On the Nonlinear Forced Vibration of the Magnetostrictive Laminated Beam in a Complex Environment

Nicolae Herisanu, Bogdan Marinca and Vasile Marinca ()
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Nicolae Herisanu: Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, Romania
Bogdan Marinca: Department of Applied Electronics, University Politehnica Timisoara, 300006 Timisoara, Romania
Vasile Marinca: Department of Mechanics and Strength of Materials, University Politehnica Timisoara, 300222 Timisoara, Romania

Mathematics, 2024, vol. 12, issue 23, 1-24

Abstract: The present study dealt with a comprehensive mathematical model to explore the nonlinear forced vibration of a magnetostrictive laminated beam. This system was subjected to mechanical impact, a nonlinear Winkler–Pasternak foundation, and an electromagnetic actuator considering the thickness effect. The expressions of the nonlinear differential equations were obtained for the pinned–pinned boundary conditions with the help of the Galerkin–Bubnov procedure and Hamiltonian approach. The nonlinear differential equations were studied using an original, explicit, and very efficient technique, namely the optimal auxiliary functions method (OAFM). It should be emphasized that our procedure assures a rapid convergence of the approximate analytical solutions after only one iteration, without the presence of a small parameter in the governing equations or boundary conditions. Detailed results are presented on the effects of some parameters, among them being analyzed were the damping, frequency, electromagnetic, and nonlinear elastic foundation coefficients. The local stability of the equilibrium points was performed by introducing two variable expansion method, the homotopy perturbation method, and then applying the Routh–Hurwitz criteria and eigenvalues of the Jacobian matrix.

Keywords: magnetostrictive material; composite beam; curvature; thickness effect; Winkler–Pasternak foundation; electromagnetic actuator; Routh–Hurwitz criteria (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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