CN112395722A - Method for acquiring motion response of hull beam under action of underwater explosion and wave load - Google Patents

Method for acquiring motion response of hull beam under action of underwater explosion and wave load Download PDF

Info

Publication number
CN112395722A
CN112395722A CN201910567669.1A CN201910567669A CN112395722A CN 112395722 A CN112395722 A CN 112395722A CN 201910567669 A CN201910567669 A CN 201910567669A CN 112395722 A CN112395722 A CN 112395722A
Authority
CN
China
Prior art keywords
bubble
hull
load
underwater explosion
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201910567669.1A
Other languages
Chinese (zh)
Other versions
CN112395722B (en
Inventor
孔祥韶
周红昌
石干
吴卫国
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan University of Technology WUT
Original Assignee
Wuhan University of Technology WUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Wuhan University of Technology WUT filed Critical Wuhan University of Technology WUT
Priority to CN201910567669.1A priority Critical patent/CN112395722B/en
Publication of CN112395722A publication Critical patent/CN112395722A/en
Application granted granted Critical
Publication of CN112395722B publication Critical patent/CN112395722B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Aerodynamic Tests, Hydrodynamic Tests, Wind Tunnels, And Water Tanks (AREA)

Abstract

The invention relates to a method for acquiring the motion response of a hull beam under the action of underwater explosion and wave load, which comprises the following steps: 1) simplifying the calculation model into simply supported beams at two ends; 2) establishing a transverse vibration equation of a calculation model; 3) simplifying the solution of the wave load; 4) establishing a motion equation of a calculation model under the action of wave load; 5) solving the underwater explosion load; 6) establishing a motion equation of a calculation model under the underwater explosion load; 7) establishing a motion equation of a calculation model under the combined action of underwater explosion and wave load; 8) and solving the motion response of the calculation model under the joint action of the underwater explosion and the wave load by using the boundary conditions. The motion model is established based on an analytical method, the analytical method can effectively improve the calculation efficiency, and simultaneously can visually analyze the influence of each parameter on the calculation model, thereby realizing the mastering of the motion rule of the hull beam under the combined action of underwater explosion and wave load on the basic principle.

Description

Method for acquiring motion response of hull beam under action of underwater explosion and wave load
Technical Field
The invention relates to the technical field of ship and ocean engineering, in particular to a method for acquiring motion response of a hull beam under the action of underwater explosion and wave load.
Background
At present, students at home and abroad mainly develop motion response of ships under the action of single load (underwater explosion or wave load), a few of students research the motion response of the ships under the coupling action of the underwater explosion and the static wave load by a simplified approximate method, the research on the dynamic collapse process of the ships under the combined action of the underwater explosion and the waves is still in a starting stage, and the related experimental research developed by the students is especially digressive. However, in actual sea battles, the ship cannot be in a calm sea area, and if the influence of the wave load on the ship is not considered or only the influence of the wave load and the underwater explosion load on the ship is simply superposed, the real coupling effect of the two loads cannot be effectively reflected, so that serious hidden danger is left for the safety evaluation of the ship.
However, as can be seen from the current research situation at home and abroad, although a large amount of basic theoretical research is conducted by scholars at home and abroad on the motion response of the hull beam under the action of a single load (underwater explosion or wave load), the research on the hull beam motion response calculation method under the combined action of underwater explosion and wave load still remains a blank at present. Therefore, a reasonable and effective simplified theoretical model and a calculation method are provided and established, and certain necessity and theoretical value are provided for researching the motion characteristics and rules of the hull beam under the coupling action of the two loads.
Disclosure of Invention
Technical problem to be solved
In order to solve the problems in the prior art, the invention provides a hull beam motion response obtaining method under the action of underwater explosion and wave load.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
a ship body beam motion response obtaining method under the action of underwater explosion and wave load is designed, and the method comprises the following steps:
step 1): the hull beam is assumed to be a non-uniform simply supported beam. Let beam length be L, take the neutralization axis of beam as the Ox axle, the origin of coordinates is the left end of beam. In the coordinate system, the bending rigidity which changes along the length direction of the beam is EI (x), the mass per unit length is m (x), the width of the ship hull beam is b (x), the non-conservative force which acts on the beam per unit length is Q (x, t), and the transverse displacement z (x, t) on the neutral axis of the beam is a function which continuously changes along the coordinate x and the time t.
Step 2): and establishing a transverse vibration equation of the calculation model.
The beam micro-section is taken as a research object, the viscous external damping force is considered to be in direct proportion to the speed of the beam micro-section, the external damping coefficient of x on the beam in unit length is set as c (x), and the damping force borne by the beam micro-section is
Figure RE-GDA0002267915740000021
In the initial state, the gravity and the buoyancy are assumed to be balanced with each other, but in the motion process, the difference between the gravity and the buoyancy is assumed to be proportional to the ship width b (x) and the transverse displacement z (x, t), the differential load between the gravity and the buoyancy is ρ gb (x) z (x, t), and the non-conservative force Q (x, t) at any time satisfies the following relation:
Figure RE-GDA0002267915740000022
the Hamilton principle is used for deducing the motion equation of the hull beam to obtain:
Figure RE-GDA0002267915740000023
step 3): the solution of the wave load is simplified.
According to the fact that when the actual ship body sails in waves, due to the fact that the relative positions of wave crests, wave troughs and the ship body are different, the ship body beams alternately generate sagging and arching motions. Taking the midspan motion of the hull beam as an example, assume that the wave load is distributed sinusoidally along the hull beam.
Assuming that wave force on each micro-segment of the hull beam is also distributed in a sine form at each moment, the specific load form is shown as formula (3):
Figure RE-GDA0002267915740000024
in the formula (3), BwIs the wave load amplitude, omegawFor the angular frequency of the wave loading action ψ is the initial phase angle.
Step 4): and establishing a motion equation of the calculation model under the wave load.
According to the knowledge of structural dynamics, the vibration mode function of the simply supported beam is as follows:
Figure RE-GDA0002267915740000031
in the formula (4), the constant AmDetermined by the initial conditions. Under the action of wave load, Am＝Amw. Solving a generalized matrix of the simply supported beam vibration under the action of the wave load by adopting a modal superposition method, wherein a solving equation is as follows:
Figure RE-GDA0002267915740000032
step 5): the underwater explosion simplifies the solving of the load. The basic assumptions are as follows:
1. it is assumed that the underwater blast shock wave loading does not cause local damage to the structure and that the hull beam structure is not plastically deformed. Therefore, the influence of the pulsating load of the underwater explosion bubbles is not considered.
2. Assuming that the fluid is incompressible and spin-free, the fluid domain satisfies the following Laplace equation:
Figure RE-GDA0002267915740000033
wherein the velocity potential
Figure RE-GDA0002267915740000034
From incident velocity potential
Figure RE-GDA0002267915740000035
Diffraction velocity potential
Figure RE-GDA0002267915740000036
And radiation velocity potential
Figure RE-GDA0002267915740000037
And satisfies the following relation:
Figure RE-GDA0002267915740000038
3. in the underwater explosion process of the far and middle fields, the influence of the hull beam on the bubbles is ignored, and only the influence of the bubbles on the hull beam is considered. Diffraction velocity potential in the fluid region around the bubble
Figure RE-GDA0002267915740000039
And radiation velocity potential
Figure RE-GDA00022679157400000310
Both are 0, and the fluid region near the hull beam satisfies equation (7).
4. The bubbles are assumed to be spherical and the transverse dimension of the hull beams is a minute amount relative to the distance between the bubbles and the hull.
It can be seen from the longitudinal section and the transverse section that the coordinate system of the hull beam is xyz, the origin of the coordinate is established at the stern, the positive direction of the x axis is from the stern to the bow, the y axis is along the width direction of the ship, and the positive direction of the z axis is from the vertical direction. The bubble coordinate system is delta zeta gamma, the bubble center is taken as the coordinate origin, and the directions of the delta axis, the zeta axis and the gamma axis are respectively the same as the directions of the x axis, the y axis and the z axis. The distance from the center of the bubble to the hull is recorded as H0And the distance from the water surface is marked as H. The hull beam is a beam with equal section, and the height of the water part is marked as H1The underwater part circle radius is denoted as R.
For the fluid domain near the bubble, the velocity potential function satisfies the Laplace equation:
Figure RE-GDA0002267915740000041
the lagrange integral of the unsteady non-rotational motion of the fluid on the surface of the bubble is:
Figure RE-GDA0002267915740000042
in formula (9), PmWhere z is the pressure at infinity on the 0 plane, P is the fluid pressure at the outer surface of the bubble, and ρ is the fluid density.
The velocity component in the radial direction of the bubble is:
Figure RE-GDA0002267915740000043
in the formula, vrIs the radial velocity of the surface of the bubble, rbIs the bubble radius.
The bubble load is regarded as a point source, the point source is positioned at the center of the bubble, and the intensity is recorded as Qb(t) of (d). The incident velocity potential caused by bubble loading in the flow field is:
Figure RE-GDA0002267915740000044
in formula (11), raThe distance from the center of the bubble to any point.
The pressure inside the bubble can be determined by the following equation of state:
Figure RE-GDA0002267915740000045
in the formula (12), PbIs the internal pressure of the bubble, PcAnd P0Respectively the saturated vapor pressure of the gas and the initial pressure of the bubbles, V0And V is the initial volume of the bubble and the volume of the bubble at an arbitrary time, γ is the adiabatic index of the gas, and γ is 1.4 for an ideal gas. Without taking into account gasThe bubble surface tension and the gas saturation vapor pressure, the fluid pressure P at the bubble outer surface is expressed as:
Figure RE-GDA0002267915740000051
the simultaneous equations (9) to (13) can be obtained:
Figure RE-GDA0002267915740000052
Figure RE-GDA0002267915740000053
the velocity potential of the flow field near the hull beam is:
Figure RE-GDA0002267915740000054
based on the 4 th assumption, it can be considered that: y is less than H, and z is less than H. Therefore, the second order trace y in equation (16)2、z2Negligible, on the basis of which the Taylor expansion of equation (16) is performed,
Figure RE-GDA0002267915740000055
omitting the higher order infinite term, equation (17) can be transformed into:
Figure RE-GDA0002267915740000056
because the invention is suitable for underwater explosion in middle and far fields, the incident velocity of the fluid around the hull beam can only consider the vertical component, and the expression is as follows:
Figure RE-GDA0002267915740000057
in the middle and far field explosion, the flow field velocity near the hull beam caused by the underwater explosion bubble load can be considered to be mainly along the y-axis and z-axis directions based on the 4 th hypothesis,
Figure RE-GDA0002267915740000061
the flow field near the hull beam can be converted into a two-dimensional flow field, and the velocity potential function of the two-dimensional flow field meets the Laplace equation:
Figure RE-GDA0002267915740000062
the velocity potential near the hull beam meets the surface impenetrable condition:
Figure RE-GDA0002267915740000063
in the formula (22), r'aThe distance between any point on the surface of the ship body beam and the ship body beam in the two-dimensional flow field is shown, and theta is an included angle between a z-axis and a normal vector of the surface of the ship body beam.
According to the Laplace equation of the two-dimensional flow field, the diffraction velocity potential and the incident velocity potential satisfy the following relationship on the surface of the ship body:
Figure RE-GDA0002267915740000064
diffraction velocity potential
Figure RE-GDA0002267915740000065
The solution is in the form:
Figure RE-GDA0002267915740000066
radiation velocity potential
Figure RE-GDA0002267915740000067
The ship surface impenetrable condition is met:
Figure RE-GDA0002267915740000068
diffraction velocity potential
Figure RE-GDA0002267915740000069
The solution is in the form:
Figure RE-GDA00022679157400000610
considering that the explosion distance is longer, the fluid velocity potential gradient near the ship body is smaller, namely the requirement of meeting
Figure RE-GDA00022679157400000611
And in the total pressure composition of the hull surface, the position water head z (x, t) is negligible, and the pressure of the hull surface meets the following linearized Bernoulli equation:
Figure RE-GDA0002267915740000071
the fluid load on any section of the hull beam can be found by integrating P over the hull surface:
Figure RE-GDA0002267915740000072
substituting the formula (18), the formula (24) and the formula (26) into the formula (28) yields:
Figure RE-GDA0002267915740000073
in the formula, ma(x)＝πρR2Is the added mass of the hull beam profile in the water.
Step 6): and establishing a motion equation of the calculation model under the underwater explosion load.
Substituting the formula (29) into the damped vibration differential equation of the simply supported beam under the action of the external load,
Figure RE-GDA0002267915740000074
in the formula (30), the first and second groups,
Figure RE-GDA0002267915740000075
solving by adopting a modal superposition method to obtain:
Figure RE-GDA0002267915740000076
in the formula, lambda is the proportionality coefficient of the additional mass and the mass of the hull beam section in water,
Figure RE-GDA0002267915740000077
B′m(t) is the mode shape force corresponding to B' (x, t), and the expression is as follows:
Figure RE-GDA0002267915740000078
in formula (33), AmbDetermined by the initial conditions of underwater explosion bubble loading.
Step 7): and 5) and 6) simultaneously, obtaining a motion equation of the calculation model under the combined action of the underwater explosion and the wave load, and further solving the motion response of the calculation model under the combined action of the underwater explosion and the wave load according to the boundary conditions.
(III) advantageous effects
The invention has the beneficial effects that: the invention combines the underwater explosion load with the wave load, provides a hull beam motion response calculation method under the combined action of the underwater explosion and the wave load, has simple operation and is easy to realize; the motion model is established based on an analytical method, the analytical method can effectively improve the calculation efficiency, and simultaneously can visually analyze the influence of each parameter on the calculation model, thereby realizing the understanding of the motion rule of the hull beam under the combined action of underwater explosion and wave load on the basic principle.
Drawings
FIG. 1 is a schematic flow chart of a hull beam motion response acquisition method under the action of underwater explosion and wave load;
FIG. 2 is a schematic diagram of a simplified model in which the hull beam is a non-uniform simply supported beam;
FIG. 3 is a result of solving a simplified model of a hull beam in an embodiment of the invention;
FIG. 4 is a schematic illustration of the sinusoidal distribution of wave loads along a hull beam;
FIG. 5 is a schematic diagram of a displacement time course curve of the middle part of a hull beam under the action of wave load in the embodiment of the invention;
FIG. 6 is a simplified model schematic view (longitudinal cross-sectional view) of a hull beam under underwater explosive bubble loading;
FIG. 7 is a simplified model schematic (cross-sectional view) of a hull beam under underwater blast bubble loading;
FIG. 8 is a schematic time-history plot of point source intensity of an underwater explosive load in an embodiment of the present invention;
FIG. 9 is a graph illustrating the time history of the bubble radius of an underwater explosive load in an embodiment of the present invention;
FIG. 10 is a schematic diagram of a displacement time course curve of the middle part of a hull beam under the action of underwater explosive load in the embodiment of the invention;
fig. 11 is a schematic diagram of a displacement response time course curve of the middle part of the hull beam under the combined action of underwater explosion and wave load in the embodiment of the invention.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
The invention provides a method for acquiring the motion response of a hull beam under the action of underwater explosion and wave load, which comprises the following steps of:
step 1): assuming that the hull beam is an uneven simply supported beam, as shown in fig. 2, let the beam length be L, take the neutralization axis of the beam as the Ox axis, and the origin of coordinates be the left end of the beam. In the coordinate system, the bending rigidity which changes along the length direction of the beam is EI (x), the mass per unit length is m (x), the width of the ship hull beam is b (x), the non-conservative force which acts on the beam per unit length is Q (x, t), and the transverse displacement z (x, t) on the neutral axis of the beam is a function which continuously changes along the coordinate x and the time t.
Step 2): and establishing a transverse vibration equation of the calculation model.
The beam micro-section is taken as a research object, the viscous external damping force is considered to be in direct proportion to the speed of the beam micro-section, the external damping coefficient of x on the beam in unit length is set as c (x), and the damping force borne by the beam micro-section is
Figure RE-GDA0002267915740000091
In the initial state, the gravity and the buoyancy are assumed to be balanced with each other, but in the motion process, the difference between the gravity and the buoyancy is assumed to be proportional to the ship width b (x) and the transverse displacement z (x, t), the differential load between the gravity and the buoyancy is ρ gb (x) z (x, t), and the non-conservative force Q (x, t) at any time satisfies the following relation:
Figure RE-GDA0002267915740000092
the Hamilton principle is used for deducing the motion equation of the hull beam to obtain:
Figure RE-GDA0002267915740000093
step 3): the solution of the wave load is simplified.
According to the fact that when the actual ship body sails in waves, due to the fact that the relative positions of wave crests, wave troughs and the ship body are different, the ship body beams alternately generate sagging and arching motions. Taking the midspan motion of the hull beam as an example, it is assumed that the wave load is distributed sinusoidally along the hull beam, as shown in fig. 4.
Assuming that wave force on each micro-segment of the hull beam is also distributed in a sine form at each moment, the specific load form is shown as formula (3):
Figure RE-GDA0002267915740000101
in the formula (3), BwIs the wave load amplitude, omegawFor the angular frequency of the wave loading action ψ is the initial phase angle.
Step 4): and establishing a motion equation of the calculation model under the wave load.
According to the knowledge of structural dynamics, the vibration mode function of the simply supported beam is as follows:
Figure RE-GDA0002267915740000102
in the formula (4), the constant AmDetermined by the initial conditions. Under the action of wave load, Am＝Amw. Solving a generalized matrix of the simply supported beam vibration under the action of the wave load by adopting a modal superposition method, wherein a solving equation is as follows:
Figure RE-GDA0002267915740000103
step 5): the underwater explosion simplifies the solving of the load. The basic assumptions are as follows:
1. it is assumed that the underwater blast shock wave loading does not cause local damage to the structure and that the hull beam structure is not plastically deformed. Therefore, the influence of the pulsating load of the underwater explosion bubbles is not considered.
2. Assuming that the fluid is incompressible and spin-free, the fluid domain satisfies the following Laplace equation:
Figure RE-GDA0002267915740000104
wherein the velocity potential
Figure RE-GDA0002267915740000105
From incident velocity potential
Figure RE-GDA0002267915740000106
Diffraction velocity potential
Figure RE-GDA0002267915740000107
And radiation velocity potential
Figure RE-GDA0002267915740000108
And satisfies the following relation:
Figure RE-GDA0002267915740000109
3. in the underwater explosion process of the far and middle fields, the influence of the hull beam on the bubbles is ignored, and only the influence of the bubbles on the hull beam is considered. Diffraction velocity potential in the fluid region around the bubble
Figure RE-GDA00022679157400001010
And radiation velocity potential
Figure RE-GDA00022679157400001011
Both are 0, and the fluid region near the hull beam satisfies equation (7).
4. The bubbles are assumed to be spherical and the transverse dimension of the hull beams is a minute amount relative to the distance between the bubbles and the hull.
As shown in fig. 6 and 7, it can be seen from the combination of the longitudinal section and the transverse section that the coordinate system of the hull beam is xyz, the origin of the coordinate is established at the stern, the positive direction of the x-axis is from the stern to the bow, the y-axis is along the width direction of the ship, and the positive direction of the z-axis is from the vertical direction. The bubble coordinate system is delta zeta gamma, the bubble center is taken as the coordinate origin, and the directions of the delta axis, the zeta axis and the gamma axis are respectively the same as the directions of the x axis, the y axis and the z axis. The distance from the center of the bubble to the hull is recorded as H0And the distance from the water surface is marked as H. The hull beams being beams of uniform cross-section, the waterborne partHeight is recorded as H1The underwater part circle radius is denoted as R.
For the fluid domain near the bubble, the velocity potential function satisfies the Laplace equation:
Figure RE-GDA0002267915740000111
the lagrange integral of the unsteady non-rotational motion of the fluid on the surface of the bubble is:
Figure RE-GDA0002267915740000112
in formula (9), PmWhere z is the pressure at infinity on the 0 plane, P is the fluid pressure at the outer surface of the bubble, and ρ is the fluid density.
The velocity component in the radial direction of the bubble is:
Figure RE-GDA0002267915740000113
in the formula, vrIs the radial velocity of the surface of the bubble, rbIs the bubble radius.
The bubble load is regarded as a point source, the point source is positioned at the center of the bubble, and the intensity is recorded as Qb(t) of (d). The incident velocity potential caused by bubble loading in the flow field is:
Figure RE-GDA0002267915740000114
in formula (11), raThe distance from the center of the bubble to any point.
The pressure inside the bubble can be determined by the following equation of state:
Figure RE-GDA0002267915740000121
in the formula (12), PbIs qiPressure inside the bulb, PcAnd P0Respectively the saturated vapor pressure of the gas and the initial pressure of the bubbles, V0And V is the initial volume of the bubble and the volume of the bubble at an arbitrary time, γ is the adiabatic index of the gas, and γ is 1.4 for an ideal gas. Irrespective of the tension on the bubble surface and the gas saturation vapor pressure, the fluid pressure P at the bubble outer surface is expressed as:
Figure RE-GDA0002267915740000122
the simultaneous equations (9) to (13) can be obtained:
Figure RE-GDA0002267915740000123
Figure RE-GDA0002267915740000124
the velocity potential of the flow field near the hull beam is:
Figure RE-GDA0002267915740000125
based on the 4 th assumption, it can be considered that: y is less than H, and z is less than H. Therefore, the second order trace y in equation (16)2、z2Negligible, on the basis of which the Taylor expansion of equation (16) is performed,
Figure RE-GDA0002267915740000126
omitting the higher order infinite term, equation (17) can be transformed into:
Figure RE-GDA0002267915740000127
because the invention is suitable for underwater explosion in middle and far fields, the incident velocity of the fluid around the hull beam can only consider the vertical component, and the expression is as follows:
Figure RE-GDA0002267915740000131
in the middle and far field explosion, the flow field velocity near the hull beam caused by the underwater explosion bubble load can be considered to be mainly along the y-axis and z-axis directions based on the 4 th hypothesis,
Figure RE-GDA0002267915740000132
the flow field near the hull beam can be converted into a two-dimensional flow field, and the velocity potential function of the two-dimensional flow field meets the Laplace equation:
Figure RE-GDA0002267915740000133
the velocity potential near the hull beam meets the surface impenetrable condition:
Figure RE-GDA0002267915740000134
in the formula (22), r'aThe distance between any point on the surface of the ship body beam and the ship body beam in the two-dimensional flow field is shown, and theta is an included angle between a z-axis and a normal vector of the surface of the ship body beam.
According to the Laplace equation of the two-dimensional flow field, the diffraction velocity potential and the incident velocity potential satisfy the following relationship on the surface of the ship body:
Figure RE-GDA0002267915740000135
diffraction velocity potential
Figure RE-GDA0002267915740000136
The solution is in the form:
Figure RE-GDA0002267915740000137
radiation velocity potential
Figure RE-GDA0002267915740000138
The ship surface impenetrable condition is met:
Figure RE-GDA0002267915740000139
diffraction velocity potential
Figure RE-GDA00022679157400001310
The solution is in the form:
Figure RE-GDA0002267915740000141
considering that the explosion distance is longer, the fluid velocity potential gradient near the ship body is smaller, namely the requirement of meeting
Figure RE-GDA0002267915740000142
And in the total pressure composition of the hull surface, the position water head z (x, t) is negligible, and the pressure of the hull surface meets the following linearized Bernoulli equation:
Figure RE-GDA0002267915740000143
the fluid load on any section of the hull beam can be found by integrating P over the hull surface:
Figure RE-GDA0002267915740000144
substituting the formula (18), the formula (24) and the formula (26) into the formula (28) yields:
Figure RE-GDA0002267915740000145
in the formula, ma(x)＝πρR2Is the added mass of the hull beam profile in the water.
Step 6): and establishing a motion equation of the calculation model under the underwater explosion load.
Substituting the formula (29) into the damped vibration differential equation of the simply supported beam under the action of the external load,
Figure RE-GDA0002267915740000146
in the formula (30), the first and second groups,
Figure RE-GDA0002267915740000147
solving by adopting a modal superposition method to obtain:
Figure RE-GDA0002267915740000148
in the formula, lambda is the proportionality coefficient of the additional mass and the mass of the hull beam section in water,
Figure RE-GDA0002267915740000149
B'm(t) is the mode shape force corresponding to B' (x, t), and the expression is as follows:
Figure RE-GDA0002267915740000151
in formula (33), AmbDetermined by the initial conditions of underwater explosion bubble loading.
Step 7): and 5) and 6) simultaneously, obtaining a motion equation of the calculation model under the combined action of the underwater explosion and the wave load, and further solving the motion response of the calculation model under the combined action of the underwater explosion and the wave load according to the boundary conditions.
The invention is applied in the following examples: step 1): as shown in fig. 2, the hull beam is simplified into an eulerian bernoulli beam with two simply-supported ends, and the structural parameters include section inertia moment I of 2.8m4Taking the length L of the ship as 40m and the elastic modulus E as 2 x 1011N · m, the external load F (x, t) is 0 when freely vibrating. The calculation model is obtained by solving through a numerical method, and a specific solving result is shown in fig. 3. Step 2): as shown in fig. 4, the wave load is reduced to a sinusoidal load form. Assuming that the displacement of the middle part of the hull beam does not exceed 0.01m under the action of the wave load, the hull beam is a straight beam with an equal section
Figure RE-GDA0002267915740000152
In addition, let
Figure RE-GDA0002267915740000153
The equation of motion of the calculation model under the wave load is solved by adopting a numerical calculation method, and an equation of motion curve when the middle part of the hull beam is displaced is obtained, as shown in fig. 5. Step 3): the simplified model of the hull beam under the underwater explosion bubble load is shown in fig. 6 and 7, and the working conditions of the underwater explosion load are as follows: 450kgTNT in an explosion of 60m under a midship, the initial radius r01.2m, initial pressure P0＝4.98×107Pa, solving the simplified load of the underwater explosion to obtain time history curves of the point source intensity and the bubble radius of the underwater explosion load, wherein the time history curves are respectively shown in fig. 8 and fig. 9. Step 4): substituting the underwater explosive load in the step 3) into the external load F (x, t) in the step 1) to obtain a motion equation of the calculation model under the action of the underwater explosive load:
Figure RE-GDA0002267915740000154
in the formula (35), the first and second groups,
Figure RE-GDA0002267915740000161
using modal stacksAnd (5) solving by adding to obtain a displacement time course curve of the middle part of the hull beam under the action of the underwater explosive load, as shown in figure 10. Step 5): combining the step 2) and the step 4) to obtain a motion equation of the calculation model under the combined action of the underwater explosion and the wave load:
Figure RE-GDA0002267915740000162
initial conditions in the step 1), the step 2) and the step 3) are taken, a modal superposition method is adopted for solving, and a hull beam middle displacement response time course curve under each working condition can be obtained, as shown in fig. 11.
While the present invention has been described with reference to the particular embodiments illustrated in the drawings, which are meant to be illustrative only and not limiting, it will be apparent to those of ordinary skill in the art in light of the teachings of the present invention that numerous modifications can be made without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (8)

1. A hull beam motion response obtaining method under the action of underwater explosion and wave load is characterized by comprising the following steps: the method comprises the following steps:
step 1): simplifying the calculation model into simply supported beams at two ends;
step 2): establishing a transverse vibration equation of a calculation model;
step 3): simplifying the solution of the wave load;
step 4): establishing a motion equation of a calculation model under the action of wave load;
step 5): solving the underwater explosion load;
step 6): establishing a motion equation of a calculation model under the underwater explosion load;
step 7): establishing a motion equation of a calculation model under the combined action of underwater explosion and wave load;
step 8): and solving the motion response of the calculation model under the joint action of the underwater explosion and the wave load by using the boundary conditions.
2. The method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in the step 1), assuming that the length of the beam is L, taking a neutralization axis of the beam as an Ox axis, and taking a coordinate origin as a left end part of the beam; in the coordinate system, the bending rigidity which changes along the length direction of the beam is EI (x), the mass per unit length is m (x), the width of the ship hull beam is b (x), the non-conservative force which acts on the beam per unit length is Q (x, t), and the transverse displacement z (x, t) on the neutral axis of the beam is a function which continuously changes along the coordinate x and the time t.
3. The method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in the step 2), the beam micro-section is taken as a research object, the viscous external damping force is in direct proportion to the speed of the beam micro-section, the external damping coefficient of x on the beam in unit length is set as c (x), and the damping force borne by the beam micro-section is
Figure RE-FDA0002267915730000011
In the initial state, assuming that gravity and buoyancy are balanced with each other, assuming that the difference between gravity and buoyancy is proportional to the ship width b (x) and the transverse displacement z (x, t) in the motion process, the differential load between gravity and buoyancy is ρ gb (x) z (x, t), and the non-conservative force Q (x, t) at any time satisfies:
Figure RE-FDA0002267915730000012
the Hamilton principle is used for deducing the motion equation of the hull beam to obtain:
Figure RE-FDA0002267915730000021
4. the method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in step 3), when the ship body navigates in the waves, the ship body beams alternately generate the motions of sagging and arching, the wave load is assumed to be distributed in a sine form along the ship body beams, the wave force on each micro-segment of the ship body beams is also assumed to be distributed in a sine form at each moment, and the specific load form is as follows:
Figure RE-FDA0002267915730000022
in the formula (3), BwIs the wave load amplitude, omegawFor the angular frequency of the wave loading action ψ is the initial phase angle.
5. The method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in the step 4), the vibration mode function of the simply supported beam is as follows:
Figure RE-FDA0002267915730000023
in the formula (4), the constant AmDetermined by initial conditions; suppose A is under wave loadm＝Amw(ii) a Solving a generalized matrix of the simply supported beam vibration under the action of the wave load by adopting a modal superposition method,
Figure RE-FDA0002267915730000024
6. the method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in said step 5), the solution is performed based on the following assumptions:
1) the influence of the underwater explosion bubble pulsation load is not considered;
2) if the fluid is incompressible and not spin-free, the fluid domain satisfies the following Laplace equation:
Figure RE-FDA0002267915730000031
wherein the velocity potential
Figure RE-FDA0002267915730000032
From incident velocity potential
Figure RE-FDA0002267915730000033
Diffraction velocity potential
Figure RE-FDA0002267915730000034
And radiation velocity potential
Figure RE-FDA0002267915730000035
And satisfies the following relation:
Figure RE-FDA0002267915730000036
3) in the underwater explosion process of the far and medium fields, the influence of the hull beam on the bubbles is ignored, and only the influence of the bubbles on the hull beam, namely the diffraction velocity potential in the fluid area around the bubbles is considered
Figure RE-FDA0002267915730000037
And radiation velocity potential
Figure RE-FDA0002267915730000038
Are all 0, the fluid area near the hull beam satisfies the formula (7);
4) the bubbles are assumed to be spherical, and the transverse size of the hull beam is a tiny amount relative to the distance between the bubbles and the hull;
the coordinate system of the hull beam is xyz, the origin of the coordinate is established at the stern, the positive direction of the x axis is from the stern to the bow, the y axis is along the width direction of the ship, and the z axis is in the vertical direction as the positive direction; bubble coordinate system deltaZeta gamma, taking the bubble center as the origin of coordinates, wherein the directions of a delta axis, a zeta axis and a gamma axis are the same as those of an x axis, a y axis and a z axis respectively; the distance from the center of the bubble to the hull is recorded as H0And the distance from the water surface is marked as H; the hull beam is a beam with equal section, and the height of the water part is marked as H1The radius of the underwater part circle is marked as R;
for the fluid domain near the bubble, the velocity potential function of the bubble satisfies the Laplace equation:
Figure RE-FDA0002267915730000039
the lagrange integral of the unsteady non-rotational motion of the fluid on the surface of the bubble is:
Figure RE-FDA00022679157300000310
in formula (9), PmThe pressure at an infinite distance on a plane z is 0, P is the fluid pressure on the outer surface of the bubble, and rho is the fluid density;
the velocity component in the radial direction of the bubble is:
Figure RE-FDA00022679157300000311
in the formula (10), vrIs the radial velocity of the surface of the bubble, rbIs the bubble radius;
the bubble load is regarded as a point source, the point source is positioned at the center of the bubble, and the intensity is recorded as Qb(t), the incident velocity potential caused by the bubble load in the flow field is:
Figure RE-FDA0002267915730000041
in formula (11), raThe distance from the center of the bubble to any point;
the pressure inside the bubble is determined by equation (12):
Figure RE-FDA0002267915730000042
in the formula (12), PbIs the internal pressure of the bubble, PcAnd P0Respectively the saturated vapor pressure of the gas and the initial pressure of the bubbles, V0V is the initial volume of the bubble and the volume of the bubble at any moment, and gamma is the adiabatic index of the gas; irrespective of the tension on the bubble surface and the gas saturation vapor pressure, the fluid pressure P at the bubble outer surface is expressed as:
Figure RE-FDA0002267915730000043
the following equations (9) to (13) yield:
Figure RE-FDA0002267915730000044
Figure RE-FDA0002267915730000045
the velocity potential of the flow field near the hull beam is:
Figure RE-FDA0002267915730000046
based on a fourth assumption, y < H, z < H; therefore, the second order trace y in equation (16)2、z2Neglecting, the Taylor expansion is performed on the basis of the formula (16),
Figure RE-FDA0002267915730000051
omitting the higher order infinite terms, equation (17) translates to:
Figure RE-FDA0002267915730000052
for medium and far field underwater explosion, only the vertical component is considered for the incident velocity of the fluid around the hull beam, and the expression is as follows:
Figure RE-FDA0002267915730000053
in the middle and far field explosion, based on the 4 th hypothesis, the flow field velocity near the hull beam caused by the underwater explosion bubble load is mainly along the y-axis and z-axis directions,
Figure RE-FDA0002267915730000054
then the flow field near the hull beam is converted into a two-dimensional flow field, and the velocity potential function of the two-dimensional flow field meets the Laplace equation:
Figure RE-FDA0002267915730000055
the velocity potential near the hull beam meets the surface impenetrable condition:
Figure RE-FDA0002267915730000056
in the formula (22), r'aThe distance between any point on the surface of the ship body beam and the ship body beam in the two-dimensional flow field is shown, and theta is an included angle between a z-axis and a normal vector of the surface of the ship body beam;
obtaining a diffraction velocity potential and an incidence velocity potential by a two-dimensional flow field Laplace equation, wherein the diffraction velocity potential and the incidence velocity potential meet the requirements on the surface of the ship body:
Figure RE-FDA0002267915730000057
diffraction velocity potential
Figure RE-FDA0002267915730000058
The solution is in the form:
Figure RE-FDA0002267915730000061
radiation velocity potential
Figure RE-FDA0002267915730000062
The ship surface impenetrable condition is met:
Figure RE-FDA0002267915730000063
diffraction velocity potential
Figure RE-FDA0002267915730000064
The solution is in the form:
Figure RE-FDA0002267915730000065
due to the far explosion distance, the fluid velocity potential gradient near the ship body is small, namely the requirement is met
Figure RE-FDA0002267915730000066
And in the total pressure composition of the hull surface, the position water head z (x, t) is ignored, and then the pressure of the hull surface meets the following linearized Bernoulli equation:
Figure RE-FDA0002267915730000067
the fluid load on any section of the hull beam is then found by the integral of P over the hull surface:
Figure RE-FDA0002267915730000068
substituting the formula (18), the formula (24) and the formula (26) into the formula (28) yields:
Figure RE-FDA0002267915730000069
7. the method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in the step 6), the formula (29) is substituted into a damped vibration differential equation of the simply supported beam under the action of the external load,
Figure RE-FDA00022679157300000610
in the formula (30), the first and second groups,
Figure RE-FDA00022679157300000611
solving by adopting a modal superposition method to obtain:
Figure RE-FDA00022679157300000612
in the formula (31), lambda is the proportionality coefficient of the additional mass and the mass of the hull beam section in water,
Figure RE-FDA0002267915730000071
B'm(t) is the mode shape force corresponding to B' (x, t), and the expression is as follows:
Figure RE-FDA0002267915730000072
in formula (33), AmbDetermined by the initial conditions of underwater explosion bubble loading.
8. The method for acquiring the motion response of the hull beam under the action of the underwater explosion and the wave load as claimed in claim 1, wherein: in step 7) and step 8), combining step 5) and step 6) to obtain a motion equation of the calculation model under the combined action of the underwater explosion and the wave load, and then solving the motion response of the calculation model under the combined action of the underwater explosion and the wave load according to the boundary conditions.
CN201910567669.1A 2019-08-15 2019-08-15 Method for acquiring motion response of hull beam under action of underwater explosion and wave load Active CN112395722B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910567669.1A CN112395722B (en) 2019-08-15 2019-08-15 Method for acquiring motion response of hull beam under action of underwater explosion and wave load

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910567669.1A CN112395722B (en) 2019-08-15 2019-08-15 Method for acquiring motion response of hull beam under action of underwater explosion and wave load

Publications (2)

Publication Number Publication Date
CN112395722A true CN112395722A (en) 2021-02-23
CN112395722B CN112395722B (en) 2022-05-31

Family

ID=74601112

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910567669.1A Active CN112395722B (en) 2019-08-15 2019-08-15 Method for acquiring motion response of hull beam under action of underwater explosion and wave load

Country Status (1)

Country Link
CN (1) CN112395722B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113184118A (en) * 2021-06-04 2021-07-30 中国人民解放军91439部队 Marine retraction device of underwater explosion test equipment and retraction method thereof

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2008110622A (en) * 2006-10-27 2008-05-15 Ihi Marine United Inc Method and program for analyzing bubble behavior and ship hull whipping response by underwater explosion
CN104657611A (en) * 2015-02-14 2015-05-27 中国人民解放军海军工程大学 Ship whole elastic-plastic movement response predication method and system under action of underwater explosion
CN104743086A (en) * 2015-02-14 2015-07-01 中国人民解放军海军工程大学 Ship whipping motion response prediction method and system under underwater explosion situation
CN107808046A (en) * 2017-10-25 2018-03-16 中国船舶工业集团公司第七0八研究所 A kind of hull beam blast impulse dynamical bending moment determines method
CN109214082A (en) * 2018-09-03 2019-01-15 北京理工大学 A kind of high resolution numerical simulation method of near field underwater blast wave load

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2008110622A (en) * 2006-10-27 2008-05-15 Ihi Marine United Inc Method and program for analyzing bubble behavior and ship hull whipping response by underwater explosion
CN104657611A (en) * 2015-02-14 2015-05-27 中国人民解放军海军工程大学 Ship whole elastic-plastic movement response predication method and system under action of underwater explosion
CN104743086A (en) * 2015-02-14 2015-07-01 中国人民解放军海军工程大学 Ship whipping motion response prediction method and system under underwater explosion situation
CN107808046A (en) * 2017-10-25 2018-03-16 中国船舶工业集团公司第七0八研究所 A kind of hull beam blast impulse dynamical bending moment determines method
CN109214082A (en) * 2018-09-03 2019-01-15 北京理工大学 A kind of high resolution numerical simulation method of near field underwater blast wave load

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
CHO-CHUNGLIANG 等: "Shock responses of a surface ship subjected to noncontact underwater explosions", 《OCEAN ENGINEERING》 *
姚熊亮 等: "《船体振动与噪声》", 31 August 2010, 北京：国防工业出版社 *
姚熊亮 等: "水下爆炸气泡与波浪载荷联合作用下的船体响应", 《哈尔滨工程大学学报》 *
张文鹏: "水下爆炸与波浪载荷作用下船体结构动力计算研究", 《万方数据库》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113184118A (en) * 2021-06-04 2021-07-30 中国人民解放军91439部队 Marine retraction device of underwater explosion test equipment and retraction method thereof
CN113184118B (en) * 2021-06-04 2024-05-31 中国人民解放军91439部队 Marine retraction device and retraction method for underwater explosion test equipment

Also Published As

Publication number Publication date
CN112395722B (en) 2022-05-31

Similar Documents

Publication Publication Date Title
Xiang et al. Maneuvering of two interacting ships in calm water
CN112395722B (en) Method for acquiring motion response of hull beam under action of underwater explosion and wave load
Tavakoli et al. An oblique 2D+ T approach for hydrodynamic modeling of yawed planing boats in calm water
Lee et al. Dynamic response of a floating crane in waves by considering the nonlinear effect of hydrostatic force
Zhao et al. A hybrid 2.5-dimensional high-speed strip theory method and its application to apply pressure loads to 3-dimensional full ship finite element models
CN104155043B (en) A kind of dynamic positioning system external environment force measuring method
Westin et al. Modeling dynamic cable–sheave contact and detachment during towing operations
Endresen Vertical wave loads and response of a floating fish farm with circular collar
Zhao et al. Applying strip theory based linear seakeeping loads to 3D full ship finite element models
Wang et al. Numerical analysis of added mass and damping of floating production, storage and offloading system
Treakle III et al. A time-domain method to evaluate the use of moving weights to reduce the roll motion of a ship
Youssef et al. Roll stabilization by passive anti-roll tanks using an improved model of the tank-liquid motion
Treakle III A time-domain numerical study of passive and active anti-roll tanks to reduce ship motions
Chatjigeorgiou et al. Wave scattering of spheroidal bodies below a free surface
Blandeau et al. Linear and non-linear wave loads on FPSOs
Van Kessel et al. The effect of aircushion division on the motions of large floating structures
Dantas et al. AUV control in the diving plane subject to waves
Jensen et al. Modeling and control of offshore pipelay operations based on a finite strain pipe model
Sun et al. Partially nonlinear time domain analysis on ship motions in waves with translating-pulsating source Green function
Hisamatsu et al. Simplified formulation of coupled system between moored ship and elastic pipe for OTEC plantship
Taravella et al. A general solution to low-aspect-ratio flat-ship theory
Chen et al. A Numerical Fluid-Solid Coupling Model for the Dynamics of Ships in Atrocious Sea Conditions
CN117360727A (en) Method for calculating vertical shearing force and vertical bending moment of ship when receiving waves
Tsubogo Reciprocal Form of the Wave Drift Force and Moment Acting on Floating Body
Ketabdari et al. Nonlinear response analysis of a SeaStar offshore Tension Leg Platform in six degrees of freedom

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant