Application of Chebyshev polynomials for the analysis of rotating Timoshenko beam
A numerical scheme based on Chebyshev Polynomials for the determination of the response of dynamic systems is presented. The approach is based on the expansion of the state vector and its coefficient matrix in terms of Chebyshev Polynomials. This expansion reduces the original differential equations to a set of linear algebraic equations where the unknowns are the coefficient of Chebyshev Polynomials. Three applications are presented. The first application is a one degree of freedom linear dynamic system. The second application is a two degree of freedom linear dynamic system. The third application is a rotating Timoshenko beam. The numerical results are compared with that o f analytical method and Newmark method. The CPU time is compared with that of Runge Kutta?s method and Newmark method. A numerical study is conducted to investigate the effect of order of Chebyshev Polynomials used and the number of subintervals on CPU time and accuracy of the method presented in this work. It is concluded that this scheme not only provide accurate solution but it is also computationally very efficient.