Dynamic characteristics of multi-layered, viscoelastic beams using the refined zig-zag theory. (1st March 2021) - Lewandowski, Roman; Wielentejczyk, Przemysław; Litewka, Przemysław
Highlights: The refined zig-zag theory is used to solve the dynamic problem for composite beams with viscoelastic layers. The fractional Zener model is used in analysis. The dynamic characteristics of multi-layered viscoelastic beams are of interest. The hierarchical FEM and the Laplace transform are used to derive the nonlinear eigenvalue problem. The continuation method is adopted to solve the nonlinear eigenvalue problem. Abstract: In the present paper the displacement based refined zig-zag theory is used, for the first time, to solve dynamic problems of composite and sandwich beams made of both elastic and VE layers. The linear constitutive relations are used to model physical properties of the VE layers. The rheological models can be in the classical or fractional versions, but the main focus is on the fractional Zener model. The dynamic characteristics of considered beams are evaluated. The hierarchical finite element and the Laplace transformation are used to derive the nonlinear eigenvalue problem and its solutions yield the required dynamic characteristics of beams. The continuation method is adopted to solve this problem numerically. Accuracy, effectiveness and efficiency of the proposed method are verified in several examples. The results of the presented calculations are summarized with some conclusions.