A SELF-ADAPTIVE FEM FOR FREE VIBRATION ANALYSIS OF PLANAR CURVED BEAMS WITH VARIABLE CROSS-SECTIONS

This paper presents a self-adaptive Finite Element Method (FEM) for the free vibration analysis of planar curved beams. The method integrates several techniques such as the Wittrick-Williams algorithm and the guided and guarded Newton method in the exact Dynamic Stiffness Method (DSM) for the vibration analysis of skeletal structures, and the self-adaptive FEM for linear BVP based on the Element Energy Projection (EEP) super-convergence calculation. The method can yield exact numerical results, i.e. the accuracy of the frequencies and the modes can satisfy the user-preset error tolerances. The finite element model on the infinitely dense mesh can be reduced to the exact dynamic stiffness model by condensation, thus it can produce exact results theoretically. Based on this comparison, the equivalence between the self-adaptive FEM and the exact DSM is set up. As a result, the corresponding equivalent formulae and equivalent algorithm are established and the two-phase algorithm for the exact DSM is extended to the self-adaptive FEM. The representative numerical examples show that this method is accurate, reliable and efficient.