DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy-Bickford beam

Abstract

The free vibration analysis of semi-rigid-connected Reddy–Bickford beams on elastic soil with/without axial force effect using the differential transform method (DTM) and the differential quadrature element method (DQEM) has not been investigated by any of the studies in the open literature so far. In this study, DTM and the recently proposed DQEM are employed in order to solve the governing differential equations of a Reddy–Bickford beam with two regions on elastic soil. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. An efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The equilibrium equations are deduced, together with the boundary conditions, and then a recently proposed DQEM is employed, in order to solve the resulting boundary value problem. The calculated natural frequencies of semi-rigid-connected Reddy–Bickford beam with two regions on elastic soil using DTM and DQEM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed. Copyright © 2009 John Wiley & Sons, Ltd.