Vibrational power flow in thick connected plates

The total vibrational power flow in connected plate structures is investigated using an analytical "Power Flow" approach. The effects of shear and rotary inertia on the flexural wave transmission and the influence of in-plane wave generation at structural discontinuities are included in the analytical model. In formulating a Power Flow model, the structure is divided into substructures whose responses may be determined analytically to obtain expressions for the input and transfer mobilities of the substructures. For the case of plate-type structures joined along a line, the mobilities are functions of both frequency and space. The power transmission between the individual plate substructures is then written as a function of these mobility expressions. The structure of concern in this dissertation consists of two plates connected in an L-configuration. In obtaining the expressions for the mobilities, the vibrational response of the individual plates is determined by solving the appropriate equations of motion. In this study the antisymmetric (flexural) motion is described using Mindlin's (1951) thick plate approximation to the three-dimensional equations of motion. The applicability of this thick plate formulation is limited to frequencies below the frequency of the first antisymmetric mode of thickness-shear vibration of the plate. The symmetric (in-plane) motion of the plates is described using the generalized theory of plane stress which neglects the direct coupling of the in-plane motion with the thickness vibration modes, and is therefore valid only for frequencies which are lower than the frequency of the first mode of pure thickness vibration of the plate. The results for the power transmission in the L-plate obtained using the Power Flow formulation are verified at high frequencies by comparison with the results obtained using the Statistical Energy Analysis (SEA) technique. The SEA formulation for the L-plate is based on Mindlin's equations for flexural motion and the theory of generalized plane stress for in-plane vibration. The results of the Power Flow formulation are verified at low frequencies by the results obtained using a Finite Element model of the L-shaped plate.