DYNAMIC ANALYSIS OF A NON-PRISMATIC DAMPED CANTILEVER THIN BEAM RESTING ON AN EXPONENTIALLY DECAYING ELASTIC FOUNDATION UNDER CONSTANT AND HARMONIC DISTRIBUTED LOADS

Abstract

This research examines the dynamic response of a non-prismatic damped cantilever thin beam (NPDCTB) under constant distributed load (CDL) and harmonic distributed load (HDL). The beam governing equation is a fourth-order partial differential equation (PDE), which is reduced into a second-order ordinary differential equation (ODE) using the generalized Galerkin method (GGM). The resulting ODEs are solved analytically for both loading cases using Laplace transforms (LT) and convolution theory (CT) to evaluate the transverse deflection of the NPDCTB. The effects of load speed c, axial force, damping coefficient, beam depth, and beam breadth on the dynamic response are examined and presented in the curve. The results showed the significant influence of cantilever boundary conditions on the vibration characteristics of non-prismatic beams under dynamic loading. The results demonstrate that load speed significantly amplifies the transverse deflection, while increases in axial force, damping coefficient, beam depth, and beam breadth lead to reductions in vibration amplitude.