CN112417561B - Method for designing dynamic coefficient of anti-exponential explosion load of damping-containing rigid structure - Google Patents

Method for designing dynamic coefficient of anti-exponential explosion load of damping-containing rigid structure Download PDF

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CN112417561B
CN112417561B CN202011304172.XA CN202011304172A CN112417561B CN 112417561 B CN112417561 B CN 112417561B CN 202011304172 A CN202011304172 A CN 202011304172A CN 112417561 B CN112417561 B CN 112417561B
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耿少波
罗干
毛慧峰
韩云山
高营
程志
刘兰
魏月娟
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Abstract

The invention relates to an anti-finger containing damping rigid structureA dynamic coefficient design method for digital explosion load belongs to the technical field of antiknock design, and a specific rigid structure refers to: under the action of exponential explosive load, the structure completes elastic maximum vibration displacement y T At the moment t corresponding to the coming plastic vibration T Is less than the real action duration t of the explosion load i After the explosive load is unloaded, the structure continues to vibrate to a certain moment t m Reaches the maximum value y of the total elastoplastic displacement of the structure m The method comprises the steps of carrying out a first treatment on the surface of the According to the action process of explosion on the building structure, dividing the process into three stages of forced vibration in an elastic stage, forced vibration in a plastic stage and free vibration in the plastic stage; through the calculation of the different stages, the influence of the structural type, the accurate description of the exponential explosion and the structural damping on the explosion load dynamic coefficient is fully considered, so that the designed building structure is more practical as much as possible, the cost is reduced, and the antiknock requirement is met.

Description

Method for designing dynamic coefficient of anti-exponential explosion load of damping-containing rigid structure
Technical Field
The invention relates to a method for designing dynamic coefficients of an anti-exponential explosion load of a damping-containing rigid structure, and belongs to the technical field of antiknock design.
Background
At present, when the antiknock design is carried out on the existing building, antiknock capability of antiknock structural components needs to be considered. Duration t of blast load applied to the structure by conventional blast i When the antiknock design is carried out on civil air defense structures in China and abroad, the antiknock design is carried out according to the linear load treatment of equal impulse, and the overpressure peak value delta p of the explosive dynamic load is further processed m And the resistance power coefficient k in the elastoplastic stage of the structure h And after multiplication, the structural antiknock design value is used as a static load. Wherein the power coefficient k given by the specification h The formula does not consider the structural damping and antiknock design structure types, and aims at the actual junctionThe structure accurate design lacks powerful support; the equivalent action duration of the normalized and simplified equivalent impulse linear attenuation load is also smaller than the actual explosion action duration. Such as: geng Shaobo, li Hong, ge Peijie. Exponential explosive empty load equivalent static load dynamic coefficient taking into account transitions [ J ]]Explosion and impact and 2019,39 (03) 33-41; BAKER W E.Explosion hazards and evaluation [ M]Amsterdam Elsevier Scientific Pub.Co.1983, two references, respectively, disclose that the use of exponential function descriptions for the real air blast shock wave attenuation modes will result in more accurate calculation results. Therefore, the existing specifications are conservative in design when the structure antiknock design is carried out, and the conservative design causes the increase of construction cost in part of application environments.
Disclosure of Invention
The invention provides a method for designing dynamic coefficients of an anti-exponential explosion load with a damping rigid structure, which aims to solve the technical problems in the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is a method for designing a dynamic coefficient for resisting exponential explosion load of a damping-containing rigid structure, wherein the rigid structure refers to: under the action of explosion, the structure completes the elastic maximum vibration displacement y T At the moment t corresponding to the coming plastic vibration T Is less than the real action duration t of the explosion load i After the explosive load is unloaded, the structure continues to vibrate to a certain moment t m Reaches the maximum value y of the total elastoplastic displacement of the structure m ；
According to the action process of explosion on the building structure, dividing the process into three stages of forced vibration in an elastic stage, forced vibration in a plastic stage and free vibration in the plastic stage;
a. forced vibration at elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t T In the internal, the dynamic equation of the structural equivalent system is
Figure BDA0002787789960000021
Wherein t is the explosion of the rigid structureTime parameter under action, t T M is the critical moment of the rigid structure from elastic vibration to plastic vibration e Is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,
Figure BDA0002787789960000024
is the vibration acceleration of the equivalent system of the rigid structure, +.>
Figure BDA0002787789960000022
The vibration speed of the equivalent system of the rigid structure is that y is the vibration displacement of the equivalent system of the rigid structure, delta P e And (t) is the explosive dynamic load which is born by the rigid structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure BDA0002787789960000023
wherein k is M Is the mass transformation coefficient in the elastic stage, m is the mass per linear meter of the real structure, l is the span length of the real structure, ζ is the damping ratio of the real structure, K is the rigidity of the real structure, and K L As the load transformation coefficient in the elastic stage, the exponential explosion dynamic load is as follows:
Figure BDA0002787789960000031
wherein t is i For the real duration of the blast load, Δp m For peak of explosive load overpressure, k l The load transformation coefficient in the plastic stage is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for the load transformation coefficient d Damping adjustment coefficient gamma, and explosion load peak value as static displacement y corresponding to static load st A ratio parameter K of the mass transformation coefficient and the load transformation coefficient in the elastic stage M-L The calculation formula of each parameter is as follows:
Figure BDA0002787789960000032
it can be known that the initial displacement and the initial velocity are all 0 before the structure bears the explosion load, and after solving the differential equation, the displacement and the velocity expression at this stage can be determined as follows:
Figure BDA0002787789960000033
Figure BDA0002787789960000041
at t T At the moment, the structure starts to change from elastic vibration to plastic vibration, and at the moment, the vibration displacement and the vibration speed corresponding to the structure are
Figure BDA0002787789960000042
Figure BDA0002787789960000051
b. Forced vibration during the plastic phase
Because the structural type of the design is rigid structural anti-explosion design, after structural vibration enters plastic vibration from elastic vibration, explosive load is not unloaded, and the vibration calculation model is provided with explosive load and y at the moment T V T Forced vibration for the plastic phase with damping in the initial condition, i.e. at t T ＜t≤t i In the inner, the dynamic equation of the structural equivalent system is:
Figure BDA0002787789960000052
wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
Figure BDA0002787789960000053
wherein k is m The mass transformation coefficient in the plastic stage is used for obtaining the unloading moment t of the explosion load effect after solving the motion equation i Corresponding displacement y i Velocity v i The following are provided:
Figure BDA0002787789960000061
Figure BDA0002787789960000062
let k M-L Is the ratio of the mass transformation coefficient to the load transformation coefficient in the elastic stage, k m-l The specific formula of the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage is as follows:
Figure BDA0002787789960000063
after substituting the formulas (10), (13) into the formulas (11), (12), t is further obtained i Displacement of time y i Velocity v i The method comprises the following steps:
Figure BDA0002787789960000064
Figure BDA0002787789960000065
wherein the method comprises the steps of
Figure BDA0002787789960000071
k h Elastic plastic for antiknock structureThe sex-stage resistance dynamic coefficient, namely the conversion coefficient when converting the explosive dynamic load into the static load for antiknock design;
c. free vibration in plastic phase
When the structural vibration time is greater than t i When the explosion load is unloaded, the structure is no external load and y is used i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i ＜t≤t m When the structural equivalent system is in use, the power equation is as follows:
Figure BDA0002787789960000072
the displacement and velocity solutions at this stage are found as:
Figure BDA0002787789960000073
Figure BDA0002787789960000074
d. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m At the corresponding time t m At this time velocity v m =0, substituting (19) formula, then:
Figure BDA0002787789960000075
let t m The maximum displacement of the elastoplastic vibration of the antiknock structure obtained by the method (18) is as follows:
Figure BDA0002787789960000081
bringing the formulas (10) and (13) into the formula (21)
Figure BDA0002787789960000082
Definition according to ductility ratio
Figure BDA0002787789960000083
Substituting the expression (22) into the expression (23), and obtaining the expression (10):
Figure BDA0002787789960000084
wherein y is i V i 、y T Expressions (14), (15), and (8) are used, respectively.
Compared with the prior art, the invention has the following technical effects: according to the practical situation, the influence of the type of the structure and the damping of the structure on the dynamic coefficient of the explosion load is fully considered, and an exponential function which describes the explosion load more accurately is adopted, so that the designed building structure is more practical as much as possible, the cost is reduced, and the antiknock requirement is met. The method can realize the accurate design of the actual structure and lay a foundation for antiknock design.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved more clear, the invention is further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The method for designing the dynamic coefficient of the damping rigid structure against the exponential explosion load comprises the following steps: under the action of explosion, the structure completes the elastic maximum vibration displacement y T At the moment t corresponding to the coming plastic vibration T Is less than the real action duration t of the explosion load i After the explosive load is unloaded, the structure continues to vibrate to a certain moment t m Reaches the maximum value y of the total elastoplastic displacement of the structure m ；
According to the action process of explosion on the building structure, dividing the process into three stages of forced vibration in an elastic stage, forced vibration in a plastic stage and free vibration in the plastic stage;
a. forced vibration at elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t T In the internal, the dynamic equation of the structural equivalent system is
Figure BDA0002787789960000091
Wherein t is a time parameter under the explosion action of the rigid structure, and t T M is the critical moment of the rigid structure from elastic vibration to plastic vibration e Is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,
Figure BDA0002787789960000092
is the vibration acceleration of the equivalent system of the rigid structure, +.>
Figure BDA0002787789960000093
The vibration speed of the equivalent system of the rigid structure is that y is the vibration displacement of the equivalent system of the rigid structure, delta P e And (t) is the explosive dynamic load which is born by the rigid structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure BDA0002787789960000094
wherein k is M Is the mass transformation coefficient in the elastic stage, m is the mass per linear meter of the real structure, l is the span length of the real structure, ζ is the damping ratio of the real structure, K is the rigidity of the real structure, and K L As the load transformation coefficient in the elastic stage, the exponential explosion dynamic load is as follows:
Figure BDA0002787789960000101
wherein t is i For the real duration of the blast load, Δp m For peak of explosive load overpressure, k l The load transformation coefficient in the plastic stage is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for the load transformation coefficient d Damping adjustment coefficient gamma, and explosion load peak value as static displacement y corresponding to static load st A ratio parameter K of the mass transformation coefficient and the load transformation coefficient in the elastic stage M-L The calculation formula of each parameter is as follows:
Figure BDA0002787789960000102
it can be known that the initial displacement and the initial velocity are all 0 before the structure bears the explosion load, and after solving the differential equation, the displacement and the velocity expression at this stage can be determined as follows:
Figure BDA0002787789960000103
Figure BDA0002787789960000111
at t T At the moment, the structure starts to change from elastic vibration to plastic vibration, and at the moment, the vibration displacement and the vibration speed corresponding to the structure are
Figure BDA0002787789960000112
Figure BDA0002787789960000121
b. Forced vibration during the plastic phase
Because the structural type of the design is rigid structure antiknock design, after the structural vibration enters plastic vibration from elastic vibration, the explosion load still existsThe vibration calculation model is not unloaded, and the vibration calculation model is provided with explosive load and y T V T Forced vibration for the plastic phase with damping in the initial condition, i.e. at t T ＜t≤t i In the inner, the dynamic equation of the structural equivalent system is:
Figure BDA0002787789960000122
wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
Figure BDA0002787789960000123
wherein k is m The mass transformation coefficient in the plastic stage is used for obtaining the unloading moment t of the explosion load effect after solving the motion equation i Corresponding displacement y i Velocity v i The following are provided:
Figure BDA0002787789960000131
Figure BDA0002787789960000132
let k M-L Is the ratio of the mass transformation coefficient to the load transformation coefficient in the elastic stage, k m-l The specific formula of the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage is as follows:
Figure BDA0002787789960000133
after substituting the formulas (10), (13) into the formulas (11), (12), t is further obtained i Displacement of time y i Velocity v i The method comprises the following steps:
Figure BDA0002787789960000134
Figure BDA0002787789960000135
wherein the method comprises the steps of
Figure BDA0002787789960000141
k h The dynamic coefficient of resistance in the elastoplastic stage of the antiknock structure is the conversion coefficient when converting the explosive dynamic load into the static load for antiknock design;
c. free vibration in plastic phase
When the structural vibration time is greater than t i When the explosion load is unloaded, the structure is no external load and y is used i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i ＜t≤t m When the structural equivalent system is in use, the power equation is as follows:
Figure BDA0002787789960000142
the displacement and velocity solutions at this stage are found as:
Figure BDA0002787789960000143
Figure BDA0002787789960000144
d. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m At the corresponding time t m At this time velocity v m =0, substituting (19) formula, then:
Figure BDA0002787789960000145
let t m The maximum displacement of the elastoplastic vibration of the antiknock structure obtained by the method (18) is as follows:
Figure BDA0002787789960000151
bringing the formulas (10) and (13) into the formula (21)
Figure BDA0002787789960000152
Definition according to ductility ratio
Figure BDA0002787789960000153
/>
Substituting the expression (22) into the expression (23), and obtaining the expression (10):
Figure BDA0002787789960000154
wherein y is i V i 、y T Expressions (14), (15), and (8) are used, respectively.
By the above method, the actual antiknock design of the structure is exemplified as follows.
1. When the protection structure is designed for antiknock, the structure is required to be designed into a rigid structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt of (2) i When the ductility ratio beta is 1.60 and the damping ratio zeta is 1%, the exponential load attenuation coefficient a is 1.27 and k is 1.8 m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower press of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas and are obtained by a rigid structureDefinition of theta T (i.e., ωt) T ) Limiting theta T <θ i (i.e., ωt) T <ωt i ) Then supposing initial value, substituting into formulas (24), (14), (8), (15), and obtaining the resistance dynamic coefficient k by iterative method h 0.692.
2. When the protection structure is designed for antiknock, the structure is required to be designed into a rigid structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt of (2) i When the ductility ratio beta is 1.8 and the damping ratio zeta is 5%, the exponential load attenuation coefficient a is 1.27 and k is 2.0 m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower publishing company of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas, are defined by a rigid structure, and are used for controlling theta T (i.e., ωt) T ) Limiting theta T <θ i (i.e., ωt) T <ωt i ) Then supposing initial value, substituting into formulas (24), (14), (8), (15), and obtaining the resistance dynamic coefficient k by iterative method h 0.611.
3. When the protection structure is designed for antiknock, the structure is required to be designed into a rigid structure, and the self-vibration circular frequency omega and the action duration t of explosion dynamic load of the structure i Product ωt of (2) i When the ductility ratio beta is 2.0 and the damping ratio zeta is 10%, the exponential load attenuation coefficient a is 1.27 and k is 3.0 m-l And k is equal to m-l The values are respectively 0.66 and 0.78 (written by the formula Qin, liu Jinchun of the underground protection structure, published by the Chinese water conservancy and hydropower publishing company of ISBN 9787508470009, 2010), other parameters are respectively calculated by other formulas, are defined by a rigid structure, and are used for controlling theta T (i.e., ωt) T ) Limiting theta T <θ i (i.e., ωt) T <ωt i ) Then supposing initial value, substituting into formulas (24), (14), (8), (15), and obtaining the resistance dynamic coefficient k by iterative method h 0.533.
The foregoing description of the preferred embodiment of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (1)

1. The method for designing the dynamic coefficient of the anti-exponential explosion load of the damping-containing rigid structure is characterized by comprising the following steps of: the rigid structure refers to: under the action of explosion, the structure completes the elastic maximum vibration displacement y T At the moment t corresponding to the coming plastic vibration T Is less than the real action duration t of the explosion load i After the explosive load is unloaded, the structure continues to vibrate to a certain moment t m Reaches the maximum value y of the total elastoplastic displacement of the structure m ；
According to the action process of explosion on the building structure, dividing the process into three stages of forced vibration in an elastic stage, forced vibration in a plastic stage and free vibration in the plastic stage;
a. forced vibration at elastic stage
In the elastic stage and under the load, the duration range of t is more than 0 and less than or equal to t T In the internal, the dynamic equation of the structural equivalent system is
Figure FDA0002787789950000011
Wherein t is a time parameter under the explosion action of the rigid structure, and t T M is the critical moment of the rigid structure from elastic vibration to plastic vibration e Is the equivalent structural mass of the elastic stage, C e Damping for equivalent structure in elastic stage, K e For the equivalent structural rigidity in the elastic phase,
Figure FDA0002787789950000013
is the vibration acceleration of the equivalent system of the rigid structure, +.>
Figure FDA0002787789950000014
The vibration speed of the equivalent system of the rigid structure is that y is the vibration displacement of the equivalent system of the rigid structure, delta P e And (t) is the explosive dynamic load which is born by the rigid structure and changes along with the time t, and the calculation formulas of the equivalent structural coefficients are respectively as follows:
Figure FDA0002787789950000012
wherein k is M Is the mass transformation coefficient in the elastic stage, m is the mass per linear meter of the real structure, l is the span length of the real structure, ζ is the damping ratio of the real structure, K is the rigidity of the real structure, and K L As the load transformation coefficient in the elastic stage, the exponential explosion dynamic load is as follows:
Figure FDA0002787789950000021
wherein t is i For the real duration of the blast load, Δp m For peak of explosive load overpressure, k l The load transformation coefficient in the plastic stage is an exponential load attenuation coefficient, and the damping-free natural vibration frequency omega and the damping-containing natural vibration frequency omega are used for the load transformation coefficient d Damping adjustment coefficient gamma, and explosion load peak value as static displacement y corresponding to static load st A ratio parameter K of the mass transformation coefficient and the load transformation coefficient in the elastic stage M-L The calculation formula of each parameter is as follows:
Figure FDA0002787789950000022
it can be known that the initial displacement and the initial velocity are all 0 before the structure bears the explosion load, and after solving the differential equation, the displacement and the velocity expression at this stage can be determined as follows:
Figure FDA0002787789950000023
Figure FDA0002787789950000031
at t T At the moment, the structure starts from elastic vibrationConverting plastic vibration, wherein the vibration displacement and vibration speed corresponding to the structure are
Figure FDA0002787789950000032
Figure FDA0002787789950000041
b. Forced vibration during the plastic phase
Because the structural type of the design is rigid structural anti-explosion design, after structural vibration enters plastic vibration from elastic vibration, explosive load is not unloaded, and the vibration calculation model is provided with explosive load and y at the moment T V T Forced vibration for the plastic phase with damping in the initial condition, i.e. at t T ＜t≤t i In the inner, the dynamic equation of the structural equivalent system is:
Figure FDA0002787789950000042
wherein m is e Is equivalent structural mass in plastic stage, c e Damping for equivalent structure in plastic phase, q m The maximum resistance in the structural plastic stage is calculated as follows:
Figure FDA0002787789950000043
wherein k is m The mass transformation coefficient in the plastic stage is used for obtaining the unloading moment t of the explosion load effect after solving the motion equation i Corresponding displacement y i Velocity v i The following are provided:
Figure FDA0002787789950000051
Figure FDA0002787789950000052
let k M-L Is the ratio of the mass transformation coefficient to the load transformation coefficient in the elastic stage, k m-l The specific formula of the ratio of the mass transformation coefficient to the load transformation coefficient in the plastic stage is as follows:
Figure FDA0002787789950000053
after substituting the formulas (10), (13) into the formulas (11), (12), t is further obtained i Displacement of time y i Velocity v i The method comprises the following steps:
Figure FDA0002787789950000054
Figure FDA0002787789950000055
wherein the method comprises the steps of
Figure FDA0002787789950000061
k h The dynamic coefficient of resistance in the elastoplastic stage of the antiknock structure is the conversion coefficient when converting the explosive dynamic load into the static load for antiknock design;
c. free vibration in plastic phase
When the structural vibration time is greater than t i When the explosion load is unloaded, the structure is no external load and y is used i V i Free vibration in the plastic phase with damping, i.e. when t, for initial conditions i ＜t≤t m When the structural equivalent system is in use, the power equation is as follows:
Figure FDA0002787789950000062
the displacement and velocity solutions at this stage are found as:
Figure FDA0002787789950000063
Figure FDA0002787789950000064
d. ductility ratio based on dynamic coefficient in elastoplastic stage
When the structure vibrates to the maximum displacement y m At the corresponding time t m At this time velocity v m =0, substituting (19) formula, then:
Figure FDA0002787789950000065
let t m The maximum displacement of the elastoplastic vibration of the antiknock structure obtained by the method (18) is as follows:
Figure FDA0002787789950000071
bringing the formulas (10) and (13) into the formula (21)
Figure FDA0002787789950000072
Definition according to ductility ratio
Figure FDA0002787789950000073
Substituting the expression (22) into the expression (23), and obtaining the expression (10):
Figure FDA0002787789950000074
wherein y is i V i 、y T Expressions (14), (15), and (8) are used, respectively.
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CN108416092A (en) * 2018-01-30 2018-08-17 中国人民解放军陆军工程大学 Wave-forming reinforcement RC beam explosion effect equivalent static load determination method
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CN111753472A (en) * 2020-06-16 2020-10-09 中国人民解放军海军工程大学 Ship motion response prediction method under underwater explosion effect considering damping effect

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