CN112417559A - Damping-containing flexible structure anti-exponential type explosive load design power coefficient method - Google Patents

Damping-containing flexible structure anti-exponential type explosive load design power coefficient method Download PDF

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CN112417559A
CN112417559A CN202011299993.9A CN202011299993A CN112417559A CN 112417559 A CN112417559 A CN 112417559A CN 202011299993 A CN202011299993 A CN 202011299993A CN 112417559 A CN112417559 A CN 112417559A
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耿少波
罗干
魏月娟
龚欣
郑亮
李建军
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Abstract

The invention relates to a method for designing a dynamic coefficient of an anti-exponential type explosive load with a damping flexible structure, belonging to the technical field of anti-explosion design, wherein the specific flexible structure refers to the following steps: real time t of exponential type explosion load actioniWithin the range, the structural vibration displacement does not reach the maximum value of the elastic vibration displacement, and after the explosive load is unloaded, the explosive load depends on the inertia force at tTReaches the maximum value y of elastic displacement at any momentTThereafter, the structural vibration becomes a plastic vibration at a certain time tmThe maximum value y of the elastic-plastic displacement of the structure is reachedm(ii) a According to the action process of explosion on the building structure, the process is divided into three stages of forced vibration in an elastic stage, free vibration in the elastic stage and free vibration in a plastic stage; through the calculation of the different stages, the influence of the structure type, the accuracy of the explosive load and the structure damping on the dynamic coefficient of the explosive load is fully considered, and the designed building is made to be as large as possibleThe structure is more practical, and the anti-explosion requirement is met while the cost is reduced.

Description

Damping-containing flexible structure anti-exponential type explosive load design power coefficient method
Technical Field
The invention relates to a method for designing a dynamic coefficient of an anti-exponential type explosive load with a damping flexible structure, and belongs to the technical field of anti-explosion design.
Background
At present, when the existing buildings are designed to resist explosion, the anti-explosion capability of an anti-explosion structural member needs to be considered. The duration of the explosive load applied to the structure by a conventional explosion is tiVery short, when the civil air defense structure and the foreign civil air defense structure are subjected to anti-explosion design, the linear load is processed according to equal impulse, and the overpressure peak value delta p of the dynamic explosive load is further processedmDynamic coefficient k of resistance in structural elastic-plastic stagehAnd multiplying the obtained product to obtain a structural antiknock design value as a static load. Wherein the kinetic coefficient k is given by the specificationhThe formula does not consider structural damping and anti-explosion design structure types, and lacks powerful support for accurate design of an actual structure; the equivalent action time of the normalized and simplified equal-impulse linear attenuation load is also shorter than the actual explosion action time. Such as: gunn few wave, plum flood, gepejj, consider the equivalent static load dynamic coefficient of the jump index type explosive air blast load]Explosion and blast and 2019,39(03): 33-41; BAKER W E. expansion hazards and evaluation [ M]The two documents of Amsterdam Elsevier Scientific pub. Co.1983 respectively introduce that the real air explosion shock wave attenuation mode is described by an exponential function, so that the calculation result is more accurate. Therefore, when the existing specification is used for structural anti-explosion design, the design is conservative, and in part of application environments, the conservative design will cause the increase of construction cost.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides a method for designing a dynamic coefficient of an exponential-type explosive load resistance with a damping flexible structure.
In order to achieve the purpose, the technical scheme adopted by the invention is a method for designing a dynamic coefficient for resisting exponential type explosive load by using a damping flexible structure, wherein the flexible structure refers to the following steps: true duration of explosive loading action tiWithin the range, the structural vibration displacement does not reach the maximum value of the elastic vibration displacement, and after the explosive load is unloaded, the explosive load depends on the inertia force at tTReaches the maximum value y of elastic displacement at any momentTAfter that, the structure is vibrated to become plasticSexual vibration, at a certain time tmThe maximum value y of the elastic-plastic displacement of the structure is reachedm
According to the action process of explosion on the building structure, the process is divided into three stages of forced vibration in an elastic stage, free vibration in the elastic stage and free vibration in a plastic stage;
a. forced vibration of elastic phase
T is more than 0 and less than or equal to t in the elastic stage and in the load action time rangeiThe dynamic equation of the structure equivalent system is as follows:
Figure BDA0002786487190000011
wherein t is a time parameter under the action of flexible structure explosion, and tiFor the actual duration of the action of the explosive load, MeFor elastic phase equivalent structural mass, CeFor damping of equivalent structures in the elastic phase, KeIn order to have the equivalent structural stiffness in the elastic phase,
Figure BDA0002786487190000012
the vibration acceleration of the equivalent system of the flexible structure,
Figure BDA0002786487190000021
the vibration speed of the flexible structure equivalent system, y the vibration displacement of the flexible structure equivalent system, delta Pe(t) is the explosive dynamic load which is born by the flexible structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure BDA0002786487190000022
wherein m is the mass per linear meter of the real structure, l is the span length of the real structure, xi is the damping ratio of the real structure, K is the rigidity of the real structure, and K isMFor the elastic phase quality transformation coefficient, kLThe exponential explosive dynamic load is the load transformation coefficient of the elastic stage:
Figure BDA0002786487190000023
wherein, tiActing for explosive loads for a long time, Δ pmIs the overpressure peak value of the explosive load, a is an exponential type load attenuation coefficient and consists of undamped natural vibration frequency omega and damped natural vibration frequency omegadDamping adjustment coefficient gamma, explosive load peak value as static displacement y corresponding to static loadstThe ratio k of the elastic phase mass transformation coefficient to the load transformation coefficientM-LThe parameters are calculated as follows:
Figure BDA0002786487190000024
it can be known that the initial displacement and the initial velocity of the structure are both 0 before the structure bears the explosive load, and after the differential equation is solved, the displacement and velocity expression at this stage can be determined:
Figure BDA0002786487190000025
Figure BDA0002786487190000031
then at t where the explosive load is unloadediAt time, the corresponding displacement and velocity are:
Figure BDA0002786487190000032
Figure BDA0002786487190000041
Figure BDA0002786487190000042
b. elastic phase free vibration
Because the structural type for carrying out the design is flexible structure antiknock design, when the blast load eliminates, the structure still does not enter plastic state, and the structure is for not having external load this moment, with displacement yiAnd velocity viFree vibration with damped elastic phase as initial condition, i.e. when ti<t≤tTThe dynamic equation of the structural equivalent system is as follows:
Figure BDA0002786487190000043
wherein, tTElastic vibration is completed for the flexible structure, namely the critical moment of plastic vibration is about to enter. After solving this equation, the displacement and velocity solution is:
Figure BDA0002786487190000044
Figure BDA0002786487190000045
substituting the formulas (7) and (8) into the formulas (10) and (11) at tTAt the moment, the elastic vibration of the structure reaches the maximum displacement, and the displacement y is at the momentTVelocity vTRespectively as follows:
Figure BDA0002786487190000051
Figure BDA0002786487190000061
Figure BDA0002786487190000071
Figure BDA0002786487190000081
c. free vibration in plastic phase
When the time of the structure vibration is more than tTAt the moment, no external load is applied, and y isTAnd vTFree vibration in plastic stage containing damping for initial condition, at tmAt the moment, the structural vibration reaches a maximum displacement, i.e. when tT<t≤tmThe dynamic equation of the structural equivalent system is as follows:
Figure BDA0002786487190000082
wherein m iseIs the equivalent structural mass of the plastic phase, ceFor equivalent structural damping in the plastic phase, qmThe maximum resistance of the plastic stage structure is calculated by the formula:
Figure BDA0002786487190000083
wherein k ismFor the transformation coefficient of mass in the plastic phase, klFor the plastic stage load transformation coefficients, the equation is solved (14), and the solution for the displacement and velocity at this stage is found as:
Figure BDA0002786487190000084
Figure BDA0002786487190000085
d. ductility ratio based on dynamic coefficient in elastoplasticity stage
When the structure vibrates to the maximum displacement ymWhen, the corresponding time is tmAt this time, the velocity vmWhen formula (17) is substituted with 0, then:
Figure BDA0002786487190000086
will tmThe maximum displacement of the elastic-plastic vibration of the structure is obtained by carrying into (16):
Figure BDA0002786487190000087
let km-lThe ratio of the mass transformation coefficient and the load transformation coefficient in the plastic stage is as follows:
Figure BDA0002786487190000088
substituting (15) and (21) into (19) gives the maximum displacement of the structure as:
Figure BDA0002786487190000091
according to the ductility ratio beta and the resistance kinetic coefficient khThe provision of (1):
Figure BDA0002786487190000092
substituting the values (12) and (21) into the beta-equation (22) of the ductility ratio
Figure BDA0002786487190000093
Y in the formula (23)TAnd vTThe calculation is performed by using the expressions (12) and (13).
Compared with the prior art, the invention has the following technical effects: according to the invention, according to the actual situation, the influence of the type of the structure and the structural damping on the dynamic coefficient of the explosion load is fully considered, the designed building structure is more practical, the cost is reduced, and the anti-explosion requirement is met. And the method can realize the precise design of the actual structure and lay a foundation for the antiknock design.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present invention more apparent, the present invention is further described in detail below with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The method for designing the dynamic coefficient of the damping flexible structure for resisting the exponential type explosive load comprises the following steps: true duration of explosive loading action tiWithin the range, the structural vibration displacement does not reach the maximum value of the elastic vibration displacement, and after the explosive load is unloaded, the explosive load depends on the inertia force at tTReaches the maximum value y of elastic displacement at any momentTThereafter, the structural vibration becomes a plastic vibration at a certain time tmThe maximum value y of the elastic-plastic displacement of the structure is reachedm
According to the action process of explosion on the building structure, the process is divided into three stages of forced vibration in an elastic stage, free vibration in the elastic stage and free vibration in a plastic stage;
a. forced vibration of elastic phase
T is more than 0 and less than or equal to t in the elastic stage and in the load action time rangeiThe dynamic equation of the structure equivalent system is as follows:
Figure BDA0002786487190000094
wherein t is a time parameter under the action of flexible structure explosion, and tiFor the actual duration of the action of the explosive load, MeFor elastic phase equivalent structural mass, CeFor damping of equivalent structures in the elastic phase, KeIn order to have the equivalent structural stiffness in the elastic phase,
Figure BDA0002786487190000095
the vibration acceleration of the equivalent system of the flexible structure,
Figure BDA0002786487190000101
the vibration speed of the flexible structure equivalent system is adopted, and y is the flexible structure equivalent systemDisplacement by vibration, Δ Pe(t) is the explosive dynamic load which is born by the flexible structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure BDA0002786487190000102
wherein m is the mass per linear meter of the real structure, l is the span length of the real structure, xi is the damping ratio of the real structure, K is the rigidity of the real structure, and K isMFor the elastic phase quality transformation coefficient, kLThe exponential explosive dynamic load is the load transformation coefficient of the elastic stage:
Figure BDA0002786487190000103
wherein, tiActing for explosive loads for a long time, Δ pmIs the overpressure peak value of the explosive load, a is an exponential type load attenuation coefficient and consists of undamped natural vibration frequency omega and damped natural vibration frequency omegadDamping adjustment coefficient gamma, explosive load peak value as static displacement y corresponding to static loadstThe ratio k of the elastic phase mass transformation coefficient to the load transformation coefficientM-LThe parameters are calculated as follows:
Figure BDA0002786487190000104
it can be known that the initial displacement and the initial velocity of the structure are both 0 before the structure bears the explosive load, and after the differential equation is solved, the displacement and velocity expression at this stage can be determined:
Figure BDA0002786487190000105
Figure BDA0002786487190000111
then at t where the explosive load is unloadediAt time, the corresponding displacement and velocity are:
Figure BDA0002786487190000112
Figure BDA0002786487190000121
Figure BDA0002786487190000122
b. elastic phase free vibration
Because the structural type for carrying out the design is flexible structure antiknock design, when the blast load eliminates, the structure still does not enter plastic state, and the structure is for not having external load this moment, with displacement yiAnd velocity viFree vibration with damped elastic phase as initial condition, i.e. when ti<t≤tTThe dynamic equation of the structural equivalent system is as follows:
Figure BDA0002786487190000123
wherein, tTElastic vibration is completed for the flexible structure, namely the critical moment of plastic vibration is about to enter. After solving this equation, the displacement and velocity solution is:
Figure BDA0002786487190000124
Figure BDA0002786487190000125
substituting the formulas (7) and (8) into the formulas (10) and (11) at tTAt the moment, the elastic vibration of the structure reaches the maximum displacement, and the displacement y is at the momentTVelocity vTRespectively as follows:
Figure BDA0002786487190000131
Figure BDA0002786487190000141
Figure BDA0002786487190000151
Figure BDA0002786487190000161
c. free vibration in plastic phase
When the time of the structure vibration is more than tTAt the moment, no external load is applied, and y isTAnd vTFree vibration in plastic stage containing damping for initial condition, at tmAt the moment, the structural vibration reaches a maximum displacement, i.e. when tT<t≤tmThe dynamic equation of the structural equivalent system is as follows:
Figure BDA0002786487190000162
wherein m iseIs the equivalent structural mass of the plastic phase, ceFor equivalent structural damping in the plastic phase, qmThe maximum resistance of the plastic stage structure is calculated by the formula:
Figure BDA0002786487190000163
wherein k ismFor the transformation coefficient of mass in the plastic phase, klFor the plastic stage load transformation coefficients, the equation is solved (14), and the solution for the displacement and velocity at this stage is found as:
Figure BDA0002786487190000164
Figure BDA0002786487190000165
d. ductility ratio based on dynamic coefficient in elastoplasticity stage
When the structure vibrates to the maximum displacement ymWhen, the corresponding time is tmAt this time, the velocity vmWhen formula (17) is substituted with 0, then:
Figure BDA0002786487190000166
will tmThe maximum displacement of the elastic-plastic vibration of the structure is obtained by carrying into (16):
Figure BDA0002786487190000167
let km-lThe ratio of the mass transformation coefficient and the load transformation coefficient in the plastic stage is as follows:
Figure BDA0002786487190000168
substituting (15) and (21) into (19) gives the maximum displacement of the structure as:
Figure BDA0002786487190000171
according to the ductility ratio beta and the resistance kinetic coefficient khThe provision of (1):
Figure BDA0002786487190000172
substituting the values (12) and (21) into the beta-equation (22) of the ductility ratio
Figure BDA0002786487190000173
Y in the formula (23)TAnd vTThe calculation is performed by using the expressions (12) and (13).
By the above method, the actual antiknock design of the structure is exemplified as follows.
1. When the protective structure is subjected to anti-explosion design, the structural design is required to be a flexible structure, and the self-vibration circular frequency omega of the structure and the action duration t of dynamic explosive load areiProduct of ω ti0.8, a ductility ratio beta of 1.20, a damping ratio xi of 1%, an exponential load attenuation coefficient a of 1.27, and a damping coefficient k of 1%m-lAnd k ism-lThe values are respectively 0.66 and 0.78 (the underground protective structure, the Fangqin, the Shuangjinchun editions, ISBN 9787508470009 Chinese water conservancy and hydropower publishing house, published in 2010), other parameters are respectively calculated by other formulas, are defined by a flexible structure, and are used for thetaT(i.e.,. omega.t)T) Make a limitation of thetaTi(i.e.,. omega.t)T>ωti) Then, assuming the initial value, substituting into equations (12), (13) and (23), and calculating the resistance kinetic coefficient k by an iterative methodhIs 0.323.
2. When the protective structure is subjected to anti-explosion design, the structural design is required to be a flexible structure, and the self-vibration circular frequency omega of the structure and the action duration t of dynamic explosive load areiProduct of ω ti0.8, a ductility ratio beta of 1.20, a damping ratio xi of 5%, an exponential load attenuation coefficient a of 1.27, and a damping coefficient k ofm-lAnd k ism-lThe values are respectively 0.66 and 0.78 (the underground protective structure, the Fangqin, the Shuangjinchun editions, ISBN 9787508470009 Chinese water conservancy and hydropower publishing house, published in 2010), other parameters are respectively calculated by other formulas, are defined by a flexible structure, and are used for thetaT(i.e.,. omega.t)T) Make a limitation of thetaTi(i.e.,. omega.t)T>ωti) Then, assuming the initial value, substituting into equations (12), (13) and (23), and calculating the resistance kinetic coefficient k by an iterative methodhIs 0.304.
3. When the protective structure is designed for anti-explosion, the structural design is required to be a flexible structure, and the structure has a natural vibration circular frequency omegaDuration t of action with explosive dynamic loadiProduct of ω ti0.6, a ductility ratio beta of 1.40, a damping ratio xi of 10%, an exponential load attenuation coefficient a of 1.27, and a damping coefficient k ofm-lAnd k ism-lThe values are respectively 0.66 and 0.78 (the underground protective structure, the Fangqin, the Shuangjinchun editions, ISBN 9787508470009 Chinese water conservancy and hydropower publishing house, published in 2010), other parameters are respectively calculated by other formulas, are defined by a flexible structure, and are used for thetaT(i.e.,. omega.t)T) Make a limitation of thetaTi(i.e.,. omega.t)T>ωti) Then, assuming the initial value, substituting into equations (12), (13) and (23), and calculating the resistance kinetic coefficient k by an iterative methodhIs 0.189.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principles of the present invention are intended to be included therein.

Claims (1)

1. The method for designing the dynamic coefficient of the damping flexible structure with the anti-exponential type explosive load is characterized by comprising the following steps: the flexible structure refers to: true duration of explosive loading action tiWithin the range, the structural vibration displacement does not reach the maximum value of the elastic vibration displacement, and after the explosive load is unloaded, the explosive load depends on the inertia force at tTReaches the maximum value y of elastic displacement at any momentTThereafter, the structural vibration becomes a plastic vibration at a certain time tmThe maximum value y of the elastic-plastic displacement of the structure is reachedm
According to the action process of explosion on the building structure, the process is divided into three stages of forced vibration in an elastic stage, free vibration in the elastic stage and free vibration in a plastic stage;
a. forced vibration of elastic phase
T is more than 0 and less than or equal to t in the elastic stage and in the load action time rangeiThe dynamic equation of the structure equivalent system is as follows:
Figure FDA0002786487180000011
wherein t is a time parameter under the action of flexible structure explosion, and tiFor the actual duration of the action of the explosive load, MeFor elastic phase equivalent structural mass, CeFor damping of equivalent structures in the elastic phase, KeIn order to have the equivalent structural stiffness in the elastic phase,
Figure FDA0002786487180000014
the vibration acceleration of the equivalent system of the flexible structure,
Figure FDA0002786487180000015
the vibration speed of the flexible structure equivalent system, y the vibration displacement of the flexible structure equivalent system, delta Pe(t) is the explosive dynamic load which is born by the flexible structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure FDA0002786487180000012
wherein m is the mass per linear meter of the real structure, l is the span length of the real structure, xi is the damping ratio of the real structure, K is the rigidity of the real structure, and K isMFor the elastic phase quality transformation coefficient, kLThe exponential explosive dynamic load is the load transformation coefficient of the elastic stage:
Figure FDA0002786487180000013
wherein, tiActing for explosive loads for a long time, Δ pmIs the overpressure peak value of the explosive load, a is an exponential type load attenuation coefficient and consists of undamped natural vibration frequency omega and damped natural vibration frequency omegadDamping adjustment coefficient gamma, explosive load peak value as static displacement y corresponding to static loadstThe ratio k of the elastic phase mass transformation coefficient to the load transformation coefficientM-LThe parameters are calculated as follows:
Figure FDA0002786487180000021
it can be known that the initial displacement and the initial velocity of the structure are both 0 before the structure bears the explosive load, and after the differential equation is solved, the displacement and velocity expression at this stage can be determined:
Figure FDA0002786487180000022
Figure FDA0002786487180000023
then at t where the explosive load is unloadediAt time, the corresponding displacement and velocity are:
Figure FDA0002786487180000031
Figure FDA0002786487180000032
Figure FDA0002786487180000041
b. elastic phase free vibration
Because the structural type for carrying out the design is flexible structure antiknock design, when the blast load eliminates, the structure still does not enter plastic state, and the structure is for not having external load this moment, with displacement yiAnd velocity viFree vibration with damped elastic phase as initial condition, i.e. when ti<t≤tTThe dynamic equation of the structural equivalent system is as follows:
Figure FDA0002786487180000042
wherein, tTElastic vibration is completed for the flexible structure, namely the critical moment of plastic vibration is about to enter. After solving this equation, the displacement and velocity solution is:
Figure FDA0002786487180000043
Figure FDA0002786487180000044
substituting the formulas (7) and (8) into the formulas (10) and (11) at tTAt the moment, the elastic vibration of the structure reaches the maximum displacement, and the displacement y is at the momentTVelocity vTRespectively as follows:
Figure FDA0002786487180000051
Figure FDA0002786487180000061
Figure FDA0002786487180000071
Figure FDA0002786487180000081
c. free vibration in plastic phase
When the time of the structure vibration is more than tTAt the moment, no external load is applied, and y isTAnd vTFree vibration in plastic stage containing damping for initial condition, at tmAt the moment, the structural vibration reaches a maximum displacement, i.e. when tT<t≤tmThe dynamic equation of the structural equivalent system is as follows:
Figure FDA0002786487180000082
wherein m iseIs the equivalent structural mass of the plastic phase, ceFor equivalent structural damping in the plastic phase, qmThe maximum resistance of the plastic stage structure is calculated by the formula:
Figure FDA0002786487180000083
wherein k ismFor the transformation coefficient of mass in the plastic phase, klFor the plastic stage load transformation coefficients, the equation is solved (14), and the solution for the displacement and velocity at this stage is found as:
Figure FDA0002786487180000084
Figure FDA0002786487180000085
d. ductility ratio based on dynamic coefficient in elastoplasticity stage
When the structure vibrates to the maximum displacement ymWhen, the corresponding time is tmAt this time, the velocity vmWhen formula (17) is substituted with 0, then:
Figure FDA0002786487180000086
will tmThe maximum displacement of the elastic-plastic vibration of the structure is obtained by carrying into (16):
Figure FDA0002786487180000091
let km-lThe ratio of the mass transformation coefficient and the load transformation coefficient in the plastic stage is as follows:
Figure FDA0002786487180000092
substituting (15) and (21) into (19) gives the maximum displacement of the structure as:
Figure FDA0002786487180000093
according to the ductility ratio beta and the resistance kinetic coefficient khThe provision of (1):
Figure FDA0002786487180000094
substituting the values (12) and (21) into the beta-equation (22) of the ductility ratio
Figure FDA0002786487180000095
Y in the formula (23)TAnd vTThe calculation is performed by using the expressions (12) and (13).
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Publication number Priority date Publication date Assignee Title
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