This paper presents a methodology for accurate free vibration analysis of planar flexible mechanisms. Each flexible body is considered as a beam and modelled using higher-order beam elements for longitudinal and flexural deformations. The global equations of motion for a mechanism consisting of multiple flexible bodies are formulated using the augmented Lagrange equations. Free vibration analyses are conducted at desired fast Fourier configurations to determine instantaneous structural natural frequencies and structural mode shapes. Dynamical frequencies and dynamical mode shapes incorporating the gyroscopic effects and dynamic axial loads are obtained using the modal summation method. Numerical results and comparisons are given for a rotating beam and two four-bar crank-rocker mechanisms.
Free Vibration Analysis of Planar Flexible Mechanisms
Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 2001; rev. March 2003. Associate Editor: H. Lankarani.
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Yu, S. D., and Xi, F. (January 22, 2004). "Free Vibration Analysis of Planar Flexible Mechanisms ." ASME. J. Mech. Des. December 2003; 125(4): 764–772. https://doi.org/10.1115/1.1626130
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