共查询到19条相似文献,搜索用时 93 毫秒
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本文以线弹簧模型为基础提出了一种近似分析裂纹梁振动响应的方法。把该方法同Euler-Bernoulli梁理论,模态分析方法以及断裂力学原理等结合起来运用。导出裂纹梁振动的特征方程。 相似文献
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在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去. 相似文献
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Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions北大核心CSCD 下载免费PDF全文
Double-curved-beam (DCB) systems are usually seen in many engineering fields. Compared to straight double-beam systems, DCB systems are more efficient in noise and vibration control problems. To obtain closed-form solutions of steady-state forced vibrations of DCB systems, the classical Euler-Bernoulli curved beam (ECB) model was employed to model vibration equations for the DCB systems. Green’s functions and the Laplace transform methods were used to get the closed-form solutions to the vibration equations for the DCB systems. These solutions apply to arbitrary boundary conditions. Numerical tests were conducted to verify the present solutions with related results from previous literatures. Effects of some important geometric and physical parameters on vibration responses and the interaction between the elastic layer stiffness and the DCB system, were discussed. The results show that, the DCB system will degenerate to a straight double-beam system when the 2 radii approach infinity, moreover, the DCB system can be simplified as one comprising a straight beam and a curved beam. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
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In this paper, free vibration analysis of cracked composite beam subjected to coupled bending–torsion loading is presented. The composite beam is assumed to have an open edge crack of length a. A first order shear deformation theory is applied to count for the effect of shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Governing equations and boundary conditions are derived using Hamilton principle. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in cracked area. After obtaining the governing equations and boundary conditions, generalized differential quadrature (GDQ) method is applied to solve the obtained eigenvalue problem. Finally, some numerical results of beams with various boundary conditions and different fiber orientations are given to show the efficiency of the method. In addition, to study the effect of shear deformations, numerical results of the current model are compared with previously given results in which shear deformations were neglected. 相似文献
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Considering the warping resistance, inertia force and moving three-directional loads, a more comprehensive set of governing equations for vertical, torsional, radial and axial motions of the curved beam are derived. The analytical solutions for vertical, torsional, radial and axial responses of the curved beam subjected to three-directional moving loads are obtained, using the Galerkin method to discretize the partial differential equations and the modal superposition method to decouple the ordinary differential equations. The analytical results are compared with the numerical integration and a published work to verify the validity of the proposed solutions. Effects of Galerkin truncation terms and damping ratio on solution convergence are also discussed. Considering first-mode and higher-mode truncation respectively, the conditions of resonance and cancellation are analyzed for vertical, torsional, radial and axial motions of the curved beam. Taking a curved bridge under passage of a vehicle as an example, the influences of system parameters, such as vehicle speed, braking acceleration, bridge curve radius, bridge span and bridge deck elastic modulus, on bridge midpoint vibration are explored. The proposed approach and results may be beneficial to enhance understanding the three-directional vehicle-induced dynamic responses of curved bridges. It is shown that when the axial motion, or the multiple moving loads are involved, the first-order truncation are not accurate enough and one should use higher-mode truncation to study the responses of curved beams. In addition, it is necessary to consider damping in the vibration study of curved beams. 相似文献
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Nonlinear dynamics of high-dimensional models of an axially moving viscoelastic beam with in-plane and out-of-plane vibration with combined parametric and forcing excitations are investigated by the incremental harmonic balance (IHB) method in this paper. Governing equations of transverse in-plane and out-of-plane and longitudinal vibration are obtained basing on the Hamilton's principle. The Galerkin method is used to separate time variable and spatial variable to obtain a set of multi-order differential equations. The IHB method with the fast Fourier transform (FFT) is used to solve periodic response of high-dimensional models of the beam for which convergent mode is reached. Stability of the steady-state periodic solutions is analyzed using the multivariable Floquet theory. Particular attention is paid to in-plane and out-of-plane vibration on convergent mode of the beam with combined parametric and forcing excitations. Multiple solutions are observed, and jump phenomena between in-plane and out-of-plane vibration with different transverse cross sections are discovered. 相似文献
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The present work is concerned with the free vibration analysis of an elastically supported cracked beam. The beam is made of a functionally graded material and rested on a Winkler–Pasternak foundation. The line spring model is employed to formulate the problem. The method of differential quadrature is applied to solve it. The obtained results agreed with the previous similar ones. Further, a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the problem on the values of natural frequencies and mode shape functions. 相似文献
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Predicting nonlinear dynamic response of internal cantilever beam system on a steadily rotating ring
This paper is focused on nonlinear dynamic response of internal cantilever beam system on a steadily rotating ring via a nonlinear dynamic model. The analytical approximate solutions to the oscillation motion are obtained by combining Newton linearization with Galerkin's method. Numerical solutions could be obtained by using the shooting method on the exact governing equation. Compared with numerical solutions, the approximate analytical solutions here show excellent accuracy and rapid convergence. Two different kinds of oscillating internal cantilever beam system on a steadily rotating ring are investigated by using the analytical approximate solutions. These include symmetric vibration through three equilibrium points, and asymmetric vibration through the only trivial equilibrium point. The effects of geometric and physical parameters on dynamic response are useful and can be easily applied to design practical engineering structures. In particular, the ring angular velocity plays a significant role on the period and periodic solution of the beam oscillation. In conclusion, the analytical approximate solutions presented here are sufficiently precise for a wide range of oscillation amplitudes. 相似文献
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In this paper, we study the vibration of an axially moving hyperelastic beam under simply supported condition. The kinematic of the axially moving beam have been described by Eulerian-Lagrangian formulation. In continuum mechanics frame, the finite deformation formula and a higher order shear deformation beam theory are applied to describe the deformation of the axially moving hyperelastic beam. In these formulas the material parameter, shear deformation and the geometric non-linearity have been taken into account. Through the Hamilton principle, the governing equations of nonlinear vibration are obtained, where the transverse vibration is coupled with the longitudinal vibration. When the velocity is a constant, the critical speed and natural frequencies are determined by solving the corresponding linear equations. Meantime, effects of the geometrical and material parameters on the critical speed and natural frequencies have been investigated. Comparisons among the critical velocities of the hyperelastic and Euler linear beam are also made. The results show that the critical velocity of hyperelastic beam is larger than that of linear Euler–Bernoulli beam. For the natural frequencies, we have the same conclusions. Lastly, by the multiple scales method, the leading order analytical solutions of the equilibrium state of axially moving hyperelastic beam in the supercritical regime are obtained. Furthermore the amplitudes of analytical solutions of the hyperelastic beam have been compared with that of linear Euler–Bernoulli beam. The effects of the material and geometrical parameters on the asymptotic solutions and the amplitude has been analyzed. 相似文献
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Stiffness modifications in engineering structures, for example due to damage and cracking, will inevitably also lead to changes in deformations, internal forces, natural frequencies and mode shapes of the structures. In this paper, an efficient and simple method for sensitivity analysis of cracked or weakened structures under time-harmonic loading is presented. The method is based on a comparison between the strain energy and the kinetic energy of an uncracked structure and that of a cracked structure in conjunction with the application of exact or approximate Green's functions as described in [3] for the static case. The present analysis enables the prediction of any changes in the displacements and stresses and has a lower computational effort as compared to available classical methods, because only the damaged region has to be re-considered in the method. Green's functions are taken as a basis of the approach, which have the ability to weight the influence of the stiffness modifications in a region of a structure and show how sensitive other regions respond to the stiffness modifications. Based on linear elastic fracture mechanics, cracked or damaged regions are approximated by spring models in the analytical solution of some simple beam problems, while cracked finite elements are used for complicated cases where analytical solutions cannot be obtained. Sensitivity analysis with Green's functions (SAGF) approach is applied to static and dynamic analysis of cracked and weakened structures, which consist of homogeneous materials or fiber reinforced composites like reinforced concretes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献