Forced vibrations of a beam elastically restrained against rotation and carrying a spring-mass system

An exact solution for the title problem is obtained in closed form fashion in the case of a Bemoulli-Euler beam. It is assumed that the exciting force is applied to the mass which is elastically mounted on the beam. The mathematical model constitutes a first order approximation to a motor or engine elastically mounted on a structural element. The operation of the machine generates a transverse, sinusoidally varying force. The problem is of basic interest in mechanical, naval and ocean engineering systems from the point of view of the determination of dynamic displacements and stresses; sound radiation calculations, etc. The present problem arose in connection with the mounting of an engine on a structural beam in a small naval vessel and when excessive vibrational level was noted. This study was undertaken in order to understand the physical problem and to correct the mechanical situation. (C) 2002 Elsevier Science Ltd. All rights reserved.