An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

摘要

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations ofthe Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the HomotopyAnalysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbucklingload-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis arevalidated with the published results, and excellent agreement is observed. The effects of some parameters,such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters arefixed.