DYNAMIC STIFFNESS METHOD FOR OUT-OF-PLANE FREE VIBRATION ANALYSIS OF PLANAR CURVED BEAMS

This paper extends the dynamic stiffness method to the out-of-plane free vibration analysis of planar curved beams. The boundary value problem (BVP) for ordinary differential equations (ODEs) which governs element’s dynamic stiffnesses is set up and solved by ODE solver COLSYS to get the numerical exact values of element’s dynamic stiffnesses. The mesh generated by COLSYS in solving such ODEs is taken as a sub-mesh to calculate the counting of element’s fixed-end frequency. On this sub-mesh, each sub-element’s dynamic stiffnesses are reduced to linear combination of such ODE solutions. Thus by implementing Wittrick-Williams algorithm on each element, its fixed-end frequency counting is obtained. The derivatives of the dynamic stiffnesses to the frequency are also reduced to solve corresponding ODEs by using COLSYS. Thus the guided and guarded Newton method is set up and structural exact frequencies and vibration modes can be obtained. The numerical examples demonstrate that this method is accurate, reliable and effective.