Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link, Using Perturbation Theory

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed

An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed

ESDA2006-95264 ON THE RESOLUTION OF EXISTING DISCONTINUITIES IN THE DYNAMIC RESPONSES OF AN EULER-BERNOULLI BEAM SUBJECTED TO THE MOVING MASS

ABSTRACT The dynamic response of a one-dimensional distributed parameter system subjected to a moving mass with constant speed is investigated. An Euler-Bernoulli beam with the uniform cross-section and finite length with specified boundary support conditions is assumed. In this paper, rather a new method based on the time dependent series expansion for calculating the bending moment and the shear force due to motion of the mass is suggested. Governing differential equations of the motion are derived and solved. The accuracy of the numerical results primarily is verified and further the rapid convergence of this new technique was illustrated over other existing methods. Finally, it is shown that a considerable improvement is obtained in capturing the incurred discontinuities at the contact point of traveling concentrated mass. INTRODUCTION The dynamic behavior of beam structures, such as bridges or railways, subjected to moving loads (moving forces and moving masses) has been investigated for over a century, and it is one of the most important problems facing structural and bridge engineers especially when the effect of the inertia of the load is accounted for, the problem is associated with serious difficulties. There are numerous reports available in the excellent monographs of Fryba In the conventional dynamic response approaches, usually the frequencies of the system are evaluated by ignoring the effects of damping, the mass of moving mass and its inertia in the solution of the eigen-problem (Pesterev et al. [2

Nonlinear dynamic analysis of a rectangular plate subjected to accelerated/decelerated moving load

In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin’s method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM) with ANSYS software, the obtained results in nonlinear form are verified by FEM results. Then, a parametric study is conducted by changing the size of moving mass/force and the velocity of the traveling mass/force with a constant acceleration/deceleration, and the outcome nonlinear results are compared to the results from linear solution