Abstract

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

곡선보(curved beam)의 회전관성(rotatory inertia) 및 전단변형(shear deformation)을 고려한 평면내(in-plane) 자유진동을 해석하는데 미분구적법(DQM)을 이용하여 고정-고정 경계조건(boundary conditions)과 다양한 굽힘각(opening angles)에 따른 진동수(frequencies)를 계산하였다. DQM의 결과는 엄밀해(exact solution) 또는 다른 수치해석(Rayleigh-Ritz, Galerkin 또는 FEM) 결과와 비교하였으며, DQM은 적은 요소(grid points)를 사용하여 정회한 해석결과를 보여주었다.

Keywords

• circular curved beam;
• DQM;
• fundamental frequencies;
• rotatory inertia;
• vibration;
• shear deformation;
• numerical solution