Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method

Abstract The stability behavior and free vibration of axially loaded tapered columns with rotational and/or translational end restraints are studied using the differential quadrature method (DQM). The governing differential equations are derived and transformed into a homogeneous system of algebraic equations using the DQM technique. The boundary conditions are discretized and substituted into the governing differential equations, then the problem is transformed into a two parameter eigenvalue problem, namely the critical load and the natural frequency. The solution of the eigenvalue problem yields the critical load for the static case ( ω  = 0) and yields the natural frequencies for the dynamic case with a prescribed value of axial load ( P o P cr ). The obtained solutions were verified against those obtained from FEM and found in close agreement.