, the method firstly obtains the holographic truncation geometric scale, the wave field truncation boundary and the longitudinal truncation point position of the suspension tunnel of an initial simulation domain of the suspension tunnel, then determining a target control signal of an interception execution structure based on the holographic interception geometric scale and a pre-established wave propagation and structure dynamic response coupling calculation numerical model, the truncation execution structure comprises a pool wave generator and a six-degree-of-freedom motion platform in a physical domain, wherein the physical domain is a model space determined by an initial simulation domain based on a holographic truncation geometric scale, a wave field truncation boundary and a suspension tunnel longitudinal truncation point position, and finally, holographic collaborative truncation control is performed on the pool wave generator and the six-degree-of-freedom motion platform based on a target control signal so as to perform holographic truncation simulation on hydro-elastic response of the suspension tunnel. According to the method, the holographic truncation geometric scale of the initial analog domain of the suspension tunnel, the wave field truncation boundary and the longitudinal truncation point position of the suspension tunnel are obtained, and the wave distribution nonuniformity, nonlinearity and directivity on the complex wave field truncation boundary are fully considered, so that the space-time continuity of the numerical value domain wave and the physical domain wave propagation process included in the initial analog domain is ensured, and the authenticity and the accuracy of the hydrodynamic load action of the complex wave are ensured; the simulation of the whole dynamic response and the local motion stress deformation hydro-elastic response of the suspension tunnel can be realized by performing holographic collaborative truncation control on the pool wave generator and the six-degree-of-freedom motion platform based on the target control signal.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a schematic flow diagram of a suspended tunnel hydro-elastic response holographic truncation simulation method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a large-scale multidirectional wave propagation and structural dynamic response coupling calculation numerical model establishment provided by an embodiment of the present invention;
fig. 3 is a schematic diagram of a suspended tunnel hydro-elastic response holographic truncation simulation method according to an embodiment of the present invention;
fig. 4 is a schematic view of a wave field and a longitudinal cutoff design of a suspended tunnel according to an embodiment of the present invention;
FIG. 5 is a schematic view of an L-shaped wave-making vehicle pool according to an embodiment of the present invention;
FIG. 6 is a schematic view of a Stewart six-degree-of-freedom motion platform provided by an embodiment of the invention;
FIG. 7 is a schematic diagram of a holographic cooperative truncation physical model test for wave propagation and suspension tunnel hydroelasticity dynamic response according to an embodiment of the present invention;
fig. 8 is a schematic flow chart of a specific suspended tunnel hydro-elastic response holographic truncation simulation method according to an embodiment of the present invention;
fig. 9 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings or the orientations or positional relationships that the products of the present invention are conventionally placed in use, and are only used for convenience in describing the present invention and simplifying the description, but do not indicate or imply that the devices or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.
Furthermore, the terms "horizontal", "vertical", "overhang" and the like do not imply that the components are required to be absolutely horizontal or overhang, but may be slightly inclined. For example, "horizontal" merely means that the direction is more horizontal than "vertical" and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.
In the description of the present invention, it should also be noted that, unless otherwise explicitly stated or limited, the terms "connected" and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in a specific case to those of ordinary skill in the art.
Some embodiments of the invention are described in detail below with reference to the accompanying drawings. The embodiments described below and the features of the embodiments can be combined with each other without conflict.
For convenience of understanding, firstly, a detailed description is given to a suspended tunnel hydro-elastic response holographic truncation simulation method provided in an embodiment of the present invention, which may be applied to a design of a super-long span suspended tunnel, and referring to a flow diagram of a suspended tunnel hydro-elastic response holographic truncation simulation method shown in fig. 1, the method mainly includes the following steps S102 to S106:
and S102, determining a holographic truncation geometric scale of an initial simulation domain of the suspended tunnel based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model, and determining a wave field truncation boundary and a longitudinal truncation point position of the suspended tunnel.
Firstly, an initial simulation domain of the whole suspension tunnel is cut into a numerical value domain and a physical domain, wherein the model space of the numerical value domain covers the model space of the physical domain. Trial calculation analysis is carried out through a pre-established wave propagation and structural dynamic response coupling calculation numerical model (also called a large-range multidirectional wave propagation and structural dynamic response coupling calculation numerical model) to determine a holographic truncation geometric scale lambda, wherein the holographic truncation geometric scale lambda is the ratio of the geometric size of the suspended tunnel prototype to the geometric size of the model. In one embodiment, the wave field truncation boundary and the vertical truncation point position of the suspension tunnel are pre-designed, wherein the wave field truncation boundary information includes the origin of the pool in the physical domain and the included angle between one side of the pool and the horizontal axis, and the pre-designed vertical truncation point position of the suspension tunnel is located in the physical domain, and the truncation point position may be, for example, two truncation points located on the same straight line.
And step S104, determining a target control signal of the truncation execution structure based on the holographic truncation geometric scale and a pre-established wave propagation and structure dynamic response coupling calculation numerical model.
In one embodiment, the truncation execution structure comprises a pool wave generator and a six-degree-of-freedom motion platform in a physical domain, wherein the physical domain is a model space determined by an initial simulation domain based on a holographic truncation geometric scale, a wave field truncation boundary and a suspension tunnel longitudinal truncation point. The ratio of the geometric dimension of the suspended tunnel prototype to the geometric dimension of the model can be determined through the holographic truncation geometric scale, and the physical domain and the numerical domain can be further determined according to the wave field truncation boundary and the position of the suspended tunnel longitudinal truncation point.
And S106, performing holographic cooperative truncation control on the pool wave maker and the six-degree-of-freedom motion platform based on the target control signal so as to perform holographic truncation simulation on the hydro-elastic response of the suspended tunnel.
The target control signal comprises a wave making control signal of the pool wave making machine and a power control signal of the six-degree-of-freedom motion platform, numerical power information at the holographic truncation boundary is extracted based on the established wave propagation and structural power response coupling calculation numerical model, the numerical power information comprises first numerical power information and second numerical power information, the wave making control signal of the pool wave making machine is determined based on the first numerical power information, and the power control signal of the six-degree-of-freedom motion platform is determined based on the second numerical power information. And then inputting a wave-making control signal into the pool wave-making machine, inputting a power control signal into the six-degree-of-freedom motion platform, and performing motion control on a suspension tunnel longitudinal truncation point of a physical domain based on a suspension tunnel hydro-elastic response truncation physical model, wherein the pool wave-making machine is in real-time data communication with the six-degree-of-freedom motion platform, and the synchronous error of the pool wave-making machine and the six-degree-of-freedom motion platform is monitored and compensated, so that holographic cooperative truncation control is performed on the pool wave-making machine and the six-degree-of-freedom motion platform.
According to the holographic truncation simulation method for the water-elastic response of the suspended tunnel, provided by the embodiment of the invention, by acquiring the holographic truncation geometric scale, the wave field truncation boundary and the longitudinal truncation point position of the suspended tunnel of the initial simulation domain of the suspended tunnel, the wave distribution nonuniformity, nonlinearity and directivity on the complex wave field truncation boundary are fully considered, so that the space-time continuity of the propagation process of waves in the numerical value domain and waves in the physical domain included in the initial simulation domain is ensured, and the authenticity and the accuracy of the hydrodynamic load action of the complex waves are ensured; the simulation of the whole dynamic response and the local motion stress deformation water elastic response of the suspension tunnel can be realized by performing holographic cooperative truncation control on the pool wave generator and the six-degree-of-freedom motion platform based on the target control signal.
In one embodiment, the pre-established wave propagation and structural dynamic response coupling calculation numerical model determines wave field parameters within a specified distance of the suspended tunnel structure through a pre-selected wave numerical model and target environmental conditions, where the target environmental conditions include submarine topography conditions and wave conditions, determines hydrodynamic forces applied to the suspended tunnel tube and the anchor cable according to the wave field parameters within the specified distance of the suspended tunnel structure, and determines motion, deformation and anchor cable tension of the tube-anchor cable system under the action of waves based on the hydrodynamic forces applied to the suspended tunnel tube and the anchor cable, so as to determine the wave propagation and structural dynamic response coupling calculation numerical model.
Further, when the motion, the deformation and the anchor cable tension of the tube body and the anchor cable system under the action of waves are determined, a stress-motion-deformation coupling model of the tube body under the action of waves is constructed on the basis of hydrodynamic forces borne by the tube body and the anchor cable of the suspension tunnel and a pre-selected elastic beam theory, and the motion and the deformation of the tube body under the action of waves are calculated on the basis of a mode superposition method and the stress-motion-deformation coupling model of the tube body under the action of waves; and establishing a numerical model of the anchor cable system by a concentrated mass method, performing iterative calculation on the motion and deformation of the pipe body and the anchor cable system, and determining the motion, deformation and anchor cable tension of the pipe body-anchor cable system. In practical application, a schematic diagram of establishing a large-scale multidirectional wave propagation and structural dynamic response coupling calculation numerical model is shown in fig. 2, and the establishing process may include the following steps 1-1 to 1-4:
step 1-1: the wave field parameters near the suspended tunnel structure are calculated and obtained by utilizing the propagation numerical simulation of far-field waves and considering possible seabed complex terrain conditions and complex wave conditions, the simulation of the far-field waves can adopt a complete nonlinear potential flow wave model (an OceanWave3D model), and the OceanWave3D wave model is widely applied to the numerical analysis of hydrodynamic problems of coastal and ocean engineering at present.
Step 1-2: and calculating to obtain hydrodynamic force borne by the suspended tunnel pipe body or the anchor cable by adopting a Morison formula according to wave field parameters near the suspended tunnel structure. The Morison formula is:
in the formula, F is hydrodynamic force borne by the suspended tunnel pipe body or the anchor cable in unit length; ρ is the density of water; cd is the drag force coefficient, CM is the inertia force coefficient, D is the diameter of the pipe body, and u is the flow velocity.
Step 1-3: on the basis of obtaining the hydrodynamic force borne by the pipe body and the anchor cable, a force-motion-deformation coupling equation of the pipe body under the action of waves is constructed by combining a classical Euler equation and an elastic beam theory, and the motion and the deformation of the pipe body under the action of waves are solved by utilizing a modal superposition method. The coupling equation is:
in the formula, m is the unit length mass of the tube body of the suspension tunnel; EI is the bending rigidity of the tunnel pipe body; w is the vertical displacement of the pipe body; y is a coordinate along the length direction of the tunnel; c is the viscous damping coefficient of the structure; f is the hydrodynamic force applied to the pipe body in unit length.
Step 1-4: and establishing a numerical model of the anchor cable system by adopting a centralized mass method, and performing iterative calculation on the motion and deformation of the pipe body and the anchor cable system to obtain the final motion, deformation and anchor cable tension of the pipe body and the anchor cable system.
In an embodiment, the whole initial analog domain is firstly truncated into two model spaces, namely a numerical domain and a physical domain, where the model space of the numerical domain covers the model space of the physical domain, see fig. 3, which shows a graphic diagram of a suspended tunnel hydro-elastic response holographic truncation analog method, where an external domain is a numerical domain, an internal domain is a physical domain, and the numerical domain covers the physical domain. The numerical value domain adopts a numerical simulation method, and mainly considers the wave propagation in a large range; a physical model test method is adopted in a physical domain, and the real hydro-elastic dynamic response of the suspension tunnel is mainly simulated; and the numerical value domain transmits numerical value dynamic information to the physical domain in real time through the wave field truncation boundary and the suspension tunnel longitudinal truncation point, so that the holographic connection of the two analog domains is realized.
The step S102 may further include the following steps 1 to 5:
step 1, pre-selecting an initial holographic truncation geometric scale, an initial wave field truncation boundary and an initial suspension tunnel longitudinal truncation point position; the holographic truncation geometric scale is the ratio of the geometric dimension of the suspended tunnel prototype to the geometric dimension of the model.
Step 2, determining prototype wave elements and the maximum motion amount of a prototype structure based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model and the overall dynamic response of the levitation tunnel; the prototype wave element at least comprises a maximum wave height and a corresponding maximum frequency of the prototype wave; maximum movement of prototype structure maximum movement amplitude of the prototype structure and corresponding maximum frequency.
And 3, calculating to obtain model wave elements and model motion elements based on the initial holographic truncation geometric scale, the prototype wave elements and the maximum motion amount of the prototype structure.
Step 4, judging whether the model wave elements and the model motion elements meet all preset constraint conditions, wherein the preset constraint conditions can include: (1) whether the model wave elements meet the maximum wave making capacity of the pool wave making machine or not; the model wave element comprises a model maximum wave height and a corresponding maximum frequency; (2) whether the model motion elements meet the maximum motion capability of the six-degree-of-freedom motion platform or not; the model motion elements comprise the maximum motion amplitude and the corresponding maximum frequency of the model structure; (3) whether the change amplitude of the terrain along the wave field truncation boundary meets the specified gradient requirement or not; (4) and whether the model length in the specified range of the longitudinal cutoff point position of the suspension tunnel exceeds the effective range of the physical domain test pool or not.
And 5, if all the requirements are met, the initial holographic truncation geometric scale, the initial wave field truncation boundary and the initial suspension tunnel longitudinal truncation point position are the corresponding holographic truncation geometric scale, wave field truncation boundary and suspension tunnel longitudinal truncation point position.
In practical application, the specific implementation steps of the step 1 to the step 5 may also refer to the following step 2-1 to step 2-7, and refer to a schematic diagram of a wave field and suspended tunnel longitudinal truncation design shown in fig. 4:
step 2-1: an initial geometric scale λ is preselected.
Step 2-2: as shown in fig. 7, an x0y coordinate system is established in the numerical domain, and an initial wave field truncation boundary information is pre-designed, wherein the truncation boundary information includes the starting point coordinates (x0, y0) of the pool in the physical domain and the included angle between one side of the pool and the x-axis
Meanwhile, an initial suspension tunnel longitudinal cutoff point position (x1, y1), (x2, y2) is designed in advance.
Step 2-3: and (3) carrying out wave numerical simulation of a prototype scale and integral dynamic response analysis of the suspended tunnel by using the numerical model established in the first step, and respectively outputting a wave surface time-course curve eta (x, y, t) along the wave field truncation boundary in the step 2-2 and a motion time-course curve S (x, y, t) at the position of the longitudinal truncation point of the suspended tunnel in the step 2-2. The wave surface time course curve refers to the time course curve of the height of waves from a hydrostatic surface, and the motion time course curve S (x, y, t) refers to the six-degree-of-freedom space motion time course curve of an object, and comprises translation along the directions of x, y and z and rotation around the directions of x, y and z.
Step 2-4: analyzing to obtain a prototype wave element eta (x, y, t) according to the wave surface time course curve along the wave field truncation boundary obtained in the step 2-3, wherein the prototype wave element includes but is not limited to the maximum wave height Hp _ max of the prototype wave and the corresponding maximum frequency fp1_ max; and analyzing to obtain the maximum movement amount Sp _ max of the prototype structure according to the movement time-course curve S (x, y, t) at the position of the longitudinal cutoff point of the suspension tunnel obtained in the step 2-3, wherein the maximum movement amount of the prototype structure comprises but is not limited to the maximum movement amplitude A p _ max of the prototype structure and the corresponding maximum frequency f p2_ max.
Step 2-5: and (3) according to the initial geometric scale lambda preselected in the step (2-1), combining the maximum wave height and the corresponding maximum frequency of the prototype wave obtained in the step (2-4) and the maximum motion amplitude and the corresponding maximum frequency of the prototype structure, and respectively calculating to obtain the maximum wave height Hm _ max and the corresponding maximum frequency fm1_ max of the model wave and the maximum motion amplitude Am _ max and the corresponding maximum frequency f m2_ max of the model structure. The method for calculating the maximum wave height and the corresponding maximum frequency of the model wave, the maximum motion amplitude of the model structure and the corresponding maximum frequency comprises the following steps:
step 2-6: judging whether the following 4 conditions are met or not:
1) whether the maximum wave height and the corresponding maximum frequency of the model wave meet the maximum wave making capacity of the L-shaped wave making machine of the pool in the physical domain or not; 2) whether the maximum motion amplitude and the corresponding maximum frequency of the model structure meet the Stewart six-degree-of-freedom motion platform in the physical domain or notMaximum exercise capacity of; 3) whether the terrain variation amplitude along the wave field truncation boundary meets the maximum gradient requirement or not can be considered according to the ratio of 1: 3; 4) and whether the length of the model in the range of the longitudinal truncation point of the suspension tunnel exceeds the effective range of the physical domain test pool or not. When all of the above 4 conditions are satisfied, then the initial chosen holographic truncation geometry scale λ, and the initial chosen wave field truncation boundaries (x0, y0,
) And the longitudinal cutoff points (x1, y1) and (x2, y2) of the suspension tunnel are obtained.
Step 2-7: and if any one of the four conditions in the step 2-6 is not met, resetting the holographic truncation geometric scale lambda, or redesigning the wave field truncation boundary and the longitudinal truncation point position of the suspension tunnel, and repeating the steps 2-3-2-6 until the four conditions in the step 2-6 meet the requirements. Then the last selected holographic truncation geometric scale, λ, and the wave field truncation boundaries (x0, y0,
) And the longitudinal cutoff points (x1, y1) and (x2, y2) of the suspension tunnel are obtained.
The target control signal comprises a wave-making control signal and a power control signal, and specifically, the embodiment of the invention provides a schematic diagram for obtaining the target control signal of the truncation execution mechanism, according to the determined holographic truncation geometric scale lambda, a pre-established large-range multidirectional wave propagation and structural power response coupling calculation numerical model is reused for carrying out detailed numerical simulation analysis, numerical power information at the holographic truncation boundary is extracted, and the control signal of the truncation execution mechanism is obtained. The truncation execution structure comprises a pool L-shaped wave making machine and a Stewart six-degree-of-freedom motion platform in the physical domain, and is shown in figures 5 and 6. The numerical dynamic information at the holographic truncation boundary mainly includes: 1) first numerical power information: namely, a real-time water depth average speed time-course curve U (x, y, t) along the cut-off boundary of the determined wave field; 2) second-class numerical dynamics information: the real-time structure motion component time-course curve S (x, y, t) at the longitudinal truncation point of the suspension tunnel is determined, and the structure motion component comprises six-degree-of-freedom space motion components of the object, such as translation along the directions x, y and z and rotation around the directions x, y and z. The step of obtaining the target control signal of the cutoff actuator includes the following steps 3-1 and 3-2:
step 3-1: based on the first numerical dynamic information U (x, y, t), the wave-making signal mu (x, z, t) of the L-shaped wave-making machine (namely the wave-making control signal of the pool wave-making machine) is obtained through a direct numerical discrete nonlinear three-dimensional wave holographic coupling differential equation. The nonlinear three-dimensional wave holographic coupling differential equation is as follows:
in the formula, (U ξ, U ζ) are the average speed of the water depth corresponding to the direction of (ξ, ζ) under xi 0 ζ of any coordinate system of each side of the L-type wave generator.
The nonlinear three-dimensional wave holographic coupling differential equation can be dispersed by using a method of combining multipoint Lagrange interpolation with fourth-order Runge-Kutta, so as to obtain a wave-making signal mu (x, z, t) of the wave machine.
Step 3-2: and based on the second numerical power information, solving a motion equation by using a servo motor of the Stewart six-freedom-degree motion platform, and solving a control signal Li (t) of a servo system (namely a power control signal of the six-freedom-degree motion platform). The inverse solution motion equation of the servo motor of the Stewart six-freedom-degree motion platform is as follows:
L＝C+RB-A(5)
C＝[c p c p c p c p c p c p ] (7)
c p ＝[x y z] T (8)
l i ＝||L i ||(i＝1,2,...,6) (9)
wherein x, y, z are the positions of the middle point of the upper motion platform 4 in three-dimensional space; α, β, γ are attitude angles of the upper motion platform 4; cp is a position vector; c is a center point location matrix; a is the coordinate of the lower universal hinge 7 in the coordinate system of the lower fixed platform 5; b is the coordinate of the upper universal hinge 6 in the coordinate system of the upper motion platform 4; r is a rotation matrix for converting the coordinate system of the upper moving platform 4 into the coordinate system of the lower fixed platform 5; l is six leg vectors; li is the ith leg vector; li is the ith leg length given by a two-norm of Li.
Further, a wave propagation cutoff model and a suspension tunnel water elastic response cutoff physical model are established. Specifically, a wave propagation truncation model and a suspension tunnel hydro-elastic response truncation physical model are respectively established by utilizing a wave pool L-shaped wave making machine and a Stewart six-freedom-degree motion platform according to the determined holographic truncation geometric scale lambda, and the models are processed and installed. The specific implementation steps comprise the following steps 4-1 and 4-2:
step 4-1: establishing a wave propagation simulation truncation physical model, and scaling the specified wave parameters (such as wave height H, period T, wave direction theta, water depth H and the like) according to a geometric similarity and gravity similarity criterion (namely a first similarity criterion) according to the holographic truncation geometric scale lambda determined in the second step, namely the Froude number Fr of the model is equal to the Froude number Fr of the prototype, namely:
in the formula, v is a flow velocity, g is a gravitational acceleration, p is a model value, and m is a model value.
Step 4-2: establishing a suspended tunnel hydro-elastic response truncation physical model, and scaling specified structural parameters (such as the length L, the diameter D, the density rho, the elastic modulus E, the rigidity EI and the like of the model) according to the holographic truncation geometric scale lambda determined in the second step according to geometric similarity, gravity similarity and elastic similarity criteria (namely a second similarity criterion), namely, the Kouchy number Ca of the model is equal to the Kouchy number Ca of the prototype in addition to the requirement that the Froude number Fr of the model is equal to the Froude number Fr of the prototype, namely:
after the model is established, a holographic cooperative truncation physical model test of wave propagation and suspension tunnel water elastic dynamic response is carried out, as shown in fig. 7. Respectively inputting wave-making control signals mu (x, z and t) along the truncation boundary of the wave field and power control signals Li (t) at the truncation point of the suspended tunnel structure into an L-shaped wave making machine of the wave pool and a Stewart six-freedom-degree motion platform, and carrying out holographic cooperative truncation physical model tests of wave propagation and suspended tunnel hydro-elastic response. The specific implementation steps comprise the following steps 5-1 to 5-4:
step 5-1: and inputting the wave making machine control signal mu (x, z, t) obtained in the third step into a pool L-shaped wave making machine to carry out a wave making test in a physical domain.
Step 5-2: and inputting the control signal Li (t) of the servo system obtained in the third step into a Stewart six-freedom-degree motion platform to perform motion control of the longitudinal interception point of the suspension tunnel in the physical domain.
Step 5-3: establishing a cooperative control mode between the L-shaped wave making machine and the Stewart six-freedom-degree motion platform, establishing real-time data communication between the two platforms, and monitoring and compensating synchronous errors of the two systems to realize holographic cooperative truncation control of the two platforms. The present embodiment can be implemented by using a cross-coupled synchronous control mode. And the multi-axis motion controller is used for connecting the two platforms and sending out control signals of different platforms. And establishing a coupling relation between the two platforms, and performing communication between the two platforms by adopting an RS485 communication/MODBUS protocol so as to realize mutual 'cooperation' between the two platforms. And when a synchronous error occurs, performing system error compensation on the two platforms, and finally realizing the coupling cooperative control of the two platforms.
Step 5-4: through the above experiment, the dynamic response result of the position of interest of the floating tunnel structure is obtained, and the dynamic response result includes, but is not limited to, displacement (dx, dy, dz), attitude (θ x, θ y, θ z), velocity vt, acceleration a, strain ∈ and the like.
In summary, an embodiment of the present invention provides a suspended tunnel hydro-elastic response holographic truncation simulation method, including: establishing a large-range multidirectional wave propagation and structural dynamic response coupling calculation numerical model; the wave field and the suspension tunnel are longitudinally cut off; acquiring a target control signal of a truncation executing mechanism, wherein the truncation executing mechanism comprises a wave generator and a six-degree-of-freedom motion platform; building a wave propagation and suspension tunnel water elastic dynamic response physical model; a control signal is input to carry out a wave propagation and suspension tunnel water elastic dynamic response holographic collaborative truncation physical model test, so that the actual dynamic response of the suspension tunnel system is obtained, and the overall technical framework and the technical route are shown in fig. 8.
Through the scheme introduced by the embodiment, the invention can provide system technical support for forecasting hydro-elastic movement or stress of a large floating or suspended structure in a complex marine environment. The method specifically comprises the following steps: 1) for the simulation of the response of the suspended tunnel structure in the numerical domain, the nonlinear wave propagation model is coupled with the structural power calculation model, and the complex open sea power condition is considered, so that the simulation result is more real and practical; 2) for the processing of the numerical value domain and the physical domain truncation boundary of the complex wave field, the holographic coupling technology is adopted, the spatial-temporal continuity of the propagation process of the numerical value domain waves and the physical domain waves is ensured by fully considering the wave distribution nonuniformity, nonlinearity and directivity on the complex wave field truncation boundary, and the authenticity and the accuracy of the hydrodynamic load action of the complex waves are ensured; 3) for the treatment of the truncation boundary of the numerical field and the physical field of the suspension tunnel test model, the invention adopts active dynamic truncation control to ensure the dynamic response time-space consistency of the numerical field and the physical field structure at the truncation position; 4) for the two truncation boundaries, the invention adopts a cooperative control mode, can simultaneously realize accurate internal transmission of the open sea complex wave load effect and instant response of the structural power, and ensures complete and real-time transmission of information from a numerical value domain to a physical domain, thereby realizing real prediction of the whole dynamic response and the local motion stress deformation hydro-elastic response of the suspended tunnel.
The invention provides a suspended tunnel hydro-elastic response holographic truncation simulation system which is used for executing the suspended tunnel hydro-elastic response holographic truncation simulation method in any one of the above embodiments.
The embodiment of the invention provides electronic equipment, which particularly comprises a processor and a storage device, wherein the processor is used for processing a plurality of data files; the storage device stores a computer program which, when executed by the processor, executes the suspended tunnel hydro-elastic response holographic truncation simulation method according to any one of the above embodiments.
Fig. 9 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, where the electronic device 100 includes: the processor 90, the memory 91, the bus 92 and the communication interface 93, wherein the processor 90, the communication interface 93 and the memory 91 are connected through the bus 92; the processor 90 is adapted to execute executable modules, such as computer programs, stored in the memory 91.
The Memory 91 may include a Random Access Memory (RAM) and a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. The communication connection between the network element of the system and at least one other network element is realized through at least one communication interface 93 (which may be wired or wireless), and the internet, a wide area network, a local network, a metropolitan area network, and the like can be used.
Bus 92 may be an ISA bus, PCI bus, EISA bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 9, but this does not indicate only one bus or one type of bus.
The memory 91 is used for storing a program, and the processor 90 executes the program after receiving an execution instruction, and the method performed by the apparatus defined by the flow program disclosed in any of the foregoing embodiments of the present invention may be applied to the processor 90, or implemented by the processor 90.
The processor 90 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware or instructions in the form of software in the processor 90. The Processor 90 may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the device can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components. The various methods, steps, and logic blocks disclosed in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software module may be located in ram, flash memory, rom, prom, or eprom, registers, etc. storage media as is well known in the art. The storage medium is located in the memory 91, and the processor 90 reads the information in the memory 91 and performs the steps of the above method in combination with the hardware thereof.
The computer program product of the suspension tunnel hydro-elastic response holographic truncation simulation method and system provided by the embodiments of the present invention includes a computer readable storage medium storing a non-volatile program code executable by a processor, and a computer program is stored on the computer readable storage medium, and when the computer program is executed by the processor, the method in the foregoing method embodiments is executed.
It can be clearly understood by those skilled in the art that, for convenience and simplicity of description, the specific working process of the system described above may refer to the corresponding process in the foregoing embodiment, and details are not described herein again.
The computer program product of the readable storage medium provided in the embodiment of the present invention includes a computer readable storage medium storing a program code, and instructions included in the program code may be used to execute the method in the foregoing method embodiment, and specific implementation may refer to the method embodiment, which is not described herein again.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and these modifications or substitutions do not depart from the spirit of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A suspended tunnel hydro-elastic response holographic truncation simulation method is characterized by comprising the following steps:
determining a holographic truncation geometric scale of an initial simulation domain of the suspended tunnel based on a pre-established wave propagation and structural dynamic response coupling calculation numerical model, and determining a wave field truncation boundary and a longitudinal truncation point position of the suspended tunnel;
determining a target control signal of an interception execution structure based on the holographic interception geometric scale and the pre-established wave propagation and structure dynamic response coupling calculation numerical model; the truncation execution structure comprises a pool wave generator and a six-degree-of-freedom motion platform in a physical domain; the physical domain is a model space determined by the initial simulation domain based on the holographic truncation geometric scale, the wave field truncation boundary and the longitudinal truncation point position of the suspended tunnel; the target control signal comprises a wave-making control signal and a six-degree-of-freedom motion platform power control signal;
performing holographic cooperative truncation control on the pool wave maker and the six-degree-of-freedom motion platform based on the target control signal so as to perform holographic truncation simulation on the hydro-elastic response of the suspended tunnel;
based on the target control signal, the pool wave maker and the six-degree-of-freedom motion platform are subjected to holographic collaborative truncation control, and the holographic truncation control comprises the following steps:
inputting the wave-making control signal into the pool wave-making machine, inputting the power control signal into the six-degree-of-freedom motion platform, and performing motion control of a suspension tunnel longitudinal truncation point of a physical domain based on a suspension tunnel hydro-elastic response truncation physical model, wherein the pool wave-making machine is in real-time data communication with the six-degree-of-freedom motion platform, and the synchronous error of the pool wave-making machine and the six-degree-of-freedom motion platform is monitored and compensated, so that holographic cooperative truncation control is performed on the pool wave-making machine and the six-degree-of-freedom motion platform.
2. The holographic truncation simulation method for suspended tunnel hydroelasticity response of claim 1, wherein the step of establishing the pre-established wave propagation and structural dynamic response coupling calculation numerical model comprises:
determining wave field parameters within a specified distance of the suspended tunnel structure through a preselected wave numerical model and a target environment condition; the target environmental conditions include seafloor terrain conditions and wave conditions;
determining hydrodynamic force borne by the suspended tunnel pipe body and the anchor cable according to wave field parameters within the specified distance of the suspended tunnel structure;
and determining the motion, deformation and anchor cable tension of the pipe body-anchor cable system under the action of waves based on the hydrodynamic force borne by the suspension tunnel pipe body and the anchor cable so as to determine the wave propagation and structural dynamic response coupling calculation numerical model.
3. The method for holographic truncation simulation of suspended tunnel hydroelastic response of claim 2, wherein the step of determining the motion, deformation and anchor line tension of the tube and anchor line system under the action of waves based on the hydrodynamic forces experienced by the suspended tunnel tubes and anchor lines comprises:
constructing a force-motion-deformation coupling model of the pipe body under the action of waves on the basis of the hydrodynamic force borne by the suspension tunnel pipe body and the anchor cable and a preselected elastic beam theory;
calculating the motion and deformation of the pipe body under the wave action based on a modal superposition method and the force-motion-deformation coupling model of the pipe body under the wave action;
and establishing a numerical model of the anchor cable system by a concentrated mass method, performing iterative calculation on the motion and deformation of the pipe body and the anchor cable system, and determining the motion, deformation and anchor cable tension of the pipe body-anchor cable system.
4. The holographic truncation simulation method of claim 1 wherein the step of determining the holographic truncation geometric scale of the initial analog domain of the suspended tunnel based on the pre-established wave propagation and structural dynamic response coupled computational numerical model, and determining the truncation boundary of the wave field and the position of the longitudinal truncation point of the suspended tunnel comprises:
pre-selecting an initial holographic truncation geometric scale, an initial wave field truncation boundary and an initial suspension tunnel longitudinal truncation point position; the holographic truncation geometric scale is the ratio of the geometric dimension of the suspended tunnel prototype to the geometric dimension of the model;
determining prototype wave elements and the maximum motion quantity of a prototype structure based on a wave propagation and structural dynamic response coupling calculation numerical model established in advance and the overall dynamic response of the levitation tunnel; the prototype wave element at least comprises a maximum wave height and a corresponding maximum frequency of the prototype wave; maximum movement of the prototype structure the maximum movement amplitude of the prototype structure and the corresponding maximum frequency;
calculating to obtain model wave elements and model motion elements based on the initial holographic truncation geometric scale, the prototype wave elements and the maximum motion amount of the prototype structure;
judging whether the model wave elements and the model motion elements meet all preset constraint conditions or not;
if yes, the initial holographic truncation geometric scale, the initial wave field truncation boundary and the initial suspension tunnel longitudinal truncation point position are determined to be corresponding to the holographic truncation geometric scale, the wave field truncation boundary and the suspension tunnel longitudinal truncation point position.
5. The suspended tunnel hydro-elastic response holographic truncation simulation method of claim 4, wherein the preset constraint condition comprises:
(1) whether the model wave element meets the maximum wave making capacity of the pool wave making machine; the model wave elements comprise a model maximum wave height and a corresponding maximum frequency;
(2) whether the model motion element meets the maximum motion capability of the six-degree-of-freedom motion platform or not; the model motion elements comprise the maximum motion amplitude and the corresponding maximum frequency of the model structure;
(3) whether the change amplitude of the terrain along the wave field truncation boundary meets the specified gradient requirement or not;
(4) and whether the model length in the specified range of the longitudinal cutoff point position of the suspension tunnel exceeds the effective range of the physical domain test pool or not.
6. The holographic truncation simulation method of claim 1 wherein the step of determining the target control signal for truncating the executive structure based on the holographic truncation geometry scale and the pre-established wave propagation and structural dynamic response coupled computational numerical model comprises:
extracting numerical dynamic information at the holographic truncation boundary based on the pre-established wave propagation and structural dynamic response coupling calculation numerical model; the numerical power information comprises first numerical power information and second numerical power information;
determining a wave generation control signal of the pool wave generator based on the first numerical power information;
and determining a power control signal of the six-degree-of-freedom motion platform based on the second numerical power information.
7. The suspended tunnel hydro-elastic response holographic truncation simulation method of claim 6, further comprising:
establishing a wave propagation truncation model according to a first similarity criterion based on the holographic truncation geometric scale and the specified wave parameters; wherein the specified wave parameters at least comprise wave height, period, wave direction and water depth; the first similarity criterion comprises geometric similarity and gravity similarity criterion;
establishing a suspended tunnel hydro-elastic response truncation physical model according to a second similarity criterion based on the holographic truncation geometric scale and the specified structural parameters; wherein the specified structural parameters include at least a length, a diameter, a density, an elastic modulus, and a stiffness of the model; the second similarity criteria include geometric similarity, gravitational similarity, and elastic similarity criteria.
8. The holographic truncation simulation method for suspended tunnel hydroelasticity response of claim 7, wherein the step of performing holographic cooperative truncation control on the pool wave generator and the six-degree-of-freedom motion platform based on the target control signal comprises:
inputting the wave-making control signal into the pool wave-making machine, and carrying out a wave-making test in a physical domain based on the wave propagation truncation model;
inputting the power control signal to the six-degree-of-freedom motion platform, and performing motion control on a suspension tunnel longitudinal truncation point of a physical domain based on the suspension tunnel hydro-elastic response truncation physical model; the pool wave making machine is in real-time data communication with the six-degree-of-freedom motion platform;
and monitoring and compensating the synchronous error of the pool wave maker and the six-degree-of-freedom motion platform so as to carry out holographic cooperative truncation control on the pool wave maker and the six-degree-of-freedom motion platform.
9. The suspended tunnel hydro-elastic response holographic truncation simulation system is used for executing the suspended tunnel hydro-elastic response holographic truncation simulation method of any one of claims 1 to 8.
10. An electronic device comprising a processor and a memory; the memory has stored thereon a computer program which, when executed by the processor, performs the suspended tunnel hydro-elastic response holographic truncation simulation method of any of claims 1 to 8.
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