Modeling of nonlocal porous functionally graded nanobeams under moving loads

This study focuses on the dynamic response of porous functionally graded nanomaterials to moving loads. The analysis was performed using two approaches: the Ritz method with the help of the benefits achieved by employing Chebyshev polynomials in the cosine form and the differential quadrature method with further inverse Laplace transformation. Both approaches utilize the formulation of a nano-thin beam considering an improved higher-order beam model and nonlocal strain gradient theory with two characteristic length scales, referred to as nonlocality and strain gradient length scales. Power-law dependencies steer the constituent designs of pore-graded materials toward pore factors that influence pore volume either with a uniform or non-uniform distribution of pores. Moreover, a variable scale modulus was adopted to further improve accuracy by considering the scale effects for graded nano-thin beams. The first part of the study addresses the equation of motion, which is solved by applying the Ritz technique with Chebyshev polynomials. In the second part, the governing equations for nanobeams are discussed where the differential quadrature method is used to discretise them further, and the inverse Laplace transform is used to obtain the dynamic deflections. The results of the present study elucidate the effects of the moving load speed, nonlocal strain gradient factors, porosity, pore number and distribution, and elastic medium on the dynamic deflection of functionally graded nanobeams.