Winkler-Pasternak弹性地基梁自由振动的二维弹性分析Two-dimensional elastic analysis for free vibration of beams set on winkler-pasternak elastic foundations

基于二维线弹性理论,应用Hamilton原理,获得Winkler-Pasternak弹性地基梁自由振动的控制微分方程,应用微分求积法(DQM)数值研究了梁自由振动的无量纲频率特性。计算结果与已有的结果(Bernoulli-Euler梁和Timoshenko梁)比较表明,本文的分析方法对弹性地基长梁和短梁自由振动的研究都有效。最后考虑了几何参数对梁频率的影响,以及不同边界条件下地基系数对频率的影响和收敛性。     

A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint

The end shear restraint, which is an un-classical type of end support, has a significant effect on the behavior of elastic composite beams. The principal aim of this paper is to present a numerical model for studying the effect of end shear restraint on static and free vibration behavior of elastic composite beams with various end conditions. The elastic composite beam, considered in this study, is composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The three types of end conditions considered in this study are simple, fixed and free supports. The numerical model is based on the combination of transfer matrix and analog beam methods. The field transfer matrices for the element of the elastic composite beam are derived. The present model is applied to the beam systems with and without end shear restraint and the static response and natural frequencies are calculated. the effect of shear stiffness between the upper slab and lower beam is also demonstrated.     

High-order ALE method for the Navier–Stokes equations on a moving hybrid unstructured mesh using flux reconstruction method

The flux reconstruction (FR) formulation can unify several popular discontinuous basis high-order methods for fluid dynamics, including the discontinuous Galerkin method, in a simple, efficient form. An arbitrary Lagrangian–Eulerian (ALE) extension to the high-order FR scheme is developed here for moving mesh fluid flow problems. The ALE Navier–Stokes equations are derived by introducing a grid velocity. The conservation law are spatially discretised on hybrid unstructured meshes using Huynh’s scheme (Huynh 2007) on anisotropic elements (quadrilaterals) and using Correction Procedure via Reconstruction scheme on isotropic elements (triangles). The temporal discretisation uses both explicit and implicit treatments. The mesh movement is described by node positions given as a time series, instead of an analytical formula. The geometric conservation law is tested using free stream preservation problem. An isentropic vortex propagation test case is performed to show the high-order accuracy of the developed method on both moving and fixed hybrid meshes. Flow around an oscillating cylinder shows the capability of the method to solve moving boundary viscous flow problems, with the numeric method further verified by comparison of the result on a smoothly deforming mesh and a rigid moving mesh.     

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

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.     

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.     

Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method

A three-dimensional free vibration analysis of circular and annular plates is presented via the Chebyshev–Ritz method. The solution procedure is based on the linear, small strain, three-dimensional elasticity theory. Selecting Chebyshev polynomials which can be expressed in terms of cosine functions as the admissible functions, a convenient governing eigenvalue equation can be derived through the Ritz method. According to the geometric properties of circular and annular plates, the vibration is divided into three distinct categories: axisymmetric vibration, torsional vibration and circumferential vibration. Each vibration category can be further subdivided into the antisymmetric and symmetric ones in the thickness direction. Convergence and comparison study demonstrated the high accuracy and efficiency of the present method. The present approach shows a distinct advantage over some other Ritz solutions in that stable numerical operation can be guaranteed even when a large number of admissible functions is employed. Therefore, not only lower-order but also higher-order eigenfrequencies can be obtained by using sufficient terms of the Chebyshev polynomials. Finally, some valuable results for annular plates with one or both edges clamped are given and discussed in detail.     

Sliding contact conditions using the master–slave approach with application on geometrically non-linear beams

Frictionless sliding conditions between two bodies are usually defined using either the method of Lagrangian multipliers or by prescribing an artificial (penalty) stiffness which resists the penetration at the contact point. Both of these methods impose the condition that the contact force should be normal to the contact surface, with the Lagrangian multiplier or the penalty parameter serving as a measure of this force. In this work, an alternative approach is undertaken: the frictionless sliding condition is defined through a relationship between nodal parameters of the virtual displacements of a discretised principle of virtual work. This method, which does not involve additional force parameters or degrees of freedom, is known as the master–slave or the minimum-set method and is particularly convenient for displacement-based finite-element implementation. The method is analysed in detail in context of bilateral sliding constraints characteristic of prismatic and cylindrical joints in flexible beam assemblies undergoing large overall motion. Two numerical examples are presented and assessed against the results in the literature.     

Determination of elastic and plastic characteristics of TiC–TiNi alloys by the ultrasonic resonance method

Elastic characteristics and propagation velocities of ultrasonic waves in a TiC–TiNi composite material are determined by the ultrasonic resonance method. The values of the elastic moduli of the solid composite obtained are used to estimate its plastic properties. The effect of various additives on the elastic and plastic properties of the composite is studied.     

The effect of dynamic normal force on the stick–slip vibration characteristics

Nonlinear Dynamics - In the experiment, we observed such a phenomenon: the alternating normal force changes the vibration state of a friction system. A single-degree-of-freedom mathematical model...     

A one-dimensional theory of wave-propagation in elastic rods based on the „method of internal constraints“

Conclusions The results obtained in this paper in the particular case of lateral vibrations of bars show an encouraging agreement between the values ofc/c ₀ andc _g/c₀ given by the approximate theory based on the assumption of internal constraints and the exact theory derived from the use of the equations of the Mathematical Theory of Elasticity.This approximate theory which will be referred to as the Theory of Internal Constraints is in the dynamic case completely contained in the constraint equation (1) and in the application ofHamiltons Principle. Accordingly the concept of Shear Coefficient is not used. In the general case of wave propagation in elastic straight rods this theory unifies a number of separate engineering treatments of the problem. Moreover, the same theory can be applied to the study of vibrations of curved bars taking into account the effects of shear and of rotatory inertia as has been shown in a previous paper.The mathematical simplicity of the theory and its degree of accuracy justify its use in dealing with engineering problems in vibrations of curved or straight bars for which more exact theories cannot be used because of their mathematical complexities.The author wants to express his best thanks to Mr.E. C. Zachmanoglou, student in the Department of Aeronautical Engineering, and to Mr.R. V. Milligan, graduate student in the Department of Mechanics, at Rensselaer Polytechnic Institute for the valuable help and assistance given to him in the preparation of the numerical tables and graphs which are presented in this paper.The material presented in this paper is based on an investigation which is being conducted under the sponsorship of the Office of Naval Research, Department of the U. S. Navy, Washington, D. C.; and is presented with the permission of the Office of Naval Research.     

Algorithm and implementation of soil–tire contact analysis code based on dynamic FE–DE method

One of the fundamental problems in terramechanics is soil–tire system. Past achievements on this topic can be observed in various literatures. Fast development on CPU power of PC system enables us to apply numerical methods to this basic subject. Among others, finite element method (FEM) has been applied to simple problems of soil–tire system not only in 2D but also in 3D approach. However, it is noted that the current FEM technology cannot handle “singular” boundary conditions with sufficient accuracy of analysis. Typical example of this limitation can be seen in an application to traction tire–soil contact problems, where the contact point of tire lug tip behaves as the singular point of stress field. On the other hand, distinct or discrete element method (DEM) has in essence the capability of analyze microscopic deformation (or flow) of soil as many researchers have already been demonstrated. It is noted that DEM suffers large calculation time that is consumed not only at contact check between particulate elements but also at incremental time step. In our present study, we try to combine both merit of FEM and DEM together in order to analyze the soil–tire system interaction, where, for example, a tire and deep soil layer are modeled as FEM and soil surface layer as DEM. We propose simple algorithm of this FE–DE coupled method and sample program is developed that can solve some basic terramechanics problems in order to verify our idea. The obtained result shows qualitatively sufficient accuracy.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

The method of the reciprocal theorem of forced vibration for the elastic thin rectangular plates (II)—Rectangular plates with two adjacent clamped edges

In this paper, applying the method of reciprocal theorem, we give the distributions of the amplitude of bending moments along clamped edges and the amplitude of deflections along free edges of rectangular plates with two adjacent clamped edges under harmonic distributed and concentrated loads.     

Effects of the dynamic wheel–rail interaction on the ground vibration generated by a moving train

Based on Biot’s fully dynamic poroelastic theory, the dynamic responses of the poroelastic half-space soil medium due to quasi-static and dynamic loads from a moving train are investigated semi-analytically. The dynamic loads are assumed to be generated from the rail surface irregularities. The vehicle dynamics model is used to simulate the axle loads (quasi-static loads) and the dynamic loads from a moving train. The compatibility of the displacements at wheel–rail contact points couple the vehicle and the track–ground subsystem, and yield equations for the dynamic wheel–rail loads. A linearized Hertzian contact spring between the wheel and rail is introduced to calculate the dynamic loads. Using the Fourier transform, the governing equations for the poroelastic half-space are then solved in the frequency–wavenumber domain. The time domain responses are evaluated by the fast inverse Fourier transform. Numerical results show that the dynamic loads can make important contribution to dynamic response of the poroelastic half-space for different train speed, and the dynamically induced responses lie in a higher frequency range. The ground vibrations caused by the moving train can be intensified as the primary suspension stiffness of the vehicle increases.     

Simulations of radiative effects on the Rayleigh–Taylor instability using the CRASH code

Future experiments at the National Ignition Facility will be able to generate diagnosable Rayleigh–Taylor instability growth in the presence of locally generated, high radiation fluxes. This interplay of radiative energy transfer and hydrodynamic instability is relevant to many astrophysical systems, such as core-collapse red supergiant supernovae. Previous simulations of high-energy-density Rayleigh–Taylor instabilities in the presence of a hot environment near a radiative shock demonstrate behavior that differs from that found in non-radiative cases. However, these simulations considered only 1D or single wavelength cases. Here we report simulations of an entire experimental system using the CRASH code. These simulations lead to modified predictions, attributed to the effects of radial energy losses.     

A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations

Nonlinear dispersive generalized Benjiamin–Bona–Mahony equations are studied by using a generalized algebraic method. New abundant families of explicit and exact traveling wave solutions, including triangular periodic, solitary wave, periodic-like, soliton-like, rational and exponential solutions are constructed, which are in agreement with the results reported in other literatures, and some new results are obtained. These solutions will be helpful to the further study of the physical meaning and laws of motion of the nature and the realistic models. The proposed method in this paper can be further extended to the 2+1 dimensional and higher dimensional nonlinear evolution equations or systems of equations.