Dynamic analysis of non-uniform beams and plates by finite elements with generalized degrees of freedom

A finite element with generalized degrees of freedom (FEGDOF) and a finite strip with generalized degrees of freedom (FSGDOF) are developed for the dynamic analyses of beams and plates with cross-section varying in a continuous or discontinuous manner. The degrees of freedom (DOF) of the finite element are transformed into generalized degrees of freedom (GDOF). The admissible interpolating functions for the FEGDOF and FSGDOF are derived accordingly. To the best knowledge of the authors, it is the first time that the second order polynomials are employed in the dynamic analysis of flexural beams and plates, which simplifies the derivation of finite element or finite strip formulation. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.