A Homogenization Procedure for Nonlinear Free Vibration Analysis of Functionally Graded Beams Resting on Nonlinear Elastic Foundations
The present work deals with a homogenization procedure (HP), which is developed to reduce the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) resting on elastic nonlinear foundation with immovable ends to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results.
A. Zerkane et al., "A Homogenization Procedure for Nonlinear Free Vibration Analysis of Functionally Graded Beams Resting on Nonlinear Elastic Foundations", Applied Mechanics and Materials, Vol. 232, pp. 427-431, 2012