共查询到19条相似文献,搜索用时 78 毫秒
1.
Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated. 相似文献
2.
A new two-eigenfunctions theory, using the amplitude deflection and the generalized curvature as two fundamental eigenfunctions, is proposed for the free vibration solutions of a rectangular Mindlin plate. The three classical eigenvalue differential equations of a Mindlin plate are reformulated to arrive at two new eigenvalue differential equations for the proposed theory. The closed form eigensolutions, which are solved from the two differential equations by means of the method of separation of variables are identical with those via Kirchhoff plate theory for thin plate, and can be employed to predict frequencies for any combinations of simply supported and clamped edge conditions. The free edges can also be dealt with if the other pair of opposite edges are simply supported. Some of the solutions were not available before. The frequency parameters agree closely with the available ones through pb-2 Rayleigh-Ritz method for different aspect ratios and relative thickness of plate. 相似文献
3.
Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams 总被引:1,自引:0,他引:1
Hu Ding · Li-Qun Chen Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China Department of Mechanics Shanghai China 《Acta Mechanica Sinica》2011,27(3):426-437
Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales. 相似文献
4.
CHARACTERISTIC EQUATIONS AND CLOSED-FORM SOLUTIONS FOR FREE VIBRATIONS OF RECTANGULAR MINDLIN PLATES
Yufeng Xing Bo Liu 《Acta Mechanica Solida Sinica》2009,22(2):125-136
The direct separation of variables is used to obtain the closed-form solutions for the free vibrations of rectangular Mindlin plates. Three different characteristic equations are derived by using three different methods. It is found that the deflection can be expressed by means of the four characteristic roots and the two rotations should be expressed by all the six characteristic roots,which is the particularity of Mindlin plate theory. And the closed-form solutions,which satisfy two of the three governing equations and all boundary conditions and are accurate for rectangular plates with moderate thickness,are derived for any combinations of simply supported and clamped edges. The free edges can also be dealt with if the other pair of opposite edges is simply supported. The present results agree well with results published previously by other methods for different aspect ratios and relative thickness. 相似文献
5.
黄道岸 《应用数学和力学(英文版)》1983,(4)
The subject discussed in this paper is the rectangular plate.Its two opposite edges are simply supported,while the othertwo are arbitrary,and the rigidity of the plate is variablealong the direction parallel to the simply supported edges.In order to solve the problem,the author adopts the finiteplate-strip element method,which is different from theusual finite element method or the finite strip method.Thesteps of the above method is no longer to establish a rigidi-ty matrix for elements or strips and gather them into a totalmatrix for solution.Now the relation of transfer betweenthe strain and inner force of every plate-strip is shown.Fi-nally a practical example is given and this method is foundto be easier and more effective. 相似文献
6.
Based on Reddy's layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress's maximum value and the in-plane stress's maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable. 相似文献
7.
付宝连 《应用数学和力学(英文版)》1985,6(11):1069-1081
This paper further extends the applications of the reciprocal theorem to calculating thenatural frequencies of rectangular elastic thin plates on the basis of [1]. Applying thepresented method. there is no need to solve governing differential equations. it is onlynecessary to solve a simple integral equation after using the reciprocal theorem between thebasic system and the actual system.Using the idea of the generalized edge simply supported and introducing the frequencymatrix. then all frequency equations of the rectangular plates with two opposite edgessimply supported and other two opposite edges variously suppored are obtained together.This is a simple convenient and general method for calculating the frequencyequations of the rectangular plates. 相似文献
8.
This paper deals with the nonlinear forced vibration of FGM rectangular plate with a boundary of two edges clamped opposite and the other two free. The plate is subjected to transversal and in-plane excitations. The present research treats the material properties of the FGM plates as temperature-dependent and graded continuously throughout the thickness direction, following the volume fraction of the constituent materials according to the power law. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. In the framework of geometrical nonlinearity the plate is modeled and the equations of motion are obtained on Hamilton's principle. With the help of Galerkin discretization, the nonlinear ordinary differential equations describing transverse vibration of the plate are proposed. By the numerical method, the nonlinear dynamical responses of the FGM plate with two clamped opposite and two free edges are analyzed. 相似文献
9.
A constitutive model for composite laminated plates with the damage effect of the intra-layers and inter-laminar interface is presented. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement on the interfaces are depicted by three shape functions, which are formulated according to solutions satisfying three equilibrium equations, By using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated plates with two different damage models are derived. Then, considering a simply supported laminated plate with damage, an analytical solution is presented using finite difference method to obtain the inter-laminar stresses. 相似文献
10.
Chun-Chuan Liu · Feng-Ming Li · Ting-Wei Liang · Wen-Hu Huang P.O.Box School of Astronautics Harbin Institute of Technology Harbin China 《Acta Mechanica Sinica》2011,27(5):785-795
In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed. 相似文献
11.
Krzysztof Marynowski 《European Journal of Mechanics - A/Solids》2010,29(5):879-886
In this paper, the viscoelastic theory is applied to the axially moving Levy-type plate with two simply supported and two free edges. On the basis of the elastic – viscoelastic equivalence, a linear mathematical model in the form of the equilibrium state equation of the moving plate is derived in the complex frequency domain. Numerical calculations of dynamic stability were conducted for a steel plate. The effects of transport speed and relaxation times modeled with two-parameter Kelvin–Voigt and three-parameter Zener rheological models on the dynamic behavior of the axially moving viscoelastic plate are analyzed. 相似文献
12.
利用粘弹性微分型本构关系和薄板理论,对线性变厚度粘弹性矩形薄板建立了在切向均布随从力作用下的运动微分方程,采用微分求积法研究了在随从力作用下线性变厚度粘弹性矩形薄板的稳定性问题,具体对对边简支对边固支和三边简支一边固支条件下体变为弹性、畸变服从Kelvin-Voigt模型的变厚度粘弹性矩形板在随从力下的广义特征值问题进行了求解,分析了薄板的长宽比、厚度比及材料的无量纲延滞时间的变化对随从力作用下矩形薄板的失稳形式及相应的临界荷载的影响. 相似文献
13.
An exact solution procedure is formulated for the stability analysis of viscoelastic rectangular plate with two opposite edges simply supported and other two edges clamped as well as the viscoelastic rectangular plate with one edge clamped and other three edges simply supported under the action of tangential follower force. Firstly, by assuming the transverse displacement (W) as independent functions which automatically satisfies the simply supported boundary conditions, the governing partial differential equation is reduced to an ordinary differential equation with variable coefficients. Then, by the normalized power series method and applying the boundary conditions yield the eigenvalue problem of finding the roots of a fourth-order characteristic determinant. The results show that the aspect ratio λ and the dimensionless delay time H have great effects on the types of instability and the critical loads of the viscoelastic plates. 相似文献
14.
《European Journal of Mechanics - A/Solids》2006,25(5):729-744
To model the axially moving viscoelastic web material a two-dimensional rheological element is used in this paper. This model is formed by elastic region and viscoelastic region. Using two-dimensional rheological model and the plate theory the differential equation of motion in the form of the eighth-order linear partial differential equation that governs the transverse vibrations of the system is derived. The Galerkin method is applied to simplify the governing equation into two-order truncated system defined by the set of ordinary differential equations. Numerical investigations of dynamic stability of the paper web were carried out. The effects of the transport speed and the internal damping on the dynamic behaviour of the axially moving web are presented in this paper. 相似文献
15.
本文研究两对边简支、中间有任意个粘弹性线支矩形板的横向振动问题,给出了一个求其动态特性的新的精确解析方法。首先将粘弹性线支反力视为是作用于板上的未知外力,求得了含有未知外力的对边简支矩形板横向振动微分方程的精确解析解,然后利用边界条件及线支处支承反力与位移的线性关系导出频率方程及振型函数,方法有独特的优越性。本文最后还给出了一些算例。 相似文献
16.
The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially
moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion
of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential
equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal
field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear
forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation
amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion,
and then the periodic motion becomes chaotic motion by period-doubling bifurcation. 相似文献
17.
18.
On the Bending, Vibration and Stability of Laminated Rectangular Plates with Transversely Isotropic Layers 总被引:4,自引:1,他引:3
IntroductionThestaticsanddynamicsofrectangularplateshavealwaysbeenofparticularresearchinterestinsolidmechanics.Inparticular,theemergenceofnewmaterialsandnewstructureshasbroughtoutendlessvitalforceintothestudy .Itiswell_knownthattheclassicalplatetheoryb… 相似文献
19.
黏弹性阻尼一直是轴向运动系统的研究热点之一.以往研究轴向运动系统大都没有考虑黏弹性阻尼的影响.但在工程实际中, 存在黏弹性阻尼的轴向运动体系更为普遍.本文研究了黏弹性阻尼作用下轴向运动Timoshenko梁的振动特性.首先, 采用广义Hamilton原理给出了轴向运动黏弹性Timoshenko梁的动力学方程组和相应的简支边界条件.其次, 应用直接多尺度法得到了轴速和相关参数的对应关系, 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似解析解.最后, 采用微分求积法分析了在有无黏弹性作用下前两阶固有频率和衰减系数随轴速的变化; 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似数值解, 验证了近似解析解的有效性.结果表明: 随着轴速的增大, 梁的固有频率逐渐减小.梁的固有频率和衰减系数随着黏弹性系数的增大而逐渐减小, 其中衰减系数与黏弹性系数成正比关系, 黏弹性系数对第一阶衰减系数和固有频率的影响很小, 对第二阶衰减系数和固有频率的影响较大. 相似文献