Dynamic Behaviours of Non-Uniform Rayleigh Beam under Variable-Magnitude Accelerating Masses and Resting on Non-Uniform Bi-parametric Foundation with General Boundary Conditions

This paper investigates the dynamic behaviours of non-uniform Rayleigh beam under variable-magnitude accelerating masses and resting on non-uniform bi-parametric foundation with general boundary conditions. The problem is governed by a fourth-order partia l differential equation, generalised Galerkin’s method use to reduces the fourth-order partial differential equation to sequence second-order ordinary differential equations. Two cases are examined: moving force (neglecting inertia term) and moving mass (considering inertia). In order to solve the moving force problem, the transverse displacement response is obtained by variation of parameters. In order to solve the moving mass problem, the Runge-Kutta of fourth order is used to obtain the approximate solution because the commonly used Struble asymptotic method was unable to simplify the coupled second order ordinary differential equation due to the variability of the load magnitude. Analytical and numerical solutions (Runge-Kutta) are compared for validation of accuracy of the Runge-kutta scheme and found compared favourably. The results are presented in plotted curves, illustrating the effects of shear modulus, rotatory inertia correction factor results show increased shear moduli and rotatory inertia decrease response amplitudes, and critical speed for moving mass is lower than for moving force, leading to earlier resonance. Resonance conditions for the dynamical system are also established.