Eventos Anais de eventos
COBEM 2017
24th ABCM International Congress of Mechanical Engineering
Flexural Wave Propagation in Slowly Varying Thin Plate Strip Using a Finite Element Approach
Submission Author:
Adriano Todorovic Fabro , DF , Brazil
Co-Authors:
Neil Ferguson, Brian Mace, Adriano Todorovic Fabro
Presenter: Adriano Todorovic Fabro
doi://10.26678/ABCM.COBEM2017.COB17-0819
Abstract
Abstract. This work investigates structural wave propagation in a thin plate strip with randomly varying properties along the axis of propagation, specifically when the properties vary slowly enough such that there is negligible backscattering, even if the net change is large. Wave-based methods are typically applied to homogeneous waveguides but the WKB (after Wentzel, Kramers and Brillouin) approximation can be used to find a suitable generalisation of the wave solution in terms of the change of phase and amplitude, but is restricted to analytical solutions of the equations of motion. A wave and finite element (WFE) approach is proposed to extend the applicability of the WKB method to cases where no analytical solution is available. The wavenumber is expressed as a function of the position along the waveguide and a Gauss-Legendre quadrature scheme is used to obtain the phase change while the wave amplitude is calculated using conservation of power. The WFE method is used to evaluate the wavenumbers at each integration point. Random field properties are expressed by a Karhunen-Loève (KL) expansion. Results are compared to a standard FE approach and to an available WKB analytical solution. They show good agreement and require only a few WFE evaluations, providing a suitable framework for spatially correlated randomness in waveguides
Keywords
Wave and finite elements, Karhunen-Loève expansion, uncertainty analysis, wkb approximation
