A substructured version of the variational theory of complex rays dedicated to the calculation of assemblies with dissipative joints in the medium‐frequency range

Abstract

PurposeThis paper deals with numerical techniques dedicated to the predictive calculation of complex structures undergoing medium‐frequency vibrations. This field presents challenging difficulties. The first difficulty is the development of an efficient computational method because with the traditional finite element method (FEM), as the frequency increases, it becomes more expensive to control the pollution error. The second difficulty is the availability of sufficiently realistic joint models to take into account damping phenomena because in vibration problems dissipation controls the magnitude of the response directly.Design/methodology/approachWe use the Variational Theory of Complex Rays (VTCR), an approach which effectively avoids the difficulties encountered with traditional FE techniques. Using two‐scale shape functions which verify the dynamic equation and the constitutive relation within each substructure, the VTCR can be viewed as a means of expressing the power balance at the different interfaces between substructures in variational form. New joint models which include heterogeneous mass, stiffness and damping are introduced to deal with the second difficulty.FindingsThis paper focuses on a new, substructured version of the VTCR which enables us to separate the realistically modeled substructures from the less accurate joints. The equations of the substructures are enforced exactly, whereas the interface equations are verified approximately through the minimization of an L2 residual. We show that this new formulation gives good results compared to the traditional VTCR or the FEM.Practical implicationsAlthough the examples presented in this paper are very simple, this new formulation shoult encounter no difficulties when dealing with more complex assemblies composed of several plates, beams, shells,…Originality/valueThis new, substructured VTCR approach provides more flexibility in the improvement of joint models, for example by carrying out experimental measurements on real structures.