Yufeng Xing^*, Ye Yuan, Gen Li

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.1, pp. 329-355, 2025, DOI:10.32604/cmes.2024.056440 - 17 December 2024

Abstract The separation-of-variable (SOV) methods, such as the improved SOV method, the variational SOV method, and the extended SOV method, have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells. By taking the free vibration of rectangular thin plates as an example, this work presents the theoretical framework of the SOV methods in an instructive way, and the bisection–based solution procedures for a group of nonlinear eigenvalue equations. Besides, the explicit equations of nodal lines of the SOV methods More >

A.S Vinod Kumar, Ranjan Ganguli²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 443-474, 2012, DOI:10.3970/cmes.2012.088.443

Abstract The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. More >