本文選題：地震響應(yīng)　切入點(diǎn)：波動方法　出處：《大連理工大學(xué)》2013年博士論文

【摘要】：結(jié)構(gòu)振動的本質(zhì)是波在結(jié)構(gòu)中不斷傳播與反射,結(jié)構(gòu)振動是結(jié)構(gòu)中波動傳播的外在表現(xiàn)形式,地震響應(yīng)是結(jié)構(gòu)中地震波傳播所導(dǎo)致的結(jié)果。通過對結(jié)構(gòu)中地震波傳播與反射過程的研究,不但可以為結(jié)構(gòu)地震響應(yīng)提供波動求解方法,而且更有利于明確結(jié)構(gòu)內(nèi)部各處地震響應(yīng)細(xì)節(jié)。結(jié)構(gòu)在地震(特別是富含高頻分量的近斷層地震)作用下的瞬態(tài)反應(yīng)問題,從波動角度出發(fā)給予求解會更為合理。另外,波傳播理論能很好地解釋建筑結(jié)構(gòu)中存在的波動傳播的時滯現(xiàn)象。因此,波動方法是研究結(jié)構(gòu)地震響應(yīng)的有效途徑。 本文針對結(jié)構(gòu)地震響應(yīng)問題,考慮了結(jié)構(gòu)或構(gòu)件的彎曲變形、剪切變形和軸向變形,分別提出高聳高層結(jié)構(gòu)、二維框架結(jié)構(gòu)以及三維框架結(jié)構(gòu)地震響應(yīng)波動分析的被研究塊體方法,通過模擬結(jié)構(gòu)中地震波傳播過程來研究結(jié)構(gòu)地震響應(yīng)。該方法主要思想是在結(jié)構(gòu)中建立被研究塊體,然后求解每個被研究塊體的動力平衡方程,得到結(jié)構(gòu)的波動響應(yīng)。該方法直接將地震加速度記錄積分得到的位移時程施加到支座上,即可實(shí)現(xiàn)時間域內(nèi)的遞推計(jì)算,不需要求解結(jié)構(gòu)動力學(xué)方程組,具有物理意義清晰,方法簡單的特點(diǎn)。對于二維和三維框架結(jié)構(gòu)的地震響應(yīng)問題,該方法在各支座處可以自然地引入行波激勵,不需要求解經(jīng)典的多點(diǎn)激勵動力學(xué)方程組。本文主要研究工作如下： (1)提出高聳、高層結(jié)構(gòu)地震響應(yīng)波動分析的被研究塊體方法。針對彎剪型串聯(lián)多自由度體系力學(xué)模型的高聳、高層結(jié)構(gòu),介紹了被研究塊體的概念；由空間離散段的端部力與端部位移之間關(guān)系式,推導(dǎo)給出離散段的段中內(nèi)力(軸力、剪力和彎矩)計(jì)算公式；考慮被研究塊體質(zhì)心與離散節(jié)點(diǎn)之間的縱向偏心,建立被研究塊體的動力平衡方程。給出算法的穩(wěn)定性條件；給出算法的實(shí)現(xiàn)過程,即在時間域上交替運(yùn)用段中內(nèi)力計(jì)算公式、被研究塊體的動力平衡方程以及被研究塊體質(zhì)心與離散節(jié)點(diǎn)加速度之間關(guān)系式進(jìn)行遞推計(jì)算。 通過彎曲波波速模擬、兩端自由梁中彎曲波傳播和自由端受靜載作用下的懸臂梁內(nèi)力分析,驗(yàn)證所提出被研究塊體方法的正確性。通過圓環(huán)型變截面梁動力響應(yīng)分析和等截面理想煙囪結(jié)構(gòu)地震響應(yīng)分析,驗(yàn)證被研究塊體方法中考慮縱向偏心的正確性。由于考慮縱向偏心的影響,使得該方法具有補(bǔ)償功能,即使空間離散段截面不同或離散網(wǎng)格不均勻也能得到精確的計(jì)算結(jié)果。 對南京電視塔地震響應(yīng)研究發(fā)現(xiàn)：在鋼桅桿的危險截面處,考慮縱向偏心影響的應(yīng)力值比常規(guī)有限元方法計(jì)算的應(yīng)力值要大。按常規(guī)方法計(jì)算結(jié)果進(jìn)行設(shè)計(jì)時,電視塔的鋼桅桿可能會偏于危險,因此,高聳結(jié)構(gòu)地震響應(yīng)分析應(yīng)考慮縱向偏心的影響。對24層框架結(jié)構(gòu)地震響應(yīng)研究表明：被研究塊體方法可以為高層結(jié)構(gòu)的彈塑性地震響應(yīng)提供一種有效的波動分析方法。 針對彎剪型串聯(lián)多自由度體系的力學(xué)模型,利用被研究塊體方法的控制方程,給出考慮縱向偏心項(xiàng)的矩陣形式結(jié)構(gòu)動力學(xué)方程。該方程修正了傳統(tǒng)彎剪型串聯(lián)多自由度體系結(jié)構(gòu)動力學(xué)方程中的質(zhì)量陣和剛度陣。 (2)提出二維框架結(jié)構(gòu)地震響應(yīng)波動分析的被研究塊體方法。將二維結(jié)構(gòu)的梁或柱離散成空間段,取與節(jié)點(diǎn)相關(guān)聯(lián)各空間離散段的一半及樓板構(gòu)成被研究塊體；推導(dǎo)給出二維局部坐標(biāo)系中,空間離散段的段中內(nèi)力計(jì)算公式；針對被研究塊體質(zhì)心建立了動力平衡方程；給出被研究塊體方法的實(shí)現(xiàn)過程,即在時間域上交替運(yùn)用段中內(nèi)力計(jì)算公式、被研究塊體動力平衡方程,并利用二維局部坐標(biāo)與總體坐標(biāo)之間位移關(guān)系式、被研究塊體質(zhì)心與節(jié)點(diǎn)加速度之間關(guān)系式進(jìn)行遞推計(jì)算。 針對三跨六層鋼筋混凝土框架結(jié)構(gòu),在一致激勵和行波激勵作用下,將被研究塊體方法的計(jì)算結(jié)果分別與基于多點(diǎn)激勵動力學(xué)方程的有限元法計(jì)算結(jié)果和MIDAS軟件的計(jì)算結(jié)果進(jìn)行對比,驗(yàn)證了被研究塊體方法的正確性。 通過對不同場地地震波作用下的四個二維框架結(jié)構(gòu)(三跨六層鋼筋混凝土框架結(jié)構(gòu)、三跨三層、三跨六層現(xiàn)澆樓板鋼筋混凝土框架結(jié)構(gòu)和二跨十層鋼-混凝土組合框架結(jié)構(gòu))的行波效應(yīng)進(jìn)行研究,結(jié)果表明：即使對于短跨結(jié)構(gòu),也不應(yīng)一概忽略地震波的行波效應(yīng)。行波效應(yīng)可導(dǎo)致框架結(jié)構(gòu)柱剪力和梁端彎矩出現(xiàn)增大現(xiàn)象,其中迎波方向的底層柱子剪力和一層梁端彎矩增加更為明顯；底層柱子變形不一致,且結(jié)構(gòu)的橫向變形增大。 (3)提出三維框架結(jié)構(gòu)地震響應(yīng)波動分析的被研究塊體方法。在三維結(jié)構(gòu)中取與節(jié)點(diǎn)相關(guān)聯(lián)各空間離散段的一半構(gòu)成被研究塊體；推導(dǎo)給出三維局部坐標(biāo)系中離散段的段中內(nèi)力計(jì)算公式；給出三維局部坐標(biāo)系與總體坐標(biāo)系之間的坐標(biāo)轉(zhuǎn)換矩陣；建立了被研究塊體的動力平衡方程；給出被研究塊體方法的實(shí)現(xiàn)過程,即在時間域上交替運(yùn)用段中內(nèi)力計(jì)算公式、被研究塊體動力平衡方程,并利用三維局部坐標(biāo)與總體坐標(biāo)之間關(guān)系式進(jìn)行遞推計(jì)算。 研究了六層三維鋼框架結(jié)構(gòu)的行波效應(yīng),結(jié)果表明：考慮行波效應(yīng)時,框架結(jié)構(gòu)柱剪力和梁端彎矩存在明顯增大現(xiàn)象。研究結(jié)果進(jìn)一步表明：不應(yīng)一概忽略短跨結(jié)構(gòu)的行波效應(yīng)。
[Abstract]:The essence of vibration wave in the structure is in continuous transmission and reflection, is the external manifestation of structural vibration propagation in structures, the seismic response is caused by seismic wave propagation in structures. Through research on seismic wave propagation and reflection process structure, can not only provide for the wave method for seismic response of structures, and more details to the seismic response everywhere within the clear structures. Structures in the earthquake (especially rich in high frequency components of the seismic response under the action of transient), starting from the wave angle give the solution will be more reasonable. In addition, the wave propagation theory can well explain the phenomenon of wave propagation delays exist in the building structure. Therefore, the fluctuation method is an effective way to study seismic response of the structure.
According to the seismic response of structures, considering the bending deformation of the structure or component, shearing deformation and axial deformation were put forward, towering high-rise structure, two-dimensional frame structure and frame structure seismic response analysis of 3D wave of the block method, through the simulation of seismic wave propagation in structure to study the earthquake response of the structure. The main idea of this method is the study of block based on the structure, the dynamic equilibrium equations for each block is then obtained, the structural response fluctuation. This method directly to the seismic records of a time history integral is applied to the bearing, can realize the recursive calculation in time domain, do not need to solve the structural dynamic equations has a clear physical meaning and characteristics of simple method for 2D and 3D seismic response of frame, the method can naturally lead in each support The traveling wave excitation, does not need to solve the classical multi excitation dynamics equations. The main research work are as follows:
(1) proposed by high volatility analysis studies the block method of seismic response of high-rise structure. Aiming at the high shear bending type series system of multi degree of freedom mechanical model of high-rise structure, introduces the concept of block; from the relationship between the spatial discretization section of the end force and tip displacement, internal forces are derived in the discrete segment (axial force, shear force and bending moment) formula; longitudinal study by the eccentricity between the heart and the physical block discrete nodes into consideration, establish the dynamic equilibrium equation of block. The stability conditions are given; the algorithm realization process, namely in the time domain using the section internal force calculation in turn the formula, the dynamic equilibrium equation of block and study the relationship between the heart and the physical block discrete nodes are recursive acceleration calculation.
The bending wave simulation, free ends Liang Zhongwan Qu Bo spread and the free end of the cantilever beam under the action of static load, verify correctness of the study by block method. The ring type variable response analysis and uniform ideal chimney structure seismic dynamic response of the beam cross section, the authentication is considered in the method of blocks the correctness of the longitudinal eccentric. Because of considering the influence of the longitudinal eccentric, makes the method with compensation function, even if the space of discrete sections or different discrete nonuniform meshes can get accurate calculation results.
Study of seismic response of Nanjing TV Tower: the dangerous section steel mast, considering the longitudinal stress value calculation of eccentric effect than the conventional finite element method, the stress value should be large. According to conventional methods of calculation results of the design, the TV tower steel mast may tend to risk, therefore, the seismic response of high-rise structure the analysis should consider the effect of longitudinal eccentric. In response to the research shows that the 24 layer frame structure seismic: Study on block method can provide an effective response analysis method of the fluctuation of high-rise structure elastic-plastic earthquake.
According to the mechanics model of bending shear type series multi degree of freedom system, the control equation is of block method, are given in matrix form structure equations. The equations of longitudinal eccentric modified bending shear type tandem mass matrix dynamics of MDOF system equation and the stiffness matrix.
(2) proposed by fluctuation analysis study on block method of seismic response of frame structure. The two-dimensional Liang Huozhu discrete two-dimensional structure into space segment, by the study on block form taking is associated with a node the space of discrete segments and half floors; deduced two-dimensional local coordinate system, the calculation formula of internal force of discrete segment in space according to the study by heart block; constitution established the dynamic equilibrium equation is given; the realization process of block method, namely in the time domain using the section internal force calculation formula in turn, by research the block dynamic equilibrium equation, and the displacement relation between two-dimensional local coordinate and global style, is the relationship between the physical heart block with the acceleration of the node type recursive calculation.
For the three span six storey reinforced concrete frame structure under uniform excitation and traveling wave excitation, the calculation will be on the block method were compared with the finite element method multi excitation dynamics equation is calculated based on the comparison of the calculated results and the results of MIDAS software, to verify the correctness of the block method.
The four dimensional structure of the earthquake wave under different site (three span six storey reinforced concrete frame structure, three span three storey, three span six storey slab reinforced concrete frame and two span ten storey steel-concrete composite frame structure) were studied, the results show that the traveling wave effect even for short the cross structure, also should not ignore the traveling wave effect of earthquake wave. The traveling wave effect can lead to bending shear frame structure column and beam end become larger, the bottom column shear wave direction of attack and a layer of beam moment was increased; the bottom pillar deformation is not consistent, and the lateral deformation of the structure increases.
(3) proposed by fluctuation analysis study on block method of three-dimensional frame structure seismic response. Associated with each node takes half space discrete segments in the three-dimensional structure of the composition block; force formula is derived for 3D discrete segments in the local coordinate system in three dimensions is given; coordinate between local coordinate system and the general coordinate transformation matrix; dynamic equilibrium equation was established on the block; the implementation process was given on the block method, namely in the time domain using the section internal force calculation formula in turn, by research the block dynamic equilibrium equation, and recursive calculation using the relationship between the local three-dimensional coordinate and global type.
Study on the effect of traveling wave, the six layer of 3D steel frame structure. The results showed that: considering the traveling wave effect, bending shear frame structure column and beam are significantly increased. The results further showed that: should not ignore the effect of traveling wave short span structure.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2013
【分類號】：TU311.3

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本文編號：1727526