A NOVEL APPROACH TO THE FREE AXIAL-BENDING VIBRATION PROBLEM OF INHOMOGENEOUS ELASTIC BEAMS WITH VARIABLE CROSS-SECTIONAL PROFILES

Abstract

In this paper, the synchronous axial and bending vibration problem of elastic beams with variable cross-sectional profile and inhomogeneous material and conjugated boundary conditions is considered. The orthogonality conditions of mode shapes are derived for the case with no repeated natural frequencies, along with the constants for the corresponding time function. In that manner the response of the beam to initial excitations is covered in the theoretical aspect. The numerical background for solving the problem is explained based on the theory of numerical “shooting” method and boundary conditions of a considered mechanical case. The case of beams with no attached end masses and rigid bodies is considered in this paper. Also, one numerical example is presented to accompany theoretical considerations. The numerical procedure which is introduced in this paper can also be applied to more complex systems of elastic and rigid bodies, for instance, those considered in references [11, 15].