Investigation of moving load-induced vibrations in layered functionally graded Terfenol-D beams: a differential quadrature method and analytical approach

Abstract

The paper investigates the potential of the full-sinusoidal Fourier series as a solution form for the deflection of layered functionally graded beams associated with smart actuators, drawing on the fundamental principles of classical Fourier series theory. The current method simplifies the difficult beam problem to a set of linear algebraic equations by using the Duhamel integration technique and the orthogonality of the trial function. The study takes into account generalized boundary conditions and moving forces, which are seldom discussed in previous research. Under the action of a moving load, the boundary value problem for a functionally graded beam integrated with Terfenol-D is efficiently addressed using the approach of combined differential and integral quadrature. The generalized boundary conditions may be easily achieved by adjusting the stiffness of the restraining springs. The significant agreement between the differential quadrature solution and the Fourier series solution underlines the efficiency and accuracy of both methods. Furthermore, the influences of various crucial physical characteristics on the natural frequencies and the essential flow velocities are explored, including boundary stiffness, foundation parameters, and geometric parameters.