Abstract
The free and forced vibrations of a uniform beam elastically restrained against rotation at one end and against translation at the other end, and carrying a lumped mass with rotary inertia and external loading at an arbitrary intermediate point, are analyzed. The analysis involves solving the exact eigenvalue problem for the base beam to obtain the exact mode shape functions which account for the effects of the elastic restraints at the beam ends. These mode shape functions are then used in conjunction with Galerkin's method, with the lumped mass and rotary inertia treated as applied loads, to obtain the approximate eigenvalue parameters and resonance response of the beam-mass system. Parametric studies are carried out to investigate the effects of the stiffness of elastic restraints, and location and magnitude of the lumped mass and rotary inertia on the eigenfrequency parameters and resonance response of the beam-mass system. Partial computational results are compared with existing data: the agreement is generally good. For convenience, the results are presented in dimensionless form.
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