Nonlinear Forced Vibration, Post‐Buckling, and Nonlinear Waves in FG Porous GOri‐Reinforced Beams Under Variable Excitation and Various Physical Conditions

ABSTRACT

Based on a two‐dimensional beam theory, linear vibration, nonlinear forced vibration, and post‐buckling analyses of functionally graded (FG) porous metal beams reinforced with FG graphene origami (GOri) are investigated here for the first time. Moreover, nonlinear waves (periodic, super‐periodic, solitary, and kink (antikink) waves) in Euler–Bernoulli composite beams are studied as a special case based on the bifurcation method. In addition, the chaotic behavior of the perturbed dynamical system is also discussed. The present beam is assumed to be resting on the Pasternak foundation and subjected to external variable excitation and in‐plane compressive load as well as various physical conditions such as elevated temperature, humidity, and magnetic field. Maxwell's relations are used to establish the Lorentz force. The beam under consideration is structured from multilayered nanocomposites, with each layer being homogeneous and isotropic, composed of a porous copper matrix reinforced by GOri. In accordance with the von Kármán nonlinearity model, the nonlinear equations of motion are developed from Hamilton's principle. The Navier method is employed to obtain the eigenfrequency. While Galerkin and the fourth‐order Runge–Kutta methods are used to solve the nonlinear equations and then obtain the post‐buckling path and nonlinear deflection. The obtained results are validated by comparing them with existing findings available in the literature. Influences of various parameters such as the length‐to‐depth ratio, porosity factor, GOri volume fraction, types of porosity and GOri distributions, temperature, humidity, magnetic parameter, and elastic foundation parameters on the linear and nonlinear vibrations, post‐buckling curves, and nonlinear waves in the porous GOri/copper beams are investigated.