In-Plane Extensional Vibration Analysis of Asymmetric Curved Beams with Linearly Varying Cross-Section Using DQM

The increasing use of curved beams in buildings, vehicles, ships, and aircraft has results in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic curved beams has been the subject of a large number of investigations. Solutions of the relevant differential equations have traditionally been obtained by the standard finite difference. These techniques require a great deal of computer time as the number of discrete nodes becomes relatively large under conditions of complex geometry and loading. One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method(DQM) has been applied to a large number of cases to overcome the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In this study, the in-plane extensional vibration for asymmetric curved beams with linearly varying cross-section is analyzed using the DQM. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The results are compared with the result by other methods for cases in which they are available. According to the analysis of the solutions, the DQM, used only a limited number of grid points, gives results which agree very well with the exact ones.