CN112634727A - Constitutive model for simulating coupled vibration of arbor and structure - Google Patents

Constitutive model for simulating coupled vibration of arbor and structure Download PDF

Info

Publication number
CN112634727A
CN112634727A CN202011417444.7A CN202011417444A CN112634727A CN 112634727 A CN112634727 A CN 112634727A CN 202011417444 A CN202011417444 A CN 202011417444A CN 112634727 A CN112634727 A CN 112634727A
Authority
CN
China
Prior art keywords
arbor
soil
module
stiffness
damping
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.)
Pending
Application number
CN202011417444.7A
Other languages
Chinese (zh)
Inventor
区彤
汪大洋
谭坚
刘雪兵
林松伟
徐昕
聂竹林
刘淼鑫
张增球
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.)
Guangzhou University
Architectural Design and Research Institute of Guangdong Province
Original Assignee
Guangzhou University
Architectural Design and Research Institute of Guangdong Province
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 Guangzhou University, Architectural Design and Research Institute of Guangdong Province filed Critical Guangzhou University
Priority to CN202011417444.7A priority Critical patent/CN112634727A/en
Publication of CN112634727A publication Critical patent/CN112634727A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
    • G09B23/38—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for botany

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Physics (AREA)
  • Algebra (AREA)
  • Computational Mathematics (AREA)
  • Botany (AREA)
  • Health & Medical Sciences (AREA)
  • Mathematical Optimization (AREA)
  • General Health & Medical Sciences (AREA)
  • Pure & Applied Mathematics (AREA)
  • Business, Economics & Management (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Educational Administration (AREA)
  • Educational Technology (AREA)
  • Theoretical Computer Science (AREA)
  • Buildings Adapted To Withstand Abnormal External Influences (AREA)

Abstract

The invention provides a constitutive model for simulating coupled vibration of trees and structures, which comprises the following components: the system comprises an arbor simplifying module, an arbor motion, position and input earthquake motion relationship simplifying module, an arbor upper structure motion operation module, an arbor displacement coordinate acquisition module, a freedom system simulation module, a dynamic balance simulation module, a freedom system equivalent parameter operation module, a horizontal earthquake influence coefficient correction module and a rigidity simulation operation module between fixed arbors and fixed structures. The spring model system can effectively simulate a system formed by arbors, soil and structures, deal with different input earthquake motions, obtain the rigidity required by the structures and effectively analyze the influence of the arbors on the building structures under different earthquake conditions.

Description

Constitutive model for simulating coupled vibration of arbor and structure
Technical Field
The invention relates to a simplified model for interaction of an arbor and a structure, in particular to a constitutive model for simulating coupled vibration of the arbor and the structure.
Background
At present, the greening area of urban residents is smaller and smaller as buildings are changed from horizontal development to longitudinal development, and the characteristic that the vertical external surface area of a high-rise building is far larger than the plane floor area of the high-rise building is utilized to improve the greening coverage rate to the greatest extent, so that the inevitable trend is formed. And the form is in accordance with the design concept of energy-saving buildings and green buildings in China, thereby being beneficial to reducing the energy consumption of the buildings and being an effective way for increasing the urban greening area.
Although the arbor greening building has a lot of researches on building, energy saving and ecological environment, the progress is still slow in structural design, and the influence degree of the load generated by greening arbors and flowers on the lower structure of the building is not a definite conclusion at present. The influence caused by roof greening is not considered structurally during the design of most of domestic buildings, and the vertical bearing capacity of many buildings is insufficient as a result of the phenomenon, so that a plurality of problems can be encountered in greening in the future.
The arbor is formed by branch, trunk and root portion group, and their wind vibration characteristic is also different under the wind load effect, and the free vibration and the interact of branch, trunk and root all can all produce the influence to the arbor wholly simultaneously. Damping in arbor vibration generally comprises three parts: the resistance of interaction between branches, the swing resistance of leaves under the action of wind, and the resistance of roots embedded in soil. In general, the bigger the leaves are, the greater the wind resistance and resistance, the firmer the roots are embedded in the soil, and the greater the resistance.
The large-scale arbor-structure wind-induced coupled vibration technology is a technology for researching the self-stress state and the extremely complex stress state of the structural part of an arbor under the action of wind load of a building structure, the large-scale arbor is complex in shape and various in category, the crown air permeability is obviously changed along with seasonal variation, the self-stress state and the stress state of the arbor and the structural part under the action of the wind load are extremely complex, and the influence factors are numerous.
The response of the arbor has a great influence with the interaction between the root of the arbor and the soil under the action of wind load, but when the vibration response is analyzed under the action of wind load of the arbor, the root of the arbor is generally regarded as a fixed end, and therefore a relative error and an actual condition in a calculation result are large. The foundation has an effect on the structure motion, but the presence of the structure also has an effect on the stress and strain of the earth and seismic waves of the original unstructured field. These effects are the interaction between the soil and the structure (hereinafter referred to as SSI). Considering the soil-structure dynamic interaction, the three parts are regarded as an organic whole under the condition that the deformation coordination of the foundation soil, the contact part between the foundation and the building is satisfied.
Theoretical analysis of soil-structure interactions: lumped parameter methods, ensemble analysis methods and substructure methods are generally employed. Selecting and adopting a substructure method for analysis: (1) the basic principle is that the upper structure is regarded as a dynamic substructure, the lower soil structure is regarded as a dynamic substructure, and the two substructures are mutually connected by utilizing the deformation coordination condition at the interface of the two substructures. (2) The soil impedance function is defined as harmonic motion which generates unit amplitude in a certain direction of soil, including radiation to far field to generate radiation damping (geometric damping) due to energy dissipation and material damping due to energy dissipation in non-ideal elastic soil body, so that the radiation is in complex form and can be expressed as k ═ k1+ ik2, and k1 is the real part of dynamic impedance, namely a spring; k2 is the imaginary part of the dynamic impedance, i.e. damping. For different types of soil and different properties of soil, the related parameters are changed continuously, and the rigidity and the damping coefficient are changed, so that the impedance function is changed accordingly.
Disclosure of Invention
The invention provides a constitutive model for simulating coupled vibration of a tree and a structure, which is used for effectively simulating a system formed by the tree, soil and the structure, coping with different input seismic motions, obtaining rigidity required by the structure and effectively analyzing the influence of the tree on the building structure under different seismic conditions.
The invention provides a constitutive model for simulating coupled vibration of trees and structures, which comprises the following components:
the arbor simplifying module is used for simplifying actual arbors, soil and structures and providing simplified arbor, soil and structure physical information;
the system comprises an arbor motion, position and input earthquake motion relationship simplification module, a signal input module and a signal output module, wherein the arbor motion, position and input earthquake motion relationship simplification module is used for determining the change relationship between input earthquake motion and arbor motion states and positions;
the upper structure movement operation module of the arbor is used for determining physical parameter information which keeps balance with soil and structures when the top of the arbor is in different movement states and different positions;
the system comprises an arbor displacement coordinate acquisition module, a control module and a control module, wherein the arbor displacement coordinate acquisition module is used for determining the relationship among the mass of a structure, the rigidity of the structure, the damping between soil and the structure and the load borne by the structure when the top point of an arbor is at different positions;
the system comprises a degree of freedom system simulation module, a degree of freedom system simulation module and a control module, wherein the degree of freedom system simulation module is used for determining the corresponding relation among the generalized mass of a structure, the generalized rigidity of the structure, the generalized damping between soil and the structure and the generalized load borne by the structure;
the dynamic balance simulation module is used for determining the balance relation between the damping between soil and a structure and the balance relation between the damping and the rigidity of the structure under different motion states of the arbor;
the system comprises a freedom system equivalent parameter operation module, a control module and a data processing module, wherein the freedom system equivalent parameter operation module is used for acquiring physical information of trees, soil and structures after SSI (structural similarity) effect is introduced;
the horizontal earthquake influence coefficient correction module is used for correcting the change relation between the input earthquake motion and the movement state and position of the arbor after the SSI effect is introduced;
the rigidity simulation operation module between the arbor and the structure fixing is used for acquiring the balance rigidity required to be provided by different positions of the structure when the arbor is in different motion states and positions after the SSI effect is introduced.
Further, the arbor simplification module comprises the following operation processes:
the interaction between the soil and the structure is equivalent to a spring-damping system;
the bottom of the arbor and the soil are equivalently in a hinged structure;
simplifying the arbor into a cantilever bar with a length H, and simplifying the arbor crown into a ball with mass, wherein the arbor mass is equivalent to the mass of a concentrated crown;
a multi-degree-of-freedom system is built by arbor, soil and structure.
Further, the arbor motion, position and input seismic motion relationship simplification module comprises the following operation processes:
determining seismic waves at bedrock
Figure BDA0002820582960000031
Will be provided with
Figure BDA0002820582960000032
Seismic oscillation is used as input;
determining the change relationship between the movement state and the position of the arbor under the input earthquake motion;
determining the rigidity and damping conditions between soil and a structure when the arbor is in different motion states and positions, and obtaining a parameter ku、cu、kθ、cθ、hn、mn、kn、xfθ, where ku、cu、kθ、cθRespectively representing the horizontal stiffness, horizontal damping, rocking stiffness and rocking damping of the horizontal and rocking interaction of the soil and the structure; h isn、mn、knRespectively representing the height, mass and rigidity of the nth layer of the structure; x is the number offAnd theta respectively represent the translation displacement and the swing rotation angle of the arbor.
Further, the operation process of the arbor superstructure motion operation module is as follows:
set up equation
Figure BDA0002820582960000033
In the formula: m, C, K are the mass matrix, stiffness matrix and damping matrix of the superstructure of the multiple degree of freedom system without considering SSI, X, Y,
Figure BDA0002820582960000034
Respectively displacement vector, velocity vector and acceleration vector of upper structure of the multi-freedom system when SSI is not considered, xfAnd theta respectively represent the translation displacement and the swing rotation angle of the foundation.
Further, the arbor displacement coordinate acquiring module operates as follows:
establishing a relation equation of the mass M of the structure, the rigidity C of the structure, the damping K between soil and the structure and the load F borne by the structure
Figure BDA0002820582960000035
The equation is converted into:
Figure BDA0002820582960000036
setting: x is phie1x1t+…+φeixit+…+φemxmt
In the formula: m is the number of selected modes, m is 1,2,3 … …, phieiIs the ith orderElastic matrix vector, xitAnd the displacement coordinates of the structural displacement peak corresponding to the ith order elastic matrix type.
Furthermore, the operation process of the degree of freedom system simulation module is as follows:
combining equations obtained by the arbor upper structure motion operation module and the arbor displacement coordinate acquisition module, and multiplying the combined equations by the equation
Figure BDA0002820582960000037
The equation is obtained as follows:
Figure BDA0002820582960000038
the conversion equation is:
Figure BDA0002820582960000039
setting up
Figure BDA00028205829600000310
The equation can be expressed as:
Figure BDA00028205829600000311
equivalent to m single degree of freedom systems;
in the formula: miTo correspond to the generalized quality of the ith order matrix,
Figure BDA0002820582960000041
Cito correspond to the generalized stiffness of the ith matrix type,
Figure BDA0002820582960000042
Kifor generalized damping corresponding to the ith matrix type,
Figure BDA0002820582960000043
Fifor generalized payload corresponding to the ith matrix type,
Figure BDA0002820582960000044
further, the dynamic balance simulation module operates as follows:
general formula
Figure BDA0002820582960000045
Substituting the equation into an equation obtained by a degree of freedom system simulation module, and finishing to obtain:
Figure BDA0002820582960000046
in the formula
Figure BDA0002820582960000047
The equation is converted into:
Figure BDA0002820582960000048
according to the balance relation of the SSI system force, the power balance equation is obtained as follows:
Figure BDA0002820582960000049
Figure BDA00028205829600000410
in the formula: k is a radical ofu、kθHorizontal stiffness and sway stiffness of soil and structure horizontal interaction and sway interaction, respectively, cu、cθHorizontal damping and swing damping for horizontal interaction and swing interaction of soil and structure, respectively.
Furthermore, the operation process of the equivalent parameter operation module of the degree of freedom system is as follows:
the SSI effect is introduced, the equivalence of a 3DOF-SSI system is obtained, and the following relation is obtained according to the balance condition of force:
ku(1+2i(cu+cg))xf＝kiXi(1+2ici)；
kθ(1+2i(cθ+cg))θ＝kiXiHi(1+2ici)；
substituting the equation obtained by the dynamic balance simulation module into the equation until the equation is as follows:
Figure BDA00028205829600000411
is provided with
Figure BDA00028205829600000412
Wherein k iseq、ωeq、
Figure BDA00028205829600000413
ceqRespectively equivalent rigidity, equivalent frequency, equivalent input seismic oscillation and equivalent damping of an equivalent single-degree-of-freedom system.
Further, the horizontal seismic influence coefficient correction module operates as follows:
and on the basis of the soil equivalent linearization model, performing seismic reaction analysis on the field soil by using the soil equivalent linearization model to obtain the shear modulus and the damping ratio of the field soil, and taking the shear modulus and the damping ratio as the parameters of the soil.
For a rigid foundation structure system, the horizontal seismic influence coefficient is
α(ω,ξ)＝kβ；
For an equivalent SDOF system, the corrected horizontal seismic influence coefficient is
Figure BDA0002820582960000051
Order to
Figure BDA0002820582960000052
Eta is input earthquake motion correction coefficient, wherein the equivalent damping ratio xieqSimplified to:
Figure BDA0002820582960000053
obtaining modified input seismic oscillation;
in the formula, omega is the fundamental frequency of the rigid foundation structure, xi is the structure damping ratio, xigIs the damping ratio of the material of the soil,
Figure BDA0002820582960000054
for the stiffness ratio of the structure to the soil, according to
Figure BDA0002820582960000055
Determination of VsIs the shear wave velocity of the soil and is,
Figure BDA0002820582960000056
the ratio of length to fineness is set as,
Figure BDA0002820582960000057
wherein a represents a characteristic length of the rigid foundation (e.g., the radius of a circular foundation);
Figure BDA0002820582960000058
in terms of the mass ratio,
Figure BDA0002820582960000059
rho is the mass density of the soil; v represents the Poisson's ratio of the soil.
Furthermore, the operation process of the rigidity simulation operation module between the arbor and the fixed structure is as follows:
according to the equivalent parameters obtained by the equivalent parameter operation module of the degree of freedom system, the fitting formula provides an approximate dynamic stiffness calculation formula of a rectangular base as follows:
the horizontal rigidity calculation formula of the surface foundation static rigidity is as follows:
Figure BDA00028205829600000510
the calculation formula of the rocking stiffness of the surface foundation static stiffness is as follows:
Figure BDA00028205829600000511
the horizontal stiffness calculation formula of the surface foundation dynamic stiffness is as follows:
Figure BDA00028205829600000512
the calculation formula of the rocking stiffness of the surface foundation dynamic stiffness is as follows:
Figure BDA00028205829600000513
the horizontal rigidity calculation formula of the static rigidity of the embedded foundation is as follows:
Figure BDA00028205829600000514
the calculation formula of the rocking stiffness of the static stiffness of the embedded foundation is as follows:
Figure BDA00028205829600000515
the horizontal stiffness calculation formula of the dynamic stiffness of the embedded foundation is as follows:
Figure BDA0002820582960000061
the calculation formula of the rocking stiffness of the dynamic stiffness of the embedded foundation is as follows:
Figure BDA0002820582960000062
wherein G is the shear modulus of homogeneous semi-space arbor foundation, i.e. G ═ rho.Vs 2(ii) a B and L are respectively half of the side length of the short side and the long side of the rectangular arbor foundation base; a is0＝ωB/VsAnd omega is angular frequency, taking a first frequency of the upper structure of the arbor; and E is the buried depth of the root of the arbor.
Compared with the prior art, the method has the advantages that the arbor simplifying module is used for simplifying the arbor, the soil and the structure, mechanical changes among the arbor, the soil and the structure under different input earthquake motions are respectively calculated, and the SSI effect is introduced to be equivalent to the real physical condition, so that the change information among the arbor, the soil and the structure under different input earthquake motions is effectively simulated, and the mechanical relation among the arbor, the soil and the structure is conveniently researched.
Drawings
FIG. 1 is a schematic diagram of an equivalent single degree of freedom system in consideration of SSI effect according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an interaction system model of soil and structure according to an embodiment of the present invention;
FIG. 3 is an equivalent diagram of the 3DOF-SSI system according to the embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments.
The embodiment of the invention discloses a constitutive model for simulating coupled vibration of trees and structures, which comprises the following steps:
the arbor simplifying module is used for simplifying actual arbors, soil and structures and providing simplified arbor, soil and structure physical information;
the system comprises an arbor motion, position and input earthquake motion relationship simplification module, a signal input module and a signal output module, wherein the arbor motion, position and input earthquake motion relationship simplification module is used for determining the change relationship between input earthquake motion and arbor motion states and positions;
the upper structure movement operation module of the arbor is used for determining physical parameter information which keeps balance with soil and structures when the top of the arbor is in different movement states and different positions;
the system comprises an arbor displacement coordinate acquisition module, a control module and a control module, wherein the arbor displacement coordinate acquisition module is used for determining the relationship among the mass of a structure, the rigidity of the structure, the damping between soil and the structure and the load borne by the structure when the top point of an arbor is at different positions;
the system comprises a degree of freedom system simulation module, a degree of freedom system simulation module and a control module, wherein the degree of freedom system simulation module is used for determining the corresponding relation among the generalized mass of a structure, the generalized rigidity of the structure, the generalized damping between soil and the structure and the generalized load borne by the structure;
the dynamic balance simulation module is used for determining the balance relation between the damping between soil and a structure and the balance relation between the damping and the rigidity of the structure under different motion states of the arbor;
the system comprises a freedom system equivalent parameter operation module, a control module and a data processing module, wherein the freedom system equivalent parameter operation module is used for acquiring physical information of trees, soil and structures after SSI (structural similarity) effect is introduced;
the horizontal earthquake influence coefficient correction module is used for correcting the change relation between the input earthquake motion and the movement state and position of the arbor after the SSI effect is introduced;
the rigidity simulation operation module between the arbor and the structure fixing is used for acquiring the balance rigidity required to be provided by different positions of the structure when the arbor is in different motion states and positions after the SSI effect is introduced.
The operation process of the spring model system for simulating the coupled vibration of the arbor and the structure provided by the embodiment of the invention is as follows:
the arbor is simplified into a vertical cantilever rod with certain rigidity and homogeneity, the crown is simplified into a sphere with mass at the top of the cantilever rod, and the soil body in the tree pool can be simplified into a spring damping system. For the arbor-tree pool model, the simplified model considering the nodes of the soil mass tree pool is provided as follows:
(1) the interaction between the soil and the structure is equivalent to a spring-damping system; (2) the bottom of the trunk is hinged with the bottom of the tree pool, and the constraint is regarded as the action of a rotating spring; (3) the trunk is simplified into a cantilever rod with a length h, and the crown is simplified into a sphere with mass, wherein the mass of the tree is equivalent to the mass of the concentrated crown.
As shown in fig. 1, the soil has two degrees of freedom, namely horizontal and rotational equivalent, and the SSI effect system is a system with multiple degrees of freedom. The earth has the functions of filtering, energy dissipation and amplification on seismic waves from bedrocks
Figure BDA0002820582960000071
Becomes when passing to the free field ground
Figure BDA0002820582960000072
Meanwhile, interaction exists between the upper layer structure and the lower layer soil, and if only the swinging and horizontal action between the upper layer structure and the lower layer soil is considered, the SSI system can be expressed in a simplified mode by using a model shown in figure 1. At this time, the maximum input at the free field surface
Figure BDA0002820582960000073
Namely input seismic motion. In the figure ku、cu、kθ、cθRespectively representing the horizontal stiffness, horizontal damping, rocking stiffness and rocking damping of the horizontal and rocking interaction of the soil and the structure; h isn、mn、knRespectively representing the height, mass and rigidity of the nth layer of the structure; x is the number offAnd theta respectively represent the translation displacement and the swing rotation angle of the foundation. Equivalent simplification of soil into a multi-degree-of-freedom system, introduction of a structural dynamics method to solve the response of the single-degree-of-freedom system and the multi-degree-of-freedom system, solving by adopting a Newmark-beta method, respectively solving the displacement and the acceleration of each mass point of the superstructure, simplifying the soil into two degrees of freedom of horizontal and rotation for comparison, respectively obtaining the displacement and acceleration results of simplified SSI effect and non-consideration of the SSI effect, simultaneously determining a hysteresis energy consumption curve of the simplified damping, and obtaining the filtering and energy dissipation of the soil in the interaction of the superstructure.
As shown in fig. 2, the equation of motion for the arbor superstructure is:
Figure BDA0002820582960000074
in the formula: m, C, K are the mass matrix, stiffness matrix and damping matrix of the superstructure of the multiple degree of freedom system without considering SSI, X, Y,
Figure BDA0002820582960000075
Respectively displacement vector, velocity vector and acceleration vector of upper structure of the multi-freedom system when SSI is not considered, xfAnd theta respectively represent the translation displacement and the swing rotation angle of the foundation.
Order to
Figure BDA0002820582960000081
Then equation (1) can be expressed as:
Figure BDA0002820582960000082
setting: x is phie1x1t+…+φeixit+…+φemxmt (3)
In the formula: m is the number of selected modes, m is 1,2,3 … …, phieiIs the ith order elastic matrix vector, xitAnd the displacement coordinates of the structural displacement peak corresponding to the ith order elastic matrix type.
Substituting the formula (3) into the formula (4), and multiplying the two sides of the formula simultaneously
Figure BDA0002820582960000083
Figure BDA0002820582960000084
Order:
Figure BDA0002820582960000085
in the formula
Figure BDA0002820582960000086
Then equation (2.7) can be expressed as:
Figure BDA0002820582960000087
in the formula: miTo correspond toThe generalized quality of the ith order matrix type,
Figure BDA0002820582960000088
Cito correspond to the generalized quality of the ith order matrix,
Figure BDA0002820582960000089
Kito correspond to the generalized quality of the ith order matrix,
Figure BDA00028205829600000810
Fifor generalized payload corresponding to the ith matrix type,
Figure BDA00028205829600000811
thus, the superstructure can be equivalent to an m-single degree-of-freedom system by equation (6).
General formula
Figure BDA00028205829600000812
Substituting into (6), finishing to obtain:
Figure BDA00028205829600000813
in the formula
Figure BDA00028205829600000814
Equation (2.10) is based on the complex damping theory, resulting in:
Figure BDA00028205829600000815
according to the balance relation of the SSI system force, the dynamic balance equation is obtained as follows:
Figure BDA00028205829600000816
Figure BDA00028205829600000817
in the formula: k is a radical ofu、kθHorizontal stiffness and sway stiffness of soil and structure horizontal interaction and sway interaction, respectively, cu、cθHorizontal damping and swing damping for horizontal interaction and swing interaction of soil and structure, respectively.
The soil and structure interaction system of the upper structure of the multi-degree-of-freedom system is decomposed into an upper multi-degree-of-freedom system structure and a soil part, and the upper multi-degree-of-freedom system structure and the soil part can be equivalent to a simplified model of an m single-degree-of-freedom SSI system through formulas (8), (9) and (10), and each system has soil which is simplified into two horizontal and rotational degrees of freedom. In the embodiment of the invention, when an SSI system model is simplified, the influence of interaction between soil and a structure is not considered temporarily, an upper structure multi-freedom system is treated as a plurality of single-freedom-degree systems according to a system assumed by a rigid foundation, then the SSI effect is considered, the single-freedom-degree simplified classical model is used, the multi-freedom-degree systems are decomposed, and then the single-freedom-degree systems are equivalent to the single-freedom-degree systems. FIG. 3 shows an equivalent single degree of freedom system model of the soil and structure interaction system.
As shown in fig. 3, the following relationship is obtained according to the equilibrium condition of the forces:
ku(1+2i(cu+cg))xf＝kiXi(1+2ici) (11)
kθ(1+2i(cθ+cg))θ＝kiXiHi(1+2ici) (12)
equations (11) and (12) are substituted into equations (8), (9) and (10), and the damping high-order terms are ignored and are derived as follows:
Figure BDA0002820582960000091
order to
Figure BDA0002820582960000092
Equivalent stiffness, equivalent frequency, equivalent input seismic oscillation and equivalent damping k of equivalent single-degree-of-freedom systemeq、ωeq、
Figure BDA0002820582960000093
ceq。
In the formula: k is a radical ofeqIn order to consider the equivalent stiffness of the SSI effect equivalent single-degree-of-freedom system, the equivalent stiffness is obtained from (14):
Figure BDA0002820582960000094
ωeqin order to consider the equivalent frequency of the SSI effect equivalent single-degree-of-freedom system, the equivalent frequency is obtained from (15):
Figure BDA0002820582960000095
Figure BDA0002820582960000096
in order to consider the equivalent input seismic motion of an SSI effect equivalent single-degree-of-freedom system, the method comprises the following steps (16):
Figure BDA0002820582960000097
ceqin order to consider the equivalent damping of an SSI effect equivalent single-degree-of-freedom system, the damping is obtained by (17):
Figure BDA0002820582960000098
after equivalence, the system input earthquake motion, the damping ratio and the system frequency are changed, and the response spectrum of the equivalent single-degree-of-freedom system is further corrected.
The correction method of the embodiment of the invention is based on a soil equivalent linearization model, and utilizes the soil equivalent linearization model to perform seismic reaction analysis on the field soil to obtain the shear modulus and the damping ratio of the field soil, and uses the shear modulus and the damping ratio as the parameters of the soil.
Horizontal seismic influence coefficient for rigid foundation structure system
α(ω,ξ)＝kβ (18)
Modified horizontal seismic influence coefficient for equivalent SDOF system
Figure BDA0002820582960000101
Order to
Figure BDA0002820582960000102
Eta is seismic motion correction coefficient, wherein the equivalent damping ratio xieqFurther simplified according to equation (19) is:
Figure BDA0002820582960000103
in the formula, omega is the fundamental frequency of the rigid foundation structure, xi is the structure damping ratio, xigIs the damping ratio of the material of the soil,
Figure BDA0002820582960000104
for the stiffness ratio of the structure to the soil, according to
Figure BDA0002820582960000105
Determination of VsIs the shear wave velocity of the soil and is,
Figure BDA0002820582960000106
the ratio of length to fineness is set as,
Figure BDA0002820582960000107
wherein a represents a characteristic length of the rigid foundation (e.g., the radius of a circular foundation);
Figure BDA0002820582960000108
in terms of the mass ratio,
Figure BDA0002820582960000109
rho is the mass density of the soil; v represents the Poisson's ratio of the soil.
An approximate dynamic stiffness calculation formula of a rectangular base is given according to a series of numerical fitting formulas.
(1) Static stiffness of surface foundation
Horizontal rigidity:
Figure BDA00028205829600001010
roll stiffness:
Figure BDA00028205829600001011
(2) dynamic stiffness of surface foundation
Horizontal rigidity:
Figure BDA00028205829600001012
roll stiffness:
Figure BDA0002820582960000111
(3) static stiffness of embedded foundations
Horizontal rigidity:
Figure BDA0002820582960000112
roll stiffness:
Figure BDA0002820582960000113
(1) dynamic stiffness of embedded foundation
Horizontal rigidity:
Figure BDA0002820582960000114
roll stiffness:
Figure BDA0002820582960000115
wherein G is the shear modulus of homogeneous half-space foundation, i.e. G ═ rho.Vs 2The method can also be determined by equivalent linear analysis of the soil body; b and L are respectively half of the length of the short side and the long side of the rectangular base; a is0＝ωB/Vs(ω is the angular frequency, taking the first frequency of the superstructure); e is the buried depth of the foundation.
According to the embodiment of the invention, the arbor simplifying module is used for simplifying the arbor, the soil and the structure, the mechanical change among the arbor, the soil and the structure under different input earthquake motions is respectively calculated, and the SSI effect is introduced to be equivalent to the real physical condition, so that the mechanical change information among the arbor, the soil and the structure under different input earthquake motions is effectively simulated, the mechanical relation among the arbor, the soil and the structure is conveniently researched, and the arbor is prevented from generating negative influence on the stability of the building structure when garden planning is carried out.
Finally, it should be noted that the above-mentioned embodiments are only used for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above-mentioned embodiments, it should be understood by those skilled in the art that the modifications and equivalents of the specific embodiments of the present invention can be made by those skilled in the art after reading the present specification, but these modifications and variations do not depart from the scope of the claims of the present application.

Claims (10)

1. A constitutive model that simulates coupled vibrations of trees and structures, the spring model system comprising:
the arbor simplifying module is used for simplifying actual arbors, soil and structures and providing simplified arbor, soil and structure physical information;
the system comprises an arbor motion, position and input earthquake motion relationship simplification module, a signal input module and a signal output module, wherein the arbor motion, position and input earthquake motion relationship simplification module is used for determining the change relationship between input earthquake motion and arbor motion states and positions;
the upper structure movement operation module of the arbor is used for determining physical parameter information which keeps balance with soil and structures when the top of the arbor is in different movement states and different positions;
the system comprises an arbor displacement coordinate acquisition module, a control module and a control module, wherein the arbor displacement coordinate acquisition module is used for determining the relationship among the mass of a structure, the rigidity of the structure, the damping between soil and the structure and the load borne by the structure when the top point of an arbor is at different positions;
the system comprises a degree of freedom system simulation module, a degree of freedom system simulation module and a control module, wherein the degree of freedom system simulation module is used for determining the corresponding relation among the generalized mass of a structure, the generalized rigidity of the structure, the generalized damping between soil and the structure and the generalized load borne by the structure;
the dynamic balance simulation module is used for determining the balance relation between the damping between soil and a structure and the balance relation between the damping and the rigidity of the structure under different motion states of the arbor;
the system comprises a freedom system equivalent parameter operation module, a control module and a data processing module, wherein the freedom system equivalent parameter operation module is used for acquiring physical information of trees, soil and structures after SSI (structural similarity) effect is introduced;
the horizontal earthquake influence coefficient correction module is used for correcting the change relation between the input earthquake motion and the movement state and position of the arbor after the SSI effect is introduced;
the rigidity simulation operation module between the arbor and the structure fixing is used for acquiring the balance rigidity required to be provided by different positions of the structure when the arbor is in different motion states and positions after the SSI effect is introduced.
2. The spring model system for simulating coupled vibrations of trees and structures according to claim 1, wherein the tree simplification module comprises the following operational procedures:
the interaction between the soil and the structure is equivalent to a spring-damping system;
the bottom of the arbor and the soil are equivalently in a hinged structure;
simplifying the arbor into a cantilever bar with a length H, and simplifying the arbor crown into a ball with mass, wherein the arbor mass is equivalent to the mass of a concentrated crown;
a multi-degree-of-freedom system is built by arbor, soil and structure.
3. A spring model system for simulating coupled vibrations of trees and structures according to claim 2, wherein said tree motion, position and input seismic relationship simplification module comprises the following operational procedures:
determining seismic waves at bedrock
Figure FDA0002820582950000011
Will be provided with
Figure FDA0002820582950000012
Seismic oscillation is used as input;
determining the change relationship between the movement state and the position of the arbor under the input earthquake motion;
determining the rigidity and damping conditions between soil and a structure when the arbor is in different motion states and positions, and obtaining a parameter ku、cu、kθ、cθ、hn、mn、kn、xfθ, where ku、cu、kθ、cθRespectively representing the horizontal stiffness, horizontal damping, rocking stiffness and rocking damping of the horizontal and rocking interaction of the soil and the structure; h isn、mn、knRespectively representing the height, mass and rigidity of the nth layer of the structure; x is the number offAnd theta respectively represent the translation displacement and the swing rotation angle of the arbor.
4. The spring model system for simulating coupled vibration of trees and structures according to claim 3, wherein the operation process of the tree superstructure motion operation module is as follows:
set up equation
Figure FDA0002820582950000021
In the formula: m, C, K are the mass matrix, stiffness matrix and damping matrix of the superstructure of the multiple degree of freedom system without considering SSI, X, Y,
Figure FDA0002820582950000022
Respectively displacement vector, velocity vector and acceleration vector of upper structure of the multi-freedom system when SSI is not considered, xfAnd theta respectively represent the translation displacement and the swing rotation angle of the foundation.
5. The spring model system for simulating coupled vibrations of trees and structures according to claim 4, wherein the tree displacement coordinate acquisition module operates as follows:
establishing a relation equation of the mass M of the structure, the rigidity C of the structure, the damping K between soil and the structure and the load F borne by the structure
Figure FDA0002820582950000023
The equation is converted into:
Figure FDA0002820582950000024
setting: x is phie1x1t+…+φeixit+…+φemxmt
In the formula: m is the number of selected modes, m is 1,2,3 … …, phieiIs the ith order elastic matrix vector, xitAnd the displacement coordinates of the structural displacement peak corresponding to the ith order elastic matrix type.
6. The spring model system for simulating coupled vibrations of trees and structures according to claim 5, wherein the degree of freedom system simulation module operates as follows:
combining equations obtained by the arbor upper structure motion operation module and the arbor displacement coordinate acquisition module, and multiplying the combined equations by the equation
Figure FDA0002820582950000025
The equation is obtained as follows:
Figure FDA0002820582950000026
the conversion equation is:
Figure FDA0002820582950000027
setting up
Figure FDA0002820582950000028
The equation can be expressed as:
Figure FDA0002820582950000029
equivalent to m single degree of freedom systems;
in the formula: miTo correspond to the generalized quality of the ith order matrix,
Figure FDA0002820582950000031
Cito correspond to the generalized stiffness of the ith matrix type,
Figure FDA0002820582950000032
Kifor generalized damping corresponding to the ith matrix type,
Figure FDA0002820582950000033
Fifor generalized payload corresponding to the ith matrix type,
Figure FDA0002820582950000034
7. the spring model system for simulating coupled vibrations of trees and structures according to claim 6, wherein the dynamic balance simulation module operates as follows:
general formula
Figure FDA0002820582950000035
Substituting the equation into an equation obtained by a degree of freedom system simulation module, and finishing to obtain:
Figure FDA0002820582950000036
in the formula
Figure FDA0002820582950000037
The equation is converted into:
Figure FDA0002820582950000038
according to the balance relation of the SSI system force, the power balance equation is obtained as follows:
Figure FDA0002820582950000039
Figure FDA00028205829500000310
in the formula: k is a radical ofu、kθHorizontal stiffness and sway stiffness of soil and structure horizontal interaction and sway interaction, respectively, cu、cθHorizontal damping and swing damping for horizontal interaction and swing interaction of soil and structure, respectively.
8. The spring model system for simulating coupled vibration of trees and structures according to claim 7, wherein the operation process of the degree of freedom system equivalent parameter operation module is as follows:
the SSI effect is introduced, the equivalence of a 3DOF-SSI system is obtained, and the following relation is obtained according to the balance condition of force:
ku(1+2i(cu+cg))xf＝kiXi(1+2ici)；
kθ(1+2i(cθ+cg))θ＝kiXiHi(1+2ici)；
substituting the equation obtained by the dynamic balance simulation module into the equation until the equation is as follows:
Figure FDA00028205829500000311
is provided with
Figure FDA00028205829500000312
Wherein k iseq、ωeq、
Figure FDA00028205829500000313
ceqRespectively equivalent rigidity, equivalent frequency, equivalent input seismic oscillation and equivalent damping of an equivalent single-degree-of-freedom system.
9. The spring model system for simulating coupled vibrations of trees and structures according to claim 8, wherein the horizontal seismic coefficient of influence modification module operates as follows:
and on the basis of the soil equivalent linearization model, performing seismic reaction analysis on the field soil by using the soil equivalent linearization model to obtain the shear modulus and the damping ratio of the field soil, and taking the shear modulus and the damping ratio as the parameters of the soil.
For a rigid foundation structure system, the horizontal seismic influence coefficient is
α(ω,ξ)＝kβ；
For an equivalent SDOF system, the corrected horizontal seismic influence coefficient is
Figure FDA0002820582950000041
Figure FDA0002820582950000042
Order to
Figure FDA0002820582950000043
Eta is input earthquake motion correction coefficient, wherein the equivalent damping ratio xieqSimplified to:
Figure FDA0002820582950000044
obtaining modified input seismic oscillation;
in the formula, omega is the fundamental frequency of the rigid foundation structure, xi is the structure damping ratio, xigIs the damping ratio of the material of the soil,
Figure FDA0002820582950000045
for the stiffness ratio of the structure to the soil, according to
Figure FDA0002820582950000046
Determination of VsIs the shear wave velocity of the soil and is,
Figure FDA0002820582950000047
the ratio of length to fineness is set as,
Figure FDA0002820582950000048
wherein a represents a characteristic length of the rigid foundation (e.g., the radius of a circular foundation);
Figure FDA0002820582950000049
in terms of the mass ratio,
Figure FDA00028205829500000410
rho is the mass density of the soil; v represents the Poisson's ratio of the soil.
10. The spring model system for simulating coupled vibration of trees and structures according to claim 8, wherein the stiffness simulation operation module between the trees and the fixed structures operates as follows:
according to the equivalent parameters obtained by the equivalent parameter operation module of the degree of freedom system, the fitting formula provides an approximate dynamic stiffness calculation formula of a rectangular base as follows:
the horizontal rigidity calculation formula of the surface foundation static rigidity is as follows:
Figure FDA00028205829500000411
the calculation formula of the rocking stiffness of the surface foundation static stiffness is as follows:
Figure FDA00028205829500000412
the horizontal stiffness calculation formula of the surface foundation dynamic stiffness is as follows:
Figure FDA00028205829500000413
the calculation formula of the rocking stiffness of the surface foundation dynamic stiffness is as follows:
Figure FDA00028205829500000414
the horizontal rigidity calculation formula of the static rigidity of the embedded foundation is as follows:
Figure FDA0002820582950000051
the calculation formula of the rocking stiffness of the static stiffness of the embedded foundation is as follows:
Figure FDA0002820582950000052
the horizontal stiffness calculation formula of the dynamic stiffness of the embedded foundation is as follows:
Figure FDA0002820582950000053
the calculation formula of the rocking stiffness of the dynamic stiffness of the embedded foundation is as follows:
Figure FDA0002820582950000054
wherein G is the shear modulus of a homogeneous semi-spatial arbor foundation, i.e.
Figure FDA0002820582950000055
B and L are respectively half of the side length of the short side and the long side of the rectangular arbor foundation base; a is0＝ωB/VsAnd omega is angular frequency, taking a first frequency of the upper structure of the arbor; and E is the buried depth of the root of the arbor.
CN202011417444.7A 2020-12-07 2020-12-07 Constitutive model for simulating coupled vibration of arbor and structure Pending CN112634727A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011417444.7A CN112634727A (en) 2020-12-07 2020-12-07 Constitutive model for simulating coupled vibration of arbor and structure

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011417444.7A CN112634727A (en) 2020-12-07 2020-12-07 Constitutive model for simulating coupled vibration of arbor and structure

Publications (1)

Publication Number Publication Date
CN112634727A true CN112634727A (en) 2021-04-09

Family

ID=75308451

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011417444.7A Pending CN112634727A (en) 2020-12-07 2020-12-07 Constitutive model for simulating coupled vibration of arbor and structure

Country Status (1)

Country Link
CN (1) CN112634727A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113378429A (en) * 2021-05-14 2021-09-10 北京科技大学 Method for determining dynamic characteristics of cantilever structure under elastic half-space

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1755362A (en) * 2004-09-27 2006-04-05 周玉成 Analysis method for determining physical and mechanical properties of wood based on wood structure parameter and instrument therefor
CN104616337A (en) * 2015-02-10 2015-05-13 西安理工大学 Method for simulating swaying of leafless trees in wind based on longitudinal segmentation
CN204728510U (en) * 2015-05-14 2015-10-28 同济大学 A kind of structure for improving the isolated building safety with degree of freedom
CN105184010A (en) * 2015-09-25 2015-12-23 天津城建大学 High-frequency seismic wave scattering simulating method based on fast multipole indirect boundary element method
CN108460212A (en) * 2018-03-02 2018-08-28 北京交通大学 Underground structure earthquake motion three-dimensional numerical simulation method
CN108647366A (en) * 2018-02-05 2018-10-12 清华大学 The non-linear course analysis method of architecture ensemble earthquake response and device
CN109271748A (en) * 2018-11-13 2019-01-25 广东电网有限责任公司 A kind of power transmission tower SSI effect model method for building up, device and storage medium
CN110555190A (en) * 2019-09-05 2019-12-10 广西科技大学 real mode method for dynamic response of non-classical damping system and application thereof
CN111709073A (en) * 2020-06-04 2020-09-25 黄淮学院 Method and system for measuring natural vibration frequency and vibration mode for building structure dynamic analysis

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1755362A (en) * 2004-09-27 2006-04-05 周玉成 Analysis method for determining physical and mechanical properties of wood based on wood structure parameter and instrument therefor
CN104616337A (en) * 2015-02-10 2015-05-13 西安理工大学 Method for simulating swaying of leafless trees in wind based on longitudinal segmentation
CN204728510U (en) * 2015-05-14 2015-10-28 同济大学 A kind of structure for improving the isolated building safety with degree of freedom
CN105184010A (en) * 2015-09-25 2015-12-23 天津城建大学 High-frequency seismic wave scattering simulating method based on fast multipole indirect boundary element method
CN108647366A (en) * 2018-02-05 2018-10-12 清华大学 The non-linear course analysis method of architecture ensemble earthquake response and device
CN108460212A (en) * 2018-03-02 2018-08-28 北京交通大学 Underground structure earthquake motion three-dimensional numerical simulation method
CN109271748A (en) * 2018-11-13 2019-01-25 广东电网有限责任公司 A kind of power transmission tower SSI effect model method for building up, device and storage medium
CN110555190A (en) * 2019-09-05 2019-12-10 广西科技大学 real mode method for dynamic response of non-classical damping system and application thereof
CN111709073A (en) * 2020-06-04 2020-09-25 黄淮学院 Method and system for measuring natural vibration frequency and vibration mode for building structure dynamic analysis

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
王辉: "大型乔木-框架结构风致耦合振动分析", 《中国优秀博硕士学位论文全文数据库(硕士)工程科技Ⅱ辑》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113378429A (en) * 2021-05-14 2021-09-10 北京科技大学 Method for determining dynamic characteristics of cantilever structure under elastic half-space

Similar Documents

Publication Publication Date Title
Banerjee et al. Dynamic analysis of an offshore wind turbine under random wind and wave excitation with soil-structure interaction and blade tower coupling
CN107958113A (en) Pole and tower foundation stability number value analysis method on a kind of unsaturated expansive soil ground
CN112634727A (en) Constitutive model for simulating coupled vibration of arbor and structure
CN115659756A (en) Method for analyzing windproof performance of transmission tower
Zhao et al. Optimal design of viscoelastic dampers in frame structures considering soil-structure interaction effect
CN105069199A (en) Method for determining load deformation of high-rise building due to wind
CN102663246B (en) Consider the analytical approach of SSI general closed planar asymmetric buildings earthquake response
Lu et al. Numerical analysis of tall buildings considering dynamic soil-structure interaction
Nie et al. Application of the Improved Multipopulation Genetic Algorithm in the TMD Controlled System considering Soil-Structure Interaction
CN107092730A (en) Suitable for the three-dimensional infinite element Artificial Boundaries method for building up of Explicit Analysis
Dalili et al. Numerical simulation of soil-structure interaction in framed and shear-wall structures
CN114491748A (en) OC-PSO-based super high-rise building wind resistance design optimization method
Zembaty et al. Estimation of rotational ground motion effects on the Bell Tower of Parma Cathedral
CN116227158B (en) Method for calculating equivalent stiffness of interface of offshore wind power suction pile and jacket
Shah et al. Experimental and computational dynamic response comparison of hybrid and mono windmill towers considering soil–structure interaction
Jayalekshmi et al. Soil-Structure Interaction Analysis of Tall Reinforced Concrete Chimney with Piled Raft and Annular Raft under Along-Wind Load
Wei et al. Multi-objective optimization of parameters and location of passive vibration isolation system excited by clamped thin plate foundation
Belostosky et al. Numerical simulation of loads and impacts, stress-strain state, strength and stability of unique structures, buildings and facilities. Experience of StaDyO research & engineering centre
Abdullah et al. The feasibility study of applying solar tracking in power plant Kuala Perlis, Malaysia
Shah et al. Comparison of Monopole and Hybrid Wind Turbine Tower Response for Seismic Loading Under Operational Conditions
CN113343536B (en) Method and device for establishing coupling model for earthquake-resistant analysis and coupling model
Li et al. Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints
Xue et al. Research status and prospects of cable domes
Piana Vibrations and stability of axially and transversely loaded structures
Kaneda et al. Centrifuge Model Simulation for Seismic Behavior of Grid-Form Deep Mixing Walls Supporting a Building

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
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20210409