An FEM-based method to evaluate and optimize vibration power flow through a beam-to-plate connection

Power flow is an important measure in vibratory energy propagation path analysis. For one-dimensional structural elements, i.e., bars or beams, power flow is obtained using a relationship involving degrees of freedom (DOF) of interest, and the respective internal forces. Several published works on vibration analysis involving the finite element method (FEM) and its optimization describe measures of interest only in terms of DOF (such as displacement and mean square velocity). However, in scenarios involving the coupling of different structures, these measures are inadequate. For example, minimizing only dynamical displacements at specific points in a structure could result in the internal forces at those points becoming unacceptably large. In such cases, minimizing power flow is preferable over minimizing displacements. In this manuscript, using FEM and a gradient-based optimization method, the authors propose a technique to evaluate and optimize vibratory power flow specifically in cases involving beam–plate coupling. The total power flow at the connection point is defined as a function of the global displacement vector, and it is evaluated for a given frequency by harmonic analysis; the relevant sensitivities are obtained using elementary matrices and the adjoint method. Geometrical parameters of the beam are used as design variables. A description of the methodology and two examples of its application to beam–plate structures are presented.