A Numerically Efficient Algorithm for Steady-State Response of Flexible Mechanism Systems

[+] Author and Article Information
Z. Yang, J. P. Sadler

Mechanical Engineering Department, University of Kentucky, Lexington, KY 40506

J. Mech. Des 115(4), 848-855 (Dec 01, 1993) (8 pages) doi:10.1115/1.2919278 History: Received June 01, 1991; Online June 02, 2008


Presented in this work is a numerically efficient algorithm for treating the periodic steady-state response of flexible mechanisms as the solution to separated two-point boundary value problems. The finite element method is applied to discretize continuous elastic mechanisms systems and a set of second-order ordinary differential equations is obtained with periodically time-varying coefficient matrices and forcing vectors. Modal analysis techniques are employed to decouple these equations into a number of single scalar ordinary differential equations in modal basis. The periodic time-boundary conditions at both ends of a fundamental period equal to a cycle of input motion are mathematically separated by introducing auxiliary variables, thus resulting in a so-called almost-block-diagonal matrix for linear algebraic systems of equations. Solving such a system is computationally less expensive than solving a general linear algebraic system. Examples are included to illustrate the procedures applied to a four-bar linkage through which computing time is compared with other approaches.

Copyright © 1993 by The American Society of Mechanical Engineers
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