The vibration of a nanobeam subjected to constant magnetic field and ramp-type heat under non-Fourier heat conduction law based on the Lord-Shulman model

Abstract

In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of the Lord-Shulman thermoelastic theorem which contains the non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using the Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.