Análise dinâmica de placas duplas e delgadas pelo método dos elementos de contorno

Abstract

Plates are structural elements widely used in engineering applications, appearing in

fields such as Civil Engineering, Mechanical Engineering, and Aerospace Engineering. Double- plate systems, in particular, are found in sandwich structures, nanometric structures, and

highway and railway pavements, the latter two often being subjected to dynamic loading conditions. Accurate analysis of these systems is essential, especially when their interaction with elastic foundations is considered. Although analytical solutions are important, they are frequently restricted to simple geometries and boundary conditions, which limits their applicability. In this context, the primary objective of this work is to develop numerical solutions, using the Boundary Element Method (BEM), for thin double-plate systems connected by a Winkler elastic foundation under steady-state dynamic conditions. In addition, secondary discussions are extended to isolated single plates or single plates supported by a Winkler elastic foundation. The construction and validation of the numerical solutions presented in this study follow these steps: initially, the differential equations of motion defined in the continuous medium (plate) are transformed into equivalent integral equations valid over the domain and/or boundary of the plate through the application of the weighted residual method (where the equations of motion are weighted by fundamental solutions). A key contribution of this work is the original derivation of the fundamental solutions for the dynamic problem of double plates, which were previously unavailable in the literature. The discrete solution of the dynamic plate problem is obtained by discretizing the boundary into linear isoparametric boundary elements. After evaluating the corresponding integrals, an algebraic system is assembled. Finally, once the boundary conditions are imposed, the dynamic responses can be determined. Several examples using the BEM solution are presented and validated against analytical and/or numerical solutions, yielding relative errors lower than 1% for a discretization with 32 straight elements in rectangular plates and 8 curved (arc) elements in circular plates, implying on consistence of BEM solution showed.