共查询到20条相似文献,搜索用时 156 毫秒
1.
基于物理中面概念和经典薄板理论,应用有限元法研究了机械工程中的二维传输结构作轴向运动时的面外自由振动特性.根据实际工程结构特点及设计要点,考虑受双向预张应力作用的传输薄板结构模型,由哈密顿原理出发严格导出了结构的有限元动力学方程,得到了体现轴向传输结构特性的陀螺矩阵.该矩阵具有反对称结构,这与加权余量法所得的陀螺矩阵结构不同.采用3 节点三角形单元离散求解域,且单元不受轴向运动影响,给出了单元密度对计算结果精度的影响.分析了传输结构预张应力和轴向速度与自由振动固有频率的关系;考察了不同结构的陀螺矩阵对数值结果的影响.将部分结果与ANSYS 软件模拟对比,显示出良好的一致性,证明了本文方法的有效性.研究结果可为典型传输带等结构的振动控制提供参考,建模方法可为ANSYS等计算软件添加轴向运动结构新模块提供理论依据. 相似文献
2.
B. Kh. Eshmatov 《Nonlinear dynamics》2007,50(1-2):353-361
The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined
Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature
formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical
convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response
of the cylindrical shell is discussed. The results obtained by various theories are compared. 相似文献
3.
A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers. 相似文献
4.
Ping Lou 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(10):707-728
This article deals with the dynamic analysis of train–track–bridge interaction system using the finite element method. In
this interaction system, each four-wheelset vehicle in the train is modeled by a mass–spring–damper system with 10 degrees
of freedom; the rails and the bridge decks are modeled as a number of Bernoulli–Euler beam elements, while the elasticity
and damping properties of the rail bed are represented by continuous springs and dampers. The equation of motion for the interaction
system is presented in matrix form with time-dependent coefficients. The correctness of the proposed procedure is illustrated
by a comparison with the numerical result from the existing literature. Several numerical examples are chosen to investigate
the effect of two types of vehicle models, two types of bridge models and three damping values of bridge on the maximum dynamic
responses of train, track and bridges. 相似文献
5.
Two-dimensional boundary characteristic orthonormal polynomials are used in the Rayleigh–Ritz method to study the free vibration
of rectangular orthotropic elliptic plates resting on a Winkler elastic foundation. Two types of varying thickness are considered:
(1) linearly varying with respect to the concentric ellipses, (2) linearly varying along both the principal axes simultaneously.
Numerical results for frequencies are presented in tables. Nodal lines are shown in figures. Effects of stiffness of elastic
foundation, aspect ratios of plates, degree of orthotropy, and types of thickness variation on vibration frequencies of elliptical
plates are also discussed. 相似文献
6.
A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for
elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied
in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact
force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact
force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact
force/transverse deflection versus impact velocity are given on the basis of the theoretical results.
The project supported by the National Natural Science Foundation of China (10532020). 相似文献
7.
曲线加筋Kirchhoff-Mindlin板自由振动分析 总被引:2,自引:2,他引:0
相比传统加筋板,曲线加筋板能够更充分地发挥材料力学性能.在加筋板力学分析中,厚板通常采用Reissner-Mindlin理论,然而当板厚较薄时易出现剪切自锁,离散的Kirchhoff-Mindlin理论采用假设剪切应变场可避免该问题.针对曲线加筋Kirchhoff-Mindlin板自由振动分析,采用离散的Kirchhoff-Mindlin三角形单元和Timoshenko曲梁单元分别模拟板和加强筋,根据板的位移插值函数及筋板交界面的位移协调条件,建立基于板单元位移自由度的有限元方程.为了验证方法的有效性和准确性,采用直线加筋薄板、曲线加筋薄板和厚板3种模型进行算例研究,通过收敛性和精度分析来选择合理的有限元网格密度.直线加筋薄板前20阶固有频率均与文献结果吻合良好;曲线加筋板算例中,本文方法满足收敛条件的板单元数目为2469,Nastran模型板单元数目为6243;本文所得曲线加筋板固有频率与Nastran计算结果最大误差为3.4%.研究结果表明,本文方法无需筋板单元共节点,可使用较少的有限元网格数量,并能够保证计算精度;在离散Kirchhoff-Mindlin三角形板单元基础上构造Timoshenko梁单元可同时适用于曲线加筋薄板与厚板自由振动分析. 相似文献
8.
Summary The present study analyzes elasto–plastic thermal stresses in some particle-reinforced functionally graded material plates
(FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling
metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface
contains distributed metal particles in a ceramic matrix. We use the thermo–elasto–plastic constitutive equation of a particle-reinforced
composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto–plastic
thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are
considered: the first kind (FGP1) represents distributed ceramic particles in the metal matrix, and the second one (FGP2)
represents distributed metal particles in the ceramic matrix. We modify the thermo–elasto–plastic constitutive equation of
a particle-reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing
effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied.
The first one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from
the room temperature, and the last one is the heating after cooling from the fabrication temperature. The particle volume
fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the finite element
method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and
the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication
temperature on the maximum tensile matrix stress are discussed.
Received 22 November 2000; accepted for publication 24 April 2001 相似文献
9.
A. Boukamel S. Méo O. Débordes M. Jaeger 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(12):785-801
Summary This paper presents a model of thermo-mechanical behaviour of viscoelastic elastomers under large strain. A formulation is
proposed with a generalisation to large strain of the Poynting–Thomson rheological model. A finite element formulation is
then exposed taking the incompressibility constraint for mechanical equilibrium into account. On the thermomechanical coupling
aspect, an algorithm of time discretisation is proposed with two time scales corresponding respectively to mechanical and
thermal behaviours. Finally, an application for the simulation of a double-shearing test is presented with an analysis of
parameters' influence and a comparison between numerical and experimental results.
Received 22 November 2000; accepted for publication 26 June 2001 相似文献
10.
In the design of electric machines, devices, and plasma generator bearing constructions, it is sometimes necessary to study
the influence of magnetic fields on the vibration frequency spectra of thin-walled elements. The main equations of magnetoelastic
vibrations of plates and shells are given in [1], where the influence of the magnetic field on the fundamental frequencies
and vibration shapes is also studied. When studying the higher frequencies and vibration modes of plates and shells, it is
very efficient to use Bolotin’s asymptotic method [2–4]. A survey of studies of its applications to problems of elastic system
vibrations and stability can be found in [5, 6]. Bolotin’s asymptotic method was used to obtain estimates for the density
of natural frequencies of shallow shell vibrations [3] and to study the influence of the membrane stressed state on the distribution
of frequencies of cylindrical and spherical shells vibrations [7, 8]. In a similar way, the influence of the longitudinal
magnetic field on the distribution of plate and shell vibration frequencies was studied [9, 10]. It was shown that there is
a decrease in the vibration frequencies of cylindrical shells under the action of a longitudinal magnetic field, and the accumulation
point of the natural frequencies moves towards the region of lower frequencies [10]. In the present paper, we study the influence
of a transverse magnetic field on the distribution of natural frequencies of shallow cylindrical and spherical shells, obtain
asymptotic estimates for the density of natural frequencies of shell vibrations, and compare the obtained results with the
empirical numerical results. 相似文献
11.
B. A. Khudayarov N. G. Bandurin 《Journal of Applied Mechanics and Technical Physics》2007,48(2):279-284
Nonlinear vibrations of viscoelastic elements of aviation structures are studied. A method and an algorithm for the numerical
solution of integrodifferential equations are proposed. The critical velocity of the flow past viscoelastic plates is determined.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 156–162, March–April, 2007. 相似文献
12.
D. A. Khodzhaev B. Kh. Éshmatov 《Journal of Applied Mechanics and Technical Physics》2007,48(6):905-914
The problem of vibrations of a viscoelastic plate with concentrated masses is studied in a geometrically nonlinear formulation.
In the equation of motion of the plate, the action of the concentrated masses is taken into account using Dirac δ-functions.
The problem is reduced to solving a system of Volterra type ordinary nonlinear integrodifferential equations using the Bubnov-Galerkin
method. The resulting system with a singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature
formulas. The effect of the viscoelastic properties of the plate material and the location and amount of concentrated masses
on the vibration amplitude and frequency characteristics is studied. A comparison is made of numerical calculation results
obtained using various theories.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007. 相似文献
13.
The governing equations of elasticity theory for natural vibration and buck- ling of anisotropic plate are derived from Hellinger-Reissner's variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions. Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations. 相似文献
14.
The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation.
Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies
the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped
thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula.
The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary
equation. The numerical results show the high accuracy of the proposed method. 相似文献
15.
求解不连续中厚板自由振动的微分容积单元法 总被引:2,自引:0,他引:2
基于区域叠加原理和微分容积法,发展了一种新型的数值方法——微分容积单元法,用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元,在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程.在相邻的单元连接处应用位移连续条件和平衡条件,引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程,由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程,并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。 相似文献
16.
The free vibration of annular thick plates with linearly varying thickness along the radial direction is studied, based on
the linear, small strain, three-dimensional (3-D) elasticity theory. Various boundary conditions, symmetrically and asymmetrically
linear variations of upper and lower surfaces are considered in the analysis. The well-known Ritz method is used to derive
the eigen-value equation. The trigonometric functions in the circumferential direction, the Chebyshev polynomials in the thickness
direction, and the Chebyshev polynomials multiplied by the boundary functions in the radial direction are chosen as the trial
functions. The present analysis includes full vibration modes, e.g., flexural, thickness-shear, extensive, and torsional.
The first eight frequency parameters accurate to at least four significant figures for five vibration categories are obtained.
Comparisons of present results for plates having symmetrically linearly varying thickness are made with others based on 2-D
classical thin plate theory, 2-D moderate thickness plate theory, and 3-D elasticity theory. The first 35 natural frequencies
for plates with asymmetrically linearly varying thickness are compared to the finite element solutions; excellent agreement
has been achieved. The asymmetry effect of upper and lower surface variations on the frequency parameters of annular plates
is discussed in detail. The first four modes of axisymmetric vibration for completely free circular plates with symmetrically
and asymmetrically linearly varying thickness are plotted. The present results for 3-D vibration of annular plates with linearly
varying thickness can be taken as benchmark data for validating results from various plate theories and numerical methods. 相似文献
17.
In this paper, a general analytical method-space variable transform method is presented for solving free vibration problems of thick cylindrical shell with arbitrary boundary conditions. Free vibration characteristics of cantilever thick cylindrical shell are evaluated by the presented method, and the numerical results are compared with the corresponding results of thin shell theory and experimental values. Theoretical analysis and calculating results show that the method presented in this paper has good convergence and accuracy and can be extended to analyze free vibration of beams. plates and shells. 相似文献
18.
Summary A constitutive model is developed for the isothermal response of particle-reinforced elastomers at finite strains. An amorphous
rubbery polymer is treated as a network of long chains bridged to permanent junctions. A strand between two neighboring junctions
is thought of as a sequence of rigid segments connected by bonds. In the stress-free state, a bond may be in one of two stable
conformations: flexed and extended. The mechanical energy of a bond in the flexed conformation is treated as a quadratic function
of the local strain, whereas that of a bond in the extended conformation is neglected. An explicit expression is developed
for the free energy of a network. Stress–strain relations and kinetic equations for the concentrations of bonds in various
conformations are derived using the laws of thermodynamics. In the case of small strains, these relations are reduced to the
constitutive equation for the standard viscoelastic solid. At finite strains, the governing equations are determined by four
adjustable parameters which are found by fitting experimental data in uniaxial tensile, compressive and cyclic tests. Fair
agreement is demonstrated between the observations for several filled and unfilled rubbery polymers and the results of numerical
simulation. We discuss the effects of the straining state, filler content, crosslink density and temperature on the adjustable
constants.
Received 3 January 2001; accepted for publication 12 July 2001 相似文献
19.
20.
Based on Mindlin's first-order shear deformable plate theory, a DSC-Ritz element method is developed for the free vibration analysis of moderately thick rectangular plates with mixed supporting edges. The rationale of the present approach is not only to apply the discrete singular convolution (DSC) delta type wavelet kernel as a trial function with the Ritz method, but also to incorporate the method in finite elements in order to handle the mixed boundary constraints. The approach is novel and flexible as it passes through a bottleneck of the global DSC-Ritz method in treating the kinematic supporting edges with assorted discontinuities. A series of numerical simulations for rectangular Mindlin plates with various edge support discontinuities, plate thicknesses and aspect ratios are presented. For verification, the vibration frequencies thus established are directly compared with those reported in the open literature. New sets of numerical results for several other cases of moderately thick plates with mixed simply supported, clamped and free edges are presented and discussed in detail. 相似文献