Natural frequencies and modes of a Timoshenko beam

Abstract

In this paper, we present a systematic approach to solving the eigenvalue problems associated with the uniform Timoshenko beam model. Properties of the natural frequencies and modes are discussed for the pinned–pinned and cantilever beam, e.g., double eigenvalues, estimates for small and large eigenvalues, significance of dimensionless parameters and remarkable mode shapes. Our results expand on and complement existing results.