A hybrid meshless–statistical energy analysis method for complex structure vibration analysis

Abstract

A new hybrid deterministic–statistical energy analysis (SEA) formulation is presented by introducing a meshless method for modeling the deterministic components. Moving least square Ritz (MLSR) meshless method is applied, in which MLS is used to build the discrete model and the Ritz method allows to obtain variational formulation of the deterministic components of the governing equations. Such governing equations can be formulated via boundary conditions by penalty method and Lagrange multipliers. The hybrid model by penalty method keeps a similar formulation with the framework of the finite element SEA, while the model by the latter increases the size of the dynamic stiffness matrix and the expanded components are determined by the constraints. For validation purpose, three case studies are provided, including beam–coupled plates and plate–coupled plates built-up structure. The results by the hybrid MLSR-SEA model are compared with those by FE-SEA and Monte Carlo simulation. Good agreements of responses between the methods demonstrate the reliability of the MLSR-SEA formulation.