Trigonometric Higher-Order Shear Deformation Theory on Exact Solution for Lateral and Longitudinal Dynamic Response of Magneto-Electric Carbon Nanotube-Reinforced Composite Beams Under Two Moving Loads Resting on Winkler-Pasternak Foundation

This paper aims to analyze the transverse and axial dynamic response of magneto-electric carbon nanotube-reinforced composite (CNTRC) beams under two moving constant loads resting on an elastic foundation. The governing equations of the magneto-electric CNTRC beam are obtained based on Mantari's shear deformation beam theory, Hamilton's principle, and Laplace transforms to solve the derived differential equations. The beams, which include a Winkler spring and shear layer, are considered as resting on the elastic foundation. The boundary conditions for this work are simply supported. This marks the inaugural instance in which a precise analytical approach rooted in mathematical principles has been employed to examine these constructions. The drawback inherent in this technique lies in its reliance on a simply supported boundary condition, stemming from the challenge associated with performing Laplace inversion on the Coupled equations. A comparison with previous studies has been conducted, which is a valuable contribution. Several examples were used to analyze the magnetic, voltage, and spring constant factors, the volume fraction of carbon nanotubes (CNTs), the velocity of a moving constant load, and their influence on the transverse and axial dynamic responses and maximum deflections.