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

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 (x = 0) and yields the natural frequencies for the dynamic case with a prescribed value of axial load (Po Pcr). The obtained solutions were verified against those obtained from FEM and found in close agreement.