Application of the Differential Quadrature Method to the Longitudinal Vibration of Non-Uniform Rods

Differential Quadrature Method (DQM) has a very wide applications in the field of structural vibration of various elements such as beams, plates, cylindrical shells and tanks. One of the most advantages of the DQM is its simple forms for nonlinear formulations using the Hadamard product. In this paper the free vibration of a general non-uniform rod were studied. The non-dimensional natural frequency and the normalized mode shapes of the non-uniform rod of free and clamped boundary conditions were obtained by using 15 point DQ method and compared to those of references [8] and [9]. Results shows good agreement with the previous analytical solutions. The effect of the varying cross section area on the vibration were studied. This work reflects the power of the DQM in solving non-uniform problems.