一种求解地下结构顶板频率和振型的方法

采用欧拉梁横向自由振动理论,发展了一种求解浅埋地下结构顶板频率和振型的方法。鉴于地下结构顶板频率求解问题的复杂性,首先将该问题假定为平面应变问题求解,推导出浅埋地下结构项板梁的自由振动方程;然后根据顶板梁的边界条件,得到了顶板梁的频率方程,从而得出了顶板梁的频率和振型;进一步得出了墙体转动刚度对顶板频率影响的规律,即转动刚度对顶板低频影响较小,对高频影响较大。还综合考虑土体刚度随埋深的变化和由于土体成拱引起的土体附加质量的变化,研究了结构顶板频率随埋深的变化。这些结果可以为地下结构的动力计算提供参考。     

长型大截面地下结构的横向自由振动方程

文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。     

简谐横荷载作用下Winkler地基上有限长梁1/3次亚谐共振分析

基于Winkler地基模型及Euler - Bernoulli梁理论,建立了Winkler地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,得到离散的非线性振动方程,利用多尺度法求得该系统1/3次亚谐共振的一阶近似解.分析了长细比、弹性模量、地基刚度、阻尼、密度等参数对其亚谐共振幅频响...     

正交加肋地基板在谐荷载作用下的动力响应

将加肋地基板作为板-梁耦合系统，考虑弹性地基模型，建立土—基础耦合系统的运动微分方程，通过富氏积分变换及其逆变换，演绎出双向正交加肋钢筋混凝土地基板在设备谐激力作用下的振动响应的半解析解法。结果说明，在土建设计中，为了减少振动对环境的有害影响，应考虑动力设备基础的隔振和减振问题。数值算例也表明，本方法有较好的计算精度。     

复合材料梁、板振动特性的分析与实验研究

本文对纤维增强层合板振动问题的近似解法作了探讨。文中采用三次B样条函数与梁函数之积的级数怍为试函数,或用梁函数之积的级数作试函数,用Ritz法解这类板的固有振动问题并与三维有限元计算结果及实验结果作了比较。通过不同宽长比、不同纤维方向、不同边界条件的复合材料梁、板的共振实验,以及梁理论、板理论的计算,可以看出:纤维增强梁的自振特性随宽长比的增大由简单变得复杂;梁理论的适用界限与纤维铺设方式及界条件有关。文中给出了初步结果。     

基于功率流法梯式轨枕轨道减振性能研究

为研究梯式轨枕轨道的减振性能,将梯式轨枕轨道系统简化为四端网络。利用功率流法,分析纵向轨枕截面宽、高以及枕下弹性垫板动刚度、材料损耗因子对梯式轨枕轨道系统减振性能的影响。分析表明:枕下弹性垫板动刚度增大,使得传递到整体道床的总功率流增大,同时纵向轨枕的自振频率也增大;枕下弹性垫板材料损耗因子、纵向轨枕横截面宽、高的增大,都能使传递到整体道床的总功率流减少,同时纵向轨枕截面宽、高的增大降低了纵向轨枕自振频率。因此,应尽量增大纵向轨枕截面面积和枕下弹性垫板材料损耗因子以及减小枕下弹性垫板动刚度,从而获得更好的减振效果。     

立式储罐与地基相互作用动力特性分析

立式储罐结构在工程实际中得到广泛的应用。本文以某大型立式储罐结构为例,考虑到液体、结构、地基的相互作用与影响,同时考虑地基与结构及液体与结构的耦合问题,采用有限元方法对浮放在地基上的储罐结构进行了自振特性计算。分别计算了满罐和空罐时系统的频率以及所对应的振型图,并研究了储罐的材料参数和地基刚度对动力特性的影响。结果表明:材料参数的影响较小,地基刚度的影响较大,对盛满液体与空罐的影响不同。     

考虑桩-弹性地基相互作用的单桩风机自振频率

考虑桩-弹性地基相互作用,采用集中质量法和柔度法对泥面线以上的单桩风机结构进行多自由度动力分析,确定单桩风机的自振频率。通过算例给出单桩风机的自振频率值,并与不考虑桩-弹性地基相互作用的单桩风机的自振频率值进行比较。     

结构-地基体系水平与扭转位移耦合效应研究

采用动力理论对地基-结构非线性相互作用体系的振动方程进行了定性分析.基于多线性随动强化模型,采用非线性有限元法求解了基础和地基土之间的水平刚度与摇摆刚度,建立了结构-地基非线性相互作用体系的力学模型.利用拉格朗日能量法推导了结构水平位移和扭转相耦合的振动方程.采用多尺度法研究了结构-地基相互作用体系的主共振.通过分析不...     

简谐横向荷载作用下弹性地基上不可伸长梁的1/2次亚谐共振响应分析

基于已建立的弹性地基上不可伸长梁的非线性动力学模型,本文针对简谐横向荷载作用下梁的1/2次亚谐共振响应进行研究。利用弹性地基梁的非线性运动方程和多尺度方法,求得梁1/2次亚谐共振响应的二次近似解。进而,运用幅频响应曲线对梁的亚谐共振响应进行研究,并分析了边界条件、地基模型、Winkler参数等对梁非线性共振响应的影响。结果表明:三参数地基模型中弹性层的引入对其支承梁的亚谐共振响应影响显著;临界激励幅值决定了弹性地基梁1/2次亚谐共振响应非平凡解的存在性;梁端约束条件在一定程上改变了Winkler参数对梁非线性动力响应的作用效应。     

Hydroelastic vibration and buckling of rectangular Mindlin plates on Pasternak foundations under linearly varying in-plane loads

Hydroelastic vibration and buckling analysis of horizontal rectangular plates resting on Pasternak foundation and subjected to linearly varying in-plane loads is investigated for different boundary conditions. Fluid is assumed to be inviscid and incompressible. To analyze the interaction of the Mindlin plate with the elastic foundation and fluid system, three displacement components of the plate are expressed in the Ritz method by adopting a set of static Timoshenko beam functions satisfying geometric boundary conditions. Convergence study is first carried out to confirm the stability of the present method. Then, a few comparisons are made for limited cases between present results and the available data in the literature. Finally, parametric study is conducted to highlight the effects of loading factors, fluid levels, foundation stiffness parameters, aspect ratios, thickness to width ratios and different boundary conditions on the critical buckling loads and wet natural frequencies of rectangular plates.     

Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the effects of the Winkler coefficient, Pasternak coefficient and damping coefficient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary differential equations with variable coefficients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verified through two numerical examples. The influences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with different taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.     

Winkler地基梁在温度场中受简谐激励3次超谐共振分析

本文研究W inkler地基梁在温度场中受简谐激励作用的3次超谐共振问题,应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程,根据非线性振动的多尺度法求得系统满足3次超谐共振情况的一次近似解,分析了温度、阻尼、激励幅值、地基刚度等参数对系统的影响。     

Vibrations of timoshenko beam-columns on two-parameter elastic foundations

A finite element procedure is developed for analysing the flexural vibrations of a uniform Timoshenko beam-column on a two-parameter elastic foundation. The beam-column is discretized into a number of simple elements with four degrees of freedom each. The governing matrix equation for small-amplitude, free vibrations of the beam-column on the elastic foundation is derived from Hamilton's principle. Several numerical examples are provided to show the effects of axial force, foundation stiffness parameters, partial elastic foundation, shear deformation and rotatory inertia on the natural frequencies of the beam-column.     

Winkler地基上有限长梁联合共振分析

为进一步完善弹性地基上梁的非线性振动理论以及满足实际工程的需要,本文对三种联合共振情况进行了研究。文中基于已建立的Winkler地基上有限长梁的非线性振动方程,运用Galerkin离散法以及多尺度法推导其稳态运动方程组,分析了主/次联合共振时,结构参数及初始条件对系统幅频响应曲线、调谐-相位曲线的影响,初步探讨了主/超联合共振、次/超联合共振的基本性质。研究结果表明:当且仅当两个激励频率是可公度关系时,联合共振才存在稳态响应;对于一个给定的调谐参数,系统最多存在七个解,而解的最终形式是由初始条件决定;系统参数及初始条件的微小变动,可能会激烈地改变系统的响应;工程中为了较好地抑制结构的振动,必须选择合适的方法提高系统的刚度。     

Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations

Elastic parameters such as Young's modulus, Poisson's ratio, and density are very important characteristic parameters that are required to properly characterise shale gas reservoir rock brittleness, evaluate gas characteristics of reservoirs, and directly interpret lithology and oil‐bearing properties. Therefore, it is significant to obtain accurate information of these elastic parameters. Conventionally, they are indirectly calculated by the rock physics method or estimated by approximate formula inversion. The cumulative errors caused by the indirect calculation and low calculation accuracy of the approximate Zoeppritz equations make accurate estimation of Young's modulus, Poisson's ratio, and density difficult in the conventional method. In this paper, based on the assumption of isotropy, we perform several substitutions to convert the Zoeppritz equations from the classical form to a new form containing the chosen elastic constants of Young's modulus, Poisson's ratio, and density. The inversion objective function is then constructed by utilising Bayesian theory. Meanwhile, the Cauchy distribution is introduced as a priori information. We then combine the idea of generalised linear inversion with an iterative reweighed least squares algorithm in order to solve the problem. Finally, we obtain the iterative updating formula of the three elastic parameters and achieve the direct inversion of these elastic parameters based on the exact Zoeppritz equations. Both synthetic and field data examples show that the new method is not only able to obtain the two elastic parameters of Young's modulus and Poisson's ratio stably and reasonably from prestack seismic data but also able to provide an accurate estimation of density information, which demonstrates the feasibility and effectiveness of the proposed method. The proposed method offers an efficient seismic method to identify a “sweet spot” within a shale gas reservoir.     

Winkler地基梁在温度场中受简谐激励的1/3次亚谐共振分析

研究W inkler地基梁在温度场中受简谐激励作用的1/3次亚谐共振问题。应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程,根据非线性振动的多尺度法求得系统满足1/3次亚谐共振情况的一次近似解,并对其进行数值计算,分析了温度、调谐值、激励、阻尼、地基刚度等参数对系统的影响。     

Transient flexural vibrations of a timoshenko column supported by an elastic half-space

Transient flexural vibrations of an elastic column supported by an elastic half-space are investigated analytically under the condition that an arbitrarily shaped free-field lateral acceleration is given as an input. Applying the Timoshenko theory to the column and making use of Laplace transformations with respect to time and numerical inverse Laplace transformations, the time histories of the column free end acceleration are presented. Numerical results obtained from the Timoshenko theory are compared with those of a previous paper¹ (applying the Bernoulli-Euler theory to the column), and the effects of column slenderness and foundation stiffness on the transient flexural vibrations of the column are clarified.     

Winkler地基梁在温度场中受简谐激励的主共振分析

研究W inkler地基梁在温度场中受简谐激励作用的主共振问题。应用弹性理论和Galerk in方法建立W inkler地基梁在温度场中受简谐激励作用的非线性动力方程。应用非线性振动的多尺度法,求得系统主共振的近似解。分析不同参数对主共振响应曲线的影响。