Dynamical Analysis of Non-Uniform Rayleigh Beam Resting on Bi-Parametric Vlasov Foundation and Under Distributed Masses Moving at Varying Velocities

O.K. Ogunbamike

Department of Mathematics, Adeyemi College of Education, Ondo, Nigeria.

In this paper, the problem of the dynamic response of non-uniform Rayleigh beams resting on two-parameter Vlasov elastic foundation and under partially distributed masses travelling at varying velocities is investigated. The governing equation is a non-homogeneous fourth order partial differential equation with variable and singular coefficients. In order to solve the problem, the solution technique is based on the Generalized Galerkin Method (GGM), the expansion of Heaviside function in series form, a modification of the Struble’s asymptotic method and then the use of Fresnel sine and cosine integrals. Analytical solutions are obtained and presented in plotted curves. Result show that as the rotatory inertia correction factor increases, the response amplitudes of the dynamical system decreases for fixed values of foundation stiffness, shear modulus and axial force. Similarly, as the foundation stiffness, shear modulus and the axial force increase, the deflection of Rayleigh beams under the distributed loads decreases. It is also shown that the moving distributed force solution is not an upper bound for the accurate solution of the moving distributed mass problem; hence, the non-reliability of the moving force solution as a safe approximation to the moving distributed mass problem is established.