Integration of Dynamic Equation of a Rotating Timoshenko Beam Via Chebyshev Polynomials

Abstract

This study presents a numerical scheme for the determination of the response of rotating Timoshenko beam based on Chebyshev polynomials. The governing differential equation is formed using finite element method. The state vector is expanded in terms of Chebyshev polynomials. This reduces the original differential equations to a set of linear algebraic equations whose unknowns are the coefficient of Chebyshev polynomials. A formal procedure to generate this coefficient matrix and right-hand side vector is discussed. The numerical efficiency of the proposed method is compared with that of the Newmark method. The scheme presented in this study is shown to be accurate and is computationally efficient.