Research on Numerical Computation of Natural Frequency of Transverse Vibration for Simply Supported Beam of Non-Uniform
Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.
Dongye Sun, Wen-Pei Sung and Ran Chen
B. Qian "Research on Numerical Computation of Natural Frequency of Transverse Vibration for Simply Supported Beam of Non-Uniform", Applied Mechanics and Materials, Vols. 71-78, pp. 3316-3319, 2011