Rayleigh-Ritz vibration analysis with the trial function considering additional elastic constraint

Abstract

Vibration analysis by Rayleigh-Ritz method (RRM) with trial function considering the additional elastic constraint is proposed and examined. Firstly, Euler beam cantilever attached with multiple linear springs is analyzed. Discontinuous shear force function (DSF) is proposed as an admissible function, because linear springs generate discontinuity of beam’s shear force. The comparison with its exact solution shows that DSF is effective and useful. Secondly, Euler beam cantilever added unilateral spring is analyzed. The non-contact and contact condition are solved by RRM with DSF, respectively, and half-periods of non-contact and contact condition are combined and whole time history is approximated as a Fourier function so as to make maximum strain energy constant. The analyzed time history agrees well with that numerically calculated with finite element method and Runge-Kutta method. Finally, thick circular plate pressed to many steel balls is analyzed by using the proposed method. The analyzed natural frequencies and mode shapes agree well with those measured by experimental modal analysis.