Accelerated Harmonic Moving Force on FG Porous Nano-Beam by Using Nonlocal Strain Gradient Theory in Thermal Environment: A New Approach

The present work investigates the forced vibrations of a functionally graded (FG) nano-beam by considering the harmonic moving force with constant acceleration and initial velocity. There is no exact solution to the vibrations of nano-beam with accelerated harmonic moving force, so the main purpose of this paper is to provide a method to obtain an accurate solution for nanoscale structures under accelerated harmonic moving force. For this purpose, the equations governing nano-beam vibrations of an FG porous with the Hamilton principle are extracted by considering Euler Bernoulli’s beam theory and using the nonlocal strain gradient theory. By applying the Galerkin method, partial equations are converted to differential equations. The Laplace transform method is used to solve the differential equations. An exact solution of the temporal response for FG nano-beam under harmonic motility with constant acceleration and initial velocity in the presence of temperature is obtained. The results section investigates the effect of various parameters such as excitation frequency, power law index, temperature, porosity, and changes in moving force acceleration on the maximum dynamic displacement of nano-beam. The simultaneous effect of nonlocal parameters and dimensionless longitudinal scale on maximum dynamic displacement has also been studied. For the accuracy of the results, the natural frequency of the nano-beam is compared with previous research work. The innovation of the presented article is in providing an accurate solution using the Laplace method to analyze the forced vibrations of a porous nano-beam with an accelerated harmonic dynamic force, which has not been done so far.