Nonlinear poro thermal vibration and parametric excitation in a magneto-elastic embedded nanobeam using homotopy perturbation technique

Abstract

The primary focus of this study is to analyze the nonlinear vibration patterns and parametric excitation of embedded Euler–Bernoulli nanobeams subjected to thermo-magneto-mechanical loads. The Euler–Bernoulli nanobeam is developed with external parametric excitation. By utilizing nonlocal continuum theory and nonlinear von Karman beam theory, the governing equation of motion is derived. Subsequently, the homotopy perturbation technique is employed to determine the vibration frequencies. Finally, the modulation equation of Euler–Bernoulli nanobeams is derived for simply supported boundary conditions. The impacts of magnetic potential, temperature, damping coefficient, Winkler coefficient, and nonlocal parameters are tested numerically on nonlinear frequency–amplitude and parametric excitation–amplitude responses. Results demonstrate that physical variables significantly influence both nonlinear frequency behavior and parametric excitation.

Keywords

• nonlinear vibration
• parametric excitation
• porosity
• thermo-magneto-mechanical load
• euler–bernoulli nanobeam
• homotopy perturbation technique