... the boundary conditions on the beam lead to vibrational modes of the beam involving bending, torsion, and extension at the same time. 18 12 2006 02 10 2008 05 03 2009 beams (structures) bending Rayleigh-Ritz methods robot dynamics torsion vibrations In this work, the well...

... of the beam which enables us to solve the dynamic pulse buckling due to the tip being loaded in the longitudinal as well as transverse directions of the beam column. The Rayleigh–Ritz method is used to convert the set of four coupled-partial differential equations into equivalent classical mass, stiffness...

... in the complete set of the governing equations of the free vibration problem of a piezoelectric continuum. The general results discussed in the paper are illustrated by the approximate calculation of the natural frequencies of a piezoelectric rod by the Rayleigh–Ritz method. Unlike in the case of elastic...

... beam functions, which are the complete solutions of a tapered Timoshenko beam under a Taylor series of static load, are developed, respectively, as the basis functions of the flexural displacement and the angle of rotation due to bending. The Rayleigh-Ritz method is applied to derive the eigenfrequency...