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1.
Curved beam finite elements are presented for out of plane coupled bending and torsional vibration. The element formulation is based upon the exact differential equations of an infinitesimal element in static equilibrium. The effects of shear deformation and rotary inertia are allowed for in the analysis. The element stiffness and mass matrices can be easily restricted to those of a ‘thin’ beam without the secondary effects. Frequencies obtained using either formulation are shown to converge onto exact values using ‘thick’ or ‘thin’ beam theories. 相似文献
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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. 相似文献
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The finite strip method is extended to the free vibration of rectangular plates continuous in one or two directions. A subroutine has been written for the computation of beam functions for continuous beams over any number of intermediate rigid supports and with simply supported or clamped end conditions. The standard finite strip method can thus be applied to plates continuous in both directions using the computed beam functions. The frequencies of 2 × 2 and 3 × 3 continuous panels with many different end conditions have been computed. The computations are also checked against published solutions and the accuracy is shown to be excellent. 相似文献
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Summary An attempt is made to study the dynamic response of a thick, homogeneous isotropic elastic sphere under the action of uniformly distributed internal and external pressure distributions which vary sinusoidally with time. An exact solution of the problem is obtained with the aid of the Laplace transform method and the theory of residues. Some main properties of the radial vibration field are examined. The frequency equation for the free vibration is derived explicitly. Several limiting cases of interest are recovered. 相似文献
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车辆-轨道系统振动响应分析--Timoshenko梁与Euler梁轨道模型的比较 总被引：1，自引：0，他引：1
近年来，铁路的高速化、高运量化以及轻微的地震灾害等因素加速了轨道结构的沉降或变形，导致车辆轨道系统振动的加剧。本文运用车辆-轨道耦合动力学理论，编制了基于Timoehenko梁钢轨模型的车辆-轨道耦合振动仿真分析软件，分析了车辆-轨道系统的垂向振动特性，并与基于Euler梁模型的VICT软件的仿真结果进行了比较分析。结果表明：仿真结果与VICT的仿真结果基本一致，但在较高频域，前者能更好地反映轮轨系统的高频特性。因而，在研究轮轨高频振动及轮轨噪声时。采用Timoshenko梁钢轨模型更具合理性。 相似文献
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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。 相似文献
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单跨简支梁竖向振动的磁悬浮半主动控制 总被引：1，自引：0，他引：1
由于传统的隔振器需要足够的竖向刚度来支撑上部结构,因而不能隔离竖向振动。为了解决这一问题,本文提出一种新的隔振策略,即磁浮式半主动控制方法,并将这一方法应用于弹性梁弯曲振动的半主动控制。将均质弹性梁简化为一带集中质量的简支梁,导出了控制系统的运动方程,讨论了系统在平衡点的稳定性,应用推广的Runge-Kutta方法,得到了系统在随机地面输入下的加速度响应。结果表明：杆件的初始悬浮位置是磁浮式半主动控制系统的平衡点,且平衡点是L稳定的;磁浮式半主动隔振系统具有类似于软弹簧的性质,与普通的弹性简支梁相比,磁浮式半主动振动控制系统的振动频率较低,加速度响应明显减小,系统具有良好的竖向隔振性能。 相似文献
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动荷载作用下欧拉梁动响应的计算是一个初边值问题,通常很难得到解析解,传统数值方法一般是把空间和时间分别离散进行求解,计算相对复杂,效率也不高.针对分布动荷载作用下欧拉梁的振动偏微分方程,采用传统微分求积法,在空间和时间上同时进行离散;对于所有非0阶的初/边值条件,采用嵌入法在权系数计算中予以考虑.算例的数值结果与精确解的对比证明采用传统微分求积法处理此问题是可行的,而且是高效的.对于实际工程中的其他类似问题,该方法同样适用. 相似文献
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This study endeavors to show the inadequacy of thin beam eigenfunctions commonly used to represent displacement profiles of tall buildings in the finite strip analysis. Particularly, the model fails to reflect the correct building behaviour whenever the storey-shear distortion may be significant. An attempt is made, therefore, to develop a new set of strip shape functions that is free of the above shortcoming. A polynomial series is specially constructed and shown to be effective for all building types. Several tall building examples are tested and the results clearly exhibit the versatility and surprisingly high accuracy of the proposed finite strip model, in both static and free vibration analyses. 相似文献
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In this paper a general dynamic analysis of a foundation beam on Green-Boussinesq soil is performed, taking into account the instabilizing effect of conservative and nonconservative applied axial loads.The beam is reduced to a finite number of rigid bars, linked together by elastic springs; the equations of motion are written by means of the Lagrange equations. The kinetic energy and the total potential energy are calculated first, and emphasis is placed on the strain energy of the Green soil; then the virtual work of the applied follower loads is detected, which allow us to define the generalized forces. The resulting equations of motion lead to an eigenvalue problem with unsymmetric matrix.Initially, the first free vibration frequencies of simply supported beams, clamped beams and free beams are plotted as functions of the two soil parameters. A more complex beam is also examined, in order to show the method potentialities. A stability analysis in the presence of conservative axial loads is then performed, and the influence of the soil on the critical load is discussed, both for simply supported beams and clamped beams. Finally, the instability mechanism of a clamped - clamped beam subjected to a uniformly distributed follower force is shown to be deeply influenced by the presence of the soil. (A number of graphs and examples conclude the paper.) 相似文献
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The problem of free vibration of non-linear structures is considered initially. It is shown that this problem can be represented as a non-linear eigenvalue problem. Variational principles for non-linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non-linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non-linear eigenvalue parameters can be used in modal expansion approximations for the non-linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non-linear circular plate are determined. 相似文献
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Earthquake simulation tests were conducted on a 1 : 15‐scale 25‐story building model to verify the seismic performance of high‐rise reinforced‐concrete flat‐plate core‐wall building structures designed per the recent seismic code KBC 2009 or IBC 2006. The following conclusions can be drawn from the test results: (1) The vertical distribution of acceleration during the table excitations revealed the effect of the higher modes, whereas free vibration after the termination of the table excitations was governed by the first mode. The maximum values of base shear and roof drift during the free vibration are either similar to or larger than the values of the maximum responses during the table excitation. (2) With a maximum roof drift ratio of 0.7% under the maximum considered earthquake in Korea, the lateral stiffness degraded to approximately 50% of the initial stiffness. (3) The crack modes appear to be a combination of flexure and shear in the slab around the peripheral columns and in the coupling beam. Energy dissipation via inelastic deformation was predominant during free vibration after the termination of table excitation rather than during table excitation. Finally, (4) the walls with special boundary elements in the first story did not exhibit any significant inelastic behavior, with a maximum curvature of only 21% of the ultimate curvature, corresponding to an ultimate concrete compressive strain of 0.00638 m/m intended in the displacement‐based design approach. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
In this study,a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom(TDOF) systems.The mathematical models of these systems are governed by second–order nonlinear partial differential equations.Nonlinear differential equations were transferred into a single equation by using some intermediate variables.The single nonlinear differential equations are solved by using the first order of the Hamiltonian approach(HA).Different parameters,which have a significant impact on the response of the systems,are considered and discussed.Some comparisons are presented to verify the results between the Hamiltonian approach and the exact solution.The maximum relative error is less than 2.2124 % for large amplitudes of vibration.It has been established that the first iteration of the Hamiltonian approach achieves very accurate results,does not require any small perturbations,and can be used for a wide range of nonlinear problems. 相似文献
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In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical‐Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical‐Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
16.
Yung-Hsiang Chen 《地震工程与结构动力学》1987,15(3):391-402
The general dynamic-stiffness matrix of a Timoshenko beam for transverse vibrations is presented in this paper. All the effects of rotary inertia of the mass, shear distortion, structural damping, axial force, elastic-spring and dashpot foundation are taken into account in the formulation. As a consequence, the deflection function of the beam vibration is in complex form, and the nature of the beam vibration and the corresponding dynamic stiffnesses of the beam are characterized by general complex wave numbers. The dynamic-stiffness matrix for any special case can be derived easily from the general formula, which may be used directly in standard structural analysis. 相似文献
17.
H. Wada 《地震工程与结构动力学》1986,14(1):121-132
The transient extensional vibrations of a slender and uniform bar, which is clamped at one end and is subjected to an axial force at the other free end, are investigated by applying three methods: the Laplace transform method, the normal mode and Newmark β methods in conjunction with the finite element method (FEM); the errors caused by the spatial discretization of the FEM and the direct integration of the Newmark β method are studied and compared with those of the previous paper where the flexural vibrations of a cantilever beam were considered. The reason why the extensional vibration problem is investigated here is that the condition seems to be severe due to the closeness of adjacent natural frequencies, the larger values of natural frequencies and the smaller number of nodal variables of the FEM in comparison with those of the flexural vibration problem. The numerical results show that the errors in response of the extensional vibration problem are large. However, if one follows the criterion proposed in this paper, accurate response is obtainable by the Newmark β method, which requires less computer time than either of the other methods mentioned above. 相似文献
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根据弹性薄板理论和振动理论,运用边界元法(BEM)分析了薄板弯曲自由振动的频率特性,从薄板自由振动的微分方程式出发,采用动态基本解推导出其相应的边界积分方程式,计算中对边界积分方程进行缩减,应用频率扫描的方法研究薄板的动态特性,准确、有效地得到了其相应的固有频率、给出的数值算例证明了本文的方法简单、可行,且具有良好的解析计算精度。 相似文献
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A simple and effective procedure for conducting the free vibration test on highway bridges is presented. The impulsive force in each direction is generated by a loaded truck that either stops suddenly or falls down from a rigid block. The feasibility of the procedure is demonstrated in identification of the dynamic properties, i.e. the vibration frequencies, mode shapes, and damping ratios, of a three-span box-girder concrete bridge using the Ibrahim Time-Domain (ITD) technique. Up to 14 modes have been identified for the present case. For the purpose of verification, ambient vibration tests were also carried out, with the data processed by the random decrement (Randomdec) technique to yield the free vibration response, followed by the ITD technique. The dynamic properties identified from the two types of test correlate very well with each other, indicating the validity of each procedure described herein. Although many more modes can be identified from the free vibration test because of the higher quality of data produced, the easiness and general applicability of the ambient vibration test can still be appreciated. A comparison of the experimental results with those by the finite element method indicated a lesser degree of correlation, implying that the finite element model adopted in design requires further refinement, say, through a more realistic evaluation of the boundary conditions, geometric and material properties of the bridge. Copyright © 1999 John Wiley & Sons Ltd. 相似文献