Free vibration analysis of beams on elastic foundation

A simple finite element method is developed and applied to treat the free vibration analysis of beams supported on elastic foundations. The entire analysis is programmed to run on a microcomputer and with few elements modelling the beam, gives quick and reliable results. Numerical examples pertaining to the free vibration of beams in some special situations are considered, such as a stepped beam on an elastic foundation, beam on a stepped elastic foundation and a continuous beam on an elastic foundation. Present results compare very well with those obtained from existing solutions, wherever possible.     

轴向运动功能梯度粘弹性梁横向振动的稳定性分析

基于Euler梁理论研究了轴向运动功能梯度粘弹性梁横向振动的稳定性问题.基于问题的数学模型和控制方程,利用微分求积法求得了轴向匀速运动功能梯度粘弹性梁亚临界区域内横向振动的复频率,分析其随着轴向运动速度、材料梯度指数等参数的变化情况,探讨上述参数对超临界区域失稳形式的影响.然后应用多尺度法结合边界条件分析了轴向速度带有周期扰动成分的变速运动功能梯度粘弹性梁的失稳问题,重点讨论了当速度扰动频率为固有频率二倍或者为两固有频率之和/差时所发生的次谐波共振及组合共振所导致的失稳.数值算例表明,随着梯度指数的增大,匀速运动功能梯度粘弹性梁的临界发散速度、耦合速度以及变速运动功能梯度粘弹性梁的稳定区域减小,且粘弹性系数的影响逐渐变弱,同等条件下,轴向运动功能梯度粘弹性固支梁比简支梁更为稳定.     

航天运载器舵类传动机构间隙影响研究

舵类传动机构内存在的间隙是影响航天运载器飞行稳定性、机动性和控制精确性等指标的关键因素.本文先依据影响特性将航天运载器舵类传动机构中存在的各种间隙归结为:连杆配合类间隙、摇臂配合类间隙和舵轴配合类间隙;然后基于运动学分析提出了三类间隙影响的理论分析方法,而后与多体动力学软件ADAMS的仿真结果进行对比与分析.研究表明本文所提理论分析方法可准确估计三类间隙对传动机构的影响,满足实际工程间隙超差影响分析的需求.     

Chaotic dynamics and forced harmonic vibration analysis of magneto-electro-viscoelastic multiscale composite nanobeam

In this article, the damping forced harmonic vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam embedded in viscoelastic foundation is evaluated based on nonlocal strain gradient elasticity theory. The viscoelastic foundation consists of Winkler–Pasternak layer. The governing equations of nonlocal strain gradient viscoelastic nanobeam in the framework of refined shear deformable beam theory are obtained using Hamilton’s principle and solved implementing an analytical solution. In addition, a parametric study is presented to examine the effect of the nonlocal strain gradient parameter, magneto-electro-mechanical loadings, and aspect ratio on the vibration characteristics of nanobeam. From the numerical evaluation, it is revealed that the effect of electric and magnetic loading on the natural frequency has a predominant influence.

     

Procedures for the forced,damped vibration analysis of structural frames using distributed parameter models

The paper summarises an approach to the forced vibration analysis of skeletal elastic structures, making use of “exact” matrix technique. The analysis is based on the modal superposition method, which has been developed in the context of models that retain characteristics of both distributed mass and stiffness. The free vibration analysis is performed using generalised dynamic stiffness functions appropriate to a Rayleigh-Timoshenko-Euler beam-column element. The contributions to dynamic displacements and dynamic internal forces by inertia effects during forced vibration are properly accounted for, and all results are obtained from explicit solutions to the relevant equations at all stages. Numerical integration or other approximate procedures are not required. It is the objective of the present paper to summarise procedures, numerical examples being available elsewhere (e.g. [1–3]). However, the paper is concluded with a practical example illustrating results obtainable by the techniques described below.     

Nonlinear forced vibration of damped plates by an asymptotic numerical method

This work deals with damped nonlinear forced vibrations of thin elastic rectangular plates subjected to harmonic excitation by an asymptotic numerical method. Using the harmonic balance method and Hamilton’s principle, the governing equation is converted into a static formulation. A mixed formulation is used to transform the problem from cubic nonlinearity to quadratic one sequence. Displacement, stress and frequency are represented by power series with respect to a path parameter. Equating the like powers of this parameter, the nonlinear governing equation is transformed into a sequence of linear problems with the same stiffness matrix. Through a single matrix inversion, a considerable number of terms of the perturbation series can easily be computed with a limited computation time. The starting point, corresponding to a regular solution, is obtained by the Newton–Raphson method. In order to increase the step length, Padé approximants are used. Numerical tests are presented and compared with numerical and analytical results in the literature, for different boundary conditions, excitations and damping coefficients.     

Application of the Green function method to flow-thermoelastic forced vibration analysis of viscoelastic carbon nanotubes

In this paper, the Green function method (GFM) is implemented for forced vibration analysis of carbon nanotubes (CNTs) conveying fluid in thermal environment. The Eringen’s nonlocal elasticity theory is used to take into account the size effect of CNT with modeling the CNT wall–fluid flow interaction by means of slip boundary condition and Knudsen number (Kn). The derived governing differential equations are solved by GFM which demonstrated to have high precision and computational efficiency in the vibration analysis of CNTs. The validity of the present analytical solution is confirmed by comparing the results with those reported in other literature, and good agreement is observed. The analytical examinations are accomplished, while the emphasis is placed on considering the influences of nonlocal parameter, boundary conditions, temperature change, structural damping of the CNT, Knudsen number, fluid velocity and visco-Pasternak foundation on the dynamic deflection response of the fluid-conveying CNTs in detail.     

Crack mathematical modeling to study the vibration analysis of cracked micro beams based on the MCST

Microsystem Technologies - In this paper, a new approach is presented to capture size effect on the dynamic behavior of a cracked micro beam based on the modified couple stress theory (MCST)....     

Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions

In this paper, we use the first-order shear deformation theory in the multiquadric radial basis function (MQRBF) procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates. The transverse deflection and two rotations of the laminate are independently approximated with the MQRBF approximation. The natural frequencies of vibration are computed for various laminated plates and compared with some available published results. Through numerical experiments, the capability and efficiency of the MQRBF method for eigenvalue problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.     

Finite element free vibration analysis of damped stiffened panels

Free vibration characleristics of a damped stiffened panel with applied viscoelastic damping on the flanges of the stiffeners are studied using finite element method. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration while deriving the stiffness and mass matrices of the damped stiffener element. The finite element method consists of representing the panel by rectangular plate elements of 12 d.o.f. and the stiffeners by beam elements of 8 d.o.f. which allow for bending, torsional and warping effects. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented.     

Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton’s principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors.

     

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, one-dimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.     

A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings

The dynamic stiffness matrix of a composite beam that exhibits both geometric and material coupling between bending and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The formulation is based on Hamilton’s principle leading to the governing differential equations of motion in free vibration, which are solved in closed analytical form for harmonic oscillation. By applying the boundary conditions the frequency dependent dynamic stiffness matrix that relates the amplitudes of loads to those of responses is then derived. Finally the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of an illustrative example. The results are discussed and some conclusions are drawn. The theory can be applied for modal analysis of high aspect ratio composite wings and can be further extended to aeroelastic studies.     

Free vibration and stability behaviour of uniform beams and columns on nonlinear elastic foundation

Free vibration and stability behaviour of uniform beams and columns on nonlinear elastic foundation are evaluated using a finite element formulation. Numerical results are presented for various end boundary conditions with varying foundation parameters.     

Correction to: Crack mathematical modeling to study the vibration analysis of cracked micro beams based on the MCST

Microsystem Technologies - In the original publication of this article, the Eqs. (20), (21), (52), (54), (55), (56) and Figs. 4–15 were incorrectly published. The author would like...     

Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

Free vibration analysis of double-viscoelastic nano-composite micro-plates reinforced by FG-SWCNTs based on the third-order shear deformation theory

Microsystem Technologies - In this paper, free vibration analysis of a double viscoelastic nano-composite plate system reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNT)...     

Free vibration analysis of multi-symmetric stiffened shells

The application of structural symmetry techniques to the free vibration analysis of cylindrical and conical shells for the prediction of natural frequencies and mode shapes is described. Appropriate boundary conditions have been developed for the analysis of only a part of the shell and have been shown to yield results comparable to the full shell analysis. Half and quarter models of the shell have been developed and analysed using semi-loof and facet shell finite elements. Unstiffened and stiffened circular cylindrical shells and stiffened conical shells have been considered.     

Effect of Porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures

This article investigates the influence of porosity on free and forced vibration characteristics of a nanoshell reinforced by graphene platelets (GPL). The material properties of piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a cylindrical nanoshell and estimated using a nanomechanical model. In addition, because of imperfection of the current structure, three kinds of porosity distributions are considered. The nanostructure is modeled using modified strain gradient theory (MSGT) which is a size-dependent theory with three length scale parameters. The novelty of the current study is to consider the effects of porosity, GPLRC and MSGT on dynamic and static behaviors of the nanostructure. Considering three length scale parameters ( $l_0=5h$, $l_1=3h$, $l_2=5h$ ) in MSGT leads to a better agreement with MD simulation in comparison by other theories. Finally, effects of different factors on static and dynamic behaviors of the porous nanostructure are examined in detail.     

Geometrically nonlinear analysis of thin-walled composite box beams

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings has been presented by using variational formulation based on the classical lamination theory. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beam under vertical load to investigate the effect of geometric nonlinearity and address the effects of the fiber orientation, laminate stacking sequence, load parameter on axial–flexural–torsional response.