Free and forced vibrations of a restrained cantilever beam carrying a concentrated mass

Abstract EN

The free and forced vibrations of a uniform cantilever beam with a translational elastic constraint at the beam tip and carrying a concentrated mass at an arbitrary intermediate point are analyzed.

In the analysis, the base beam equation of motion is solved to obtain mode shape functions which satisfy all the geometric and natural boundary conditions at the beam ends.

These functions are used in conjunction with Galerkin’s method to obtain the free and the forced response.

The key parameters are stiffness ratio, mass ratio and the position of the intermediate load.

Partial computational results are compared with existing data: the agreement i^ good.

For convenient use, the results are presented in dimensionless forms.