Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

摘要: In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, both cantilever and pinned-free boundary conditions. The bending displacement rotation due to are assumed be simple polynomials which satisfy all four It found that certain polynomial variations material mass density, elastic modulus shear modulus, along length serve as closed form solutions coupled second order differential with variable coefficients. there infinite number analytical functions possible distributions, share same frequency mode shape particular mode. derived results intended benchmark testing approximate or numerical methods used analysis beams.