Mid-frequency vibration analysis of built-up structures using WFE-SEA method

Abstract

The idea of classifying built-up structures into hybrid deterministic-statistical subsystems is formed as a framework to deal with the dynamical response in the mid-frequency region. This paper explores the potential combination of the wavelet finite element method and SEA, resulting in the hybrid WFE-SEA method, to achieve a solution with reduced computational burdens and increased accuracy. The development of the hybrid WFE-SEA method commences with the formulation of a 3-D B-spline wavelet theory, utilizing the semi-orthogonality of B-spline wavelet. A multi-resolution analysis of this theory facilitates the creation of a 3-D B-spline wavelet on an interval element model, incorporating nodes distributed on both the surface and inside of the hexahedron. Subsequently, the 3-D B-spline wavelet on an interval element is integrated with SEA theory, producing in a hybrid WFE-SEA framework suitable for examining dynamic problems of built-up structures. The energy-balance equation is derived by coupling the 3-D B-spline wavelet theory with diffuse field reciprocity relation to estimate the mid-frequency dynamic response. Furthermore, the validity of the proposed approach is rigorously assessed by comparing it against detailed mid-frequency analyses, including the hybrid FE-SEA method and the hybrid ES-FE-SEA method. The conclusion highlights the substantial agreement of the present hybrid method with other approaches, achieved at a small cost in terms of degrees of freedom.