CN114608788A - Steel skeleton supporting type membrane structure wind-induced dynamic response measuring method and system - Google Patents
Steel skeleton supporting type membrane structure wind-induced dynamic response measuring method and system Download PDFInfo
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Abstract
The invention provides a steel skeleton supporting type membrane structure wind-induced dynamic response measuring method, which comprises the steps of S1, establishing a control equation set with damping nonlinear forced vibration of the steel skeleton supporting type membrane structure according to a Von-Karman large deflection theory and a Dalabel principle; s2, converting the vibration into a non-homogeneous forced vibration differential equation by using a Galerkin method; s3, measuring a wind speed time-course curve by an anemometer arranged on the membrane structure; s4, decomposing the wind speed time-course curve into time-varying average wind and steady pulsating wind by using an EMD method, and fitting the curve to obtain a mathematical expression of aerodynamic load; s5, substituting the basic parameters of the steel skeleton supported membrane structure and the mathematical expression of aerodynamic load into an inhomogeneous forced vibration differential equation, and solving by using a classical fourth-order Runge-Kutta method to obtain a numerical solution of the wind-induced dynamic response of the steel skeleton supported membrane structure. The invention is convenient and fast, has wide application range and high precision, and realizes the accurate measurement of the wind-induced dynamic response of the steel skeleton supporting type membrane structure.
Description
Technical Field
The invention relates to the field of measurement, in particular to a method and a system for measuring wind-induced dynamic response of a steel skeleton supporting type membrane structure.
Background
The building membrane structure is a flexible large-span space structure formed by high-strength composite membrane materials and supporting members through tensioning membrane surfaces. As a novel building structure form, the building structure is rapidly developed into an important component in the field of large-span space structures by virtue of abundant and variable building shapes, light and transparent structural characteristics and low-carbon concepts of energy conservation and environmental protection. The steel skeleton supported membrane structure is the most common membrane structure form in practical engineering, accounts for more than 50% of all membrane structure engineering, and is widely applied to large-span space structures such as airports, parking lots, gymnasiums and the like.
The building membrane structure has the characteristics of light dead weight, small rigidity, low natural vibration frequency, small damping and the like, and is easy to generate large-amplitude vibration and deformation under the action of dynamic load (such as wind, wind driven rain, hail and the like). When the membrane surface stress exceeds the material ultimate strength or the membrane surface deformation cannot meet the use requirement of the building function, the membrane surface is torn or is considered to fail in structure. Wind loads are generally the dominant negative loads in the design of membrane structures, while the negative effects of other negative loads are also taken into account. However, after the strict wind resistance design, the membrane structure in practical engineering still appears in the condition of far below the critical unstable wind speed, and the structure is seriously damaged, so that the wind-induced dynamic response problem of the membrane structure needs to be researched to avoid the occurrence of safety accidents.
The existing building membrane structure engineering basically stays at the design and construction stage, and lacks of dynamic response monitoring in the service process. In actual engineering, safety inspection is carried out on a membrane structure after the membrane structure is subjected to severe weather such as strong wind, and safety assessment on dynamic response generated by wind load in advance is lacked, so that safety accidents of the membrane structure are frequent. Therefore, the accurate membrane structure wind-induced dynamic response measuring method has important engineering application significance for disaster prevention and reduction of the membrane structure.
Disclosure of Invention
The invention aims to disclose a method and a system for measuring the wind-induced dynamic response of a steel skeleton supporting type membrane structure, and solve the problem that no method and system for accurately measuring the wind-induced dynamic response of the steel skeleton supporting type membrane structure exist at present.
In order to achieve the purpose, the invention adopts the following technical scheme:
on one hand, the invention discloses a steel skeleton supporting type membrane structure wind-induced dynamic response measuring method, which comprises the following steps:
s1, establishing a control equation set of damped nonlinear forced vibration of the steel skeleton supporting type membrane structure according to the Von-Karman large deflection theory and the Dalabel principle;
s2, converting the vibration into a non-homogeneous forced vibration differential equation by using a Galerkin method;
s3, measuring a wind speed time-course curve by an anemometer arranged on the membrane structure;
s4, decomposing the wind speed time-course curve into time-varying average wind and steady pulsating wind by using an EMD method, and fitting the curve to obtain a mathematical expression of aerodynamic load;
s5, substituting the basic parameters of the steel skeleton supported membrane structure and the mathematical expression of aerodynamic load into an inhomogeneous forced vibration differential equation, and solving by using a classical fourth-order Runge-Kutta method to obtain a numerical solution of the wind-induced dynamic response of the steel skeleton supported membrane structure.
Preferably, the S1 includes:
obtaining a dynamic motion equation of the steel skeleton supported membrane according to the Von-Karman large deflection theory and the Dalnbel principle, wherein the dynamic motion equation is represented by the formula (1) and a compatibility equation, and the formula (2):
in the formula, ρ0The surface density of the film material is shown; c represents a viscous damping coefficient;
representing a stress function
N0xAnd N0yRepresenting the pretension in the x and y directions, respectively; w represents a displacement function w (x, y, t); h represents the thickness of the membrane material; e1And E2Young's modulus of elasticity in the x and y directions, respectively; k is a radical of0xRepresents the initial principal curvature in the x-direction; pWRepresenting aerodynamic loading.
The displacement and stress boundary conditions of the steel skeleton supporting type film structure corresponding to the simple four-side support are respectively as follows:
where a and b represent the length of the film in the x and y directions, respectively.
The displacement function and the stress function satisfying the boundary conditions of equations (3) and (4) are separated as follows:
w(x,y,t)＝Tmn(t)·Wmn(x,y) (5)
in the formula, Tmn(t) is a function of time;
for a given mode function; m and n are sine half wave numbers in the x direction and the y direction respectively and are positive integers; let Tmn(T) is T, let Wmn(x,y)＝W。
The researched model is a symmetrical structure, the stress function is an even function and satisfies the stress boundary condition formula (4), and the stress function can be obtained by the basic theory of differential equation
One solution of (a) is:
in the formula (I), the compound is shown in the specification,
preferably, the S2 includes:
substituting the formula (5) and the formula (7) into the formula (1), and converting into the compound by using a Galerkin method:
preferably, the S4 includes:
aerodynamic load expression P acting on unit area of projection surface of thin film structureWCan be expressed as:
PW＝-γ1T″-γ2VT′-γ3V2T-γ4V2 (9)
in the formula, T 'and T' respectively represent a first derivative and a second derivative of a time function;
wherein xi and eta are position coordinates of the air flow when arching along the membrane surface;
an integral region S belongs to {0 is larger than or equal to xi and is smaller than or equal to a, and 0 is larger than or equal to eta and is smaller than or equal to b }; rhoaIs the gas density; f. of2Is a mid-span arch on the x-axis; v is the measured wind speed, and the measured wind speed is decomposed into time-varying average wind V by an EMD methodaAnd smooth pulsating wind vfI.e. vaRES and
IMFidenotes the ith eigenmode function, N denotes the total number of eigenmode functions, RES denotes the residual signal function, and IMF denotes the eigenmode function.
Preferably, the S5 includes:
the pneumatic load expression (9) is substituted into the formula (8), and the wind-induced dynamic response differential equation can be obtained through simplification:
T″(t)+λ1T′(t)+λ2T(t)+λ3T2(t)+λ4T3(t)＝λ5T′(t)V(t)+λ6T(t)V(t)2+λ7V(t)2 (10)
in the formula (I), the compound is shown in the specification,
and finally, solving the differential equation (10) by adopting a fourth-order Runge-Kutta method, and obtaining a wind-induced dynamic response numerical solution of the steel skeleton supported membrane structure by solving the differential equation (10).
On the other hand, the invention also provides a steel skeleton supported membrane structure wind-induced dynamic response measuring system, which is used for realizing a steel skeleton supported membrane structure wind-induced dynamic response method and comprises the following steps: an anemometer, a steel bracket and a console;
the control console comprises a switch control module and a signal processing module, and the switch control module is electrically connected with the anemometer and the signal processing module respectively;
the signal processing module is connected with the anemometer;
the anemometer is fixedly connected with the top end of the steel bracket;
the bottom end of the steel bracket is fixedly connected with the steel framework of the membrane structure.
The invention has the advantages of convenience, rapidness, wide application range and high precision, and realizes the accurate measurement of the wind-induced dynamic response of the steel skeleton supporting type membrane structure.
Drawings
The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
Fig. 1 is a diagram of an exemplary embodiment of a method for measuring wind-induced dynamic response of a steel skeleton-supported membrane structure according to the present invention.
Fig. 2 is a diagram of an exemplary embodiment of a steel skeleton-supported film structure according to the present invention.
Fig. 3 is a diagram of an exemplary embodiment of a C-point displacement time course curve solved by the present invention.
Fig. 4 is a diagram of an exemplary embodiment of a wind-induced dynamic response measurement system of a steel skeleton-supported membrane structure according to the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In one aspect, as shown in an embodiment of fig. 1, the invention discloses a method for measuring wind-induced dynamic response of a steel skeleton-supported membrane structure, which includes:
s1, establishing a control equation set of damped nonlinear forced vibration of the steel skeleton supporting type membrane structure according to the Von-Karman large deflection theory and the Dalabel principle;
s2, converting the vibration into a non-homogeneous forced vibration differential equation by using a Galerkin method;
s3, measuring a wind speed time-course curve by an anemometer arranged on the membrane structure;
s4, decomposing the wind speed time-course curve into time-varying average wind and steady pulsating wind by using an EMD method, and fitting the curve to obtain a mathematical expression of aerodynamic load;
s5, substituting the basic parameters of the steel skeleton supported membrane structure and the mathematical expression of aerodynamic load into an inhomogeneous forced vibration differential equation, and solving by using a classical fourth-order Runge-Kutta method to obtain a numerical solution of the wind-induced dynamic response of the steel skeleton supported membrane structure.
The theoretical structure model researched by the invention is a steel skeleton supporting type membrane structure as shown in figure 2, a membrane material is made of an elastic material, four sides are simply supported, and the orthogonal directions x and y are two main fiber directions with different Young modulus; a and b represent the length of the film in the x and y directions, respectively; n is a radical of0xAnd NoyRepresenting pretension in x and y directions, respectively; f. of1And f2Mid-span arch height in the y and x axes, respectively.
Preferably, the S1 includes:
obtaining a dynamic motion equation of the steel skeleton supported membrane according to the Von-Karman large deflection theory and the Dalnbel principle, wherein the dynamic motion equation is represented by the formula (1) and a compatibility equation, and the formula (2):
in the formula, ρ0The surface density of the film material is shown; c represents a viscous damping coefficient;
representing a stress function
N0xAnd N0yRepresenting the pretension in the x and y directions, respectively; w represents a displacement function w (x, y, t); h represents the thickness of the membrane material; e1And E2Young's modulus of elasticity in the x and y directions, respectively; k is a radical of0xRepresents the initial principal curvature in the x-direction; p isWRepresenting aerodynamic loads;
the displacement and stress boundary conditions of the steel skeleton supporting type film structure corresponding to the simple four-side support are respectively as follows:
a and b represent the length of the film in the x and y directions, respectively.
The displacement function and the stress function satisfying the boundary conditions of equations (3) and (4) are separated as follows:
w(x,y,t)＝Tmn(t)·Wmn(x,y) (5)
in the formula, Tmn(t) is a function of time;
for a given mode function; m and n are sine half wave numbers in the x direction and the y direction respectively, and are positive integers; let Tmn(T) is equal to T, let Wmn(x,y)＝W；
The studied model is a symmetrical structure, the stress function is an even function and satisfies the stress boundary condition formula (4), and the stress function can be obtained by the basic theory of differential equation
One solution of (a) is:
in the formula (I), the compound is shown in the specification,
preferably, the S2 includes:
substituting the formula (5) and the formula (7) into the formula (1), and converting into the compound by using a Galerkin method:
preferably, the S4 includes:
aerodynamic load expression P acting on unit area of projection surface of thin film structureWCan be expressed as:
PW＝-γ1T″-γ2VT′-γ3V2T-γ4V2 (9)
in the formula, T 'and T' respectively represent a first derivative and a second derivative of a time function;
wherein xi and eta are position coordinates of the air flow when arching along the membrane surface;
the integration region S belongs to {0 is more than or equal to xi and less than or equal to a, and 0 is more than or equal to eta and less than or equal to b }; ρ is a unit of a gradientaIs the gas density; f. of2Is a mid-span arch on the x-axis; v is the measured wind speed, and the measured wind speed is decomposed into time-varying average wind V by an EMD methodaAnd smooth pulsating wind vfI.e. va＝RESAnd
IMFidenotes the ith eigenmode function, N denotes the total number of eigenmode functions, RES denotes the residual signal function, and IMF denotes the eigenmode function.
Preferably, the S5 includes:
the pneumatic load expression (9) is substituted into the formula (8), and the wind-induced dynamic response differential equation can be obtained through simplification:
T″(t)+λ1T′(t)+λ2T(t)+λ3T2(t)+λ4T3(t)＝λ5T′(t)V(t)+λ6T(t)V(t)2+λ7V(t)2 (10)
in the formula (I), the compound is shown in the specification,
and finally, solving the differential equation (10) by adopting a fourth-order Runge-Kutta method, and obtaining a wind-induced dynamic response numerical solution of the steel skeleton supported membrane structure by solving the differential equation (10).
On the other hand, as shown in fig. 4, the invention also provides a wind-induced dynamic response measuring system of a steel skeleton supported membrane structure, which is used for implementing a wind-induced dynamic response method of a steel skeleton supported membrane structure, and the method comprises the following steps: an anemometer, a steel bracket and a console;
the control console comprises a switch control module and a signal processing module, and the switch control module is electrically connected with the anemometer and the signal processing module respectively;
the signal processing module is connected with the anemometer;
the anemometer is fixedly connected with the top end of the steel bracket;
the bottom end of the steel bracket is fixedly connected with the steel framework of the film structure.
The measuring system is used as follows:
(1) the anemometer is arranged at the top end of the steel bracket, the length of the steel bracket is adjusted to enable the anemometer to be slightly higher than the top end of the membrane surface, and the bottom end of the steel bracket is fixedly connected to a steel framework on the windward side through a bolt. And connecting the lines of the anemometers to the signal processing module, debugging the installed equipment and ensuring that all the equipment is in a state to be measured.
(2) When wind load acts on the membrane structure, the switch control module controls the anemometer to enter a working state, and information collection software of the signal processing module is clicked to complete information collection at the moment. And after the data acquisition is finished, clicking the background software to stop the measurement and closing the power supply of the anemometer.
(3) Decomposing the collected wind speed time-course curve in a signal processing module by an EMD method, and fitting the decomposed curve to obtain time-varying average wind vaAnd smooth pulsating wind vfThe mathematical expression of (1).
(4) Relevant parameters (structural geometric dimension parameters, membrane material mechanical property parameters and pretension) and wind load expressions of the steel skeleton supporting type membrane structure are substituted into a wind-induced dynamic response differential equation in a signal processing module, and the differential equation is solved by a four-order Runge-Kutta method, so that a wind-induced dynamic response numerical solution of the steel skeleton supporting type membrane structure can be obtained.
The invention has the advantages of convenience, rapidness, wide application range and high precision, and realizes the accurate measurement of the wind-induced dynamic response of the steel skeleton supporting type membrane structure.
Take the steel skeleton supported membrane structure shown in fig. 2 as an example. Selecting the film material with the surface density rho of 14kg/m2Thickness h is 10mm, and elastic modulus E is1＝E2920Mpa, and the damping coefficient c is 86.4 Ns/m. The plane size of the membrane structure is a multiplied by b which is 10m multiplied by 10m, and the vector span ratio of the membrane surface is as follows: f. of21/12, film face pretension N0x＝N0y51.1 kN/m. The sine half wave number m in the x and y directions is 1, and n is 2. The actual wind speed time-course curve is obtained by an anemometer and the result is decomposed by an EMD method as follows:
and calculating a displacement time-course curve of the membrane surface C (x is 2.5, and y is 5) under the action of aerodynamic force.
Solution: the coefficients of the respective terms can be obtained by substituting the known data into the formula (10). And solving a differential equation by using a fourth-order Runge-Kutta method to obtain a numerical solution of the C point wind-induced power response. Fig. 3 is a solved time course curve of the displacement of the point C.
While embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
It should be noted that, functional units/modules in the embodiments of the present invention may be integrated into one processing unit/module, or each unit/module may exist alone physically, or two or more units/modules are integrated into one unit/module. The integrated units/modules may be implemented in the form of hardware, or may be implemented in the form of software functional units/modules.
From the above description of the embodiments, it is clear for a person skilled in the art that the embodiments described herein can be implemented in hardware, software, firmware, middleware, code or any appropriate combination thereof. For a hardware implementation, a processor may be implemented in one or more of the following units: an Application Specific Integrated Circuit (ASIC), a Digital Signal Processor (DSP), a Digital Signal Processing Device (DSPD), a Programmable Logic Device (PLD), a Field Programmable Gate Array (FPGA), a processor, a controller, a microcontroller, a microprocessor, other electronic units designed to perform the functions described herein, or a combination thereof. For a software implementation, some or all of the procedures of an embodiment may be performed by a computer program instructing associated hardware.
In practice, the program may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. Computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer.
Claims (6)
1. A steel skeleton supporting type membrane structure wind-induced dynamic response measuring method is characterized by comprising the following steps:
s1, establishing a control equation set of damped nonlinear forced vibration of the steel skeleton supporting type membrane structure according to the von Karman large deflection theory and the Dalnbel principle;
s2, converting the vibration into a non-homogeneous forced vibration differential equation by using a Galerkin method;
s3, measuring a wind speed time-course curve by an anemometer arranged on the membrane structure;
s4, decomposing the wind speed time-course curve into time-varying average wind and steady pulsating wind by using an EMD method, and fitting the curve to obtain a mathematical expression of aerodynamic load;
s5, substituting the basic parameters of the steel skeleton supporting type membrane structure and the mathematical expression of aerodynamic load into the heterogeneous forced vibration differential equation, and solving by using a classical fourth-order Runge-Kutta method to obtain the numerical solution of the wind-induced dynamic response of the steel skeleton supporting type membrane structure.
2. The method as claimed in claim 1, wherein the step S1 includes:
obtaining a dynamic motion equation of the steel skeleton supported membrane according to the Von-Karman large deflection theory and the Dalnbel principle, wherein the dynamic motion equation is represented by the formula (1) and a compatibility equation, and the formula (2):
in the formula, ρ0The surface density of the film material is shown; c represents a viscous damping coefficient;
representing a stress function
N0xAnd N0yRepresenting the pretension in the x and y directions, respectively; w represents a displacement function w (x, y, t); h represents the thickness of the membrane material; e1And E2Young's modulus of elasticity in the x and y directions, respectively; k is a radical of0xRepresents the initial principal curvature in the x-direction; pWRepresenting aerodynamic loading.
The displacement and stress boundary conditions of the corresponding four-side simple support of the steel skeleton supporting type membrane structure are respectively as follows:
where a and b represent the length of the film in the x and y directions, respectively.
The displacement function and the stress function satisfying the boundary conditions of equations (3) and (4) are separated as follows:
w(x,y,t)＝Tmn(t)·Wmn(x,y) (5)
in the formula, Tmn(t) is a function of time;
for a given mode function; m and n are sine half wave numbers in the x direction and the y direction respectively and are positive integers; let Tmn(T) is T, let Wmn(x,y)＝W。
The researched model is a symmetrical structure, the stress function is an even function and satisfies the stress boundary condition formula (4), and the stress function can be obtained by the basic theory of differential equation
One solution of (a) is:
in the formula (I), the compound is shown in the specification,
3. the method for measuring wind-induced dynamic response of a steel skeleton supported membrane structure according to claim 2, wherein the step S2 includes:
substituting the formula (5) and the formula (7) into the formula (1), and converting into the compound by using a Galerkin method:
4. the method for measuring wind-induced dynamic response of a steel skeleton supported membrane structure according to claim 3, wherein the step S4 includes:
aerodynamic load expression P acting on unit area of projection surface of thin film structureWCan be expressed as:
PW＝-γ1T″-γ2VT′-γ3V2T-γ4V2 (9)
in the formula, T 'and T' respectively represent a first derivative and a second derivative of a time function;
wherein xi and eta are position coordinates of the air flow when arching along the membrane surface;
an integral region S belongs to {0 is larger than or equal to xi and is smaller than or equal to a, and 0 is larger than or equal to eta and is smaller than or equal to b }; rhoaIs the gas density; f. of2Is a mid-span arch on the x-axis; v is the measured wind speed, and the measured wind speed is decomposed into time-varying average wind V by an EMD methodaAnd smooth pulsating wind vfI.e. vaRES and
wherein IMFiDenotes the ith eigenmode function, N denotes the total number of eigenmode functions, RES denotes the residual signal function, and IMF denotes the eigenmode function.
5. The method for measuring wind-induced dynamic response of a steel skeleton supported membrane structure according to claim 4, wherein the step S5 includes:
the pneumatic load expression (9) is substituted into the formula (8), and the wind-induced dynamic response differential equation can be obtained through simplification:
T″(t)+λ1T′(t)+λ2T(t)+λ3T2(t)+λ4T3(t)＝λ5T′(t)V(t)+λ6T(t)V(t)2+λ7V(t)2 (10)
in the formula (I), the compound is shown in the specification,
the differential equation (10) is solved by adopting a fourth-order Runge-Kutta method, and the wind-induced dynamic response numerical solution of the steel skeleton supported membrane structure can be obtained by solving the differential equation (10).
6. A wind-induced dynamic response measurement system of a steel skeleton supported membrane structure, which is used for realizing the wind-induced dynamic response method of the steel skeleton supported membrane structure as claimed in any one of claims 1 to 5, and is characterized by comprising the following steps: an anemometer, a steel bracket and a console;
the control console comprises a switch control module and a signal processing module, and the switch control module is electrically connected with the anemometer and the signal processing module respectively;
the signal processing module is connected with the anemometer;
the anemometer is fixedly connected with the top end of the steel bracket;
the bottom end of the steel bracket is fixedly connected with the steel framework of the membrane structure.
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| CN202210204339.8A CN114608788A (en) | 2022-03-02 | 2022-03-02 | Steel skeleton supporting type membrane structure wind-induced dynamic response measuring method and system |
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| CN112883667A (en) * | 2021-03-29 | 2021-06-01 | 辽宁工程技术大学 | Membrane structure wind resistance optimization method based on large vortex simulation under vertical pulsating wind load effect |
| CN113125104A (en) * | 2021-04-13 | 2021-07-16 | 广州大学 | Dynamic response testing device and method of membrane structure under wind-driven rain load action |
| CN113654759A (en) * | 2021-08-24 | 2021-11-16 | 广州大学 | System and method for testing aerodynamic force of building membrane structure under wind load action |
| CN113670572A (en) * | 2021-08-24 | 2021-11-19 | 广州大学 | System and method for testing wind-driven rain load of building membrane structure |
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| CN112883667A (en) * | 2021-03-29 | 2021-06-01 | 辽宁工程技术大学 | Membrane structure wind resistance optimization method based on large vortex simulation under vertical pulsating wind load effect |
| CN113125104A (en) * | 2021-04-13 | 2021-07-16 | 广州大学 | Dynamic response testing device and method of membrane structure under wind-driven rain load action |
| JP7018234B1 (en) * | 2021-04-13 | 2022-02-10 | ▲広▼州大学 | Power response test method under wind and rain load action of membrane structure |
| CN113654759A (en) * | 2021-08-24 | 2021-11-16 | 广州大学 | System and method for testing aerodynamic force of building membrane structure under wind load action |
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