The structural power flow through the junction between two flat plates, coupled in an L-shaped configuration, is considered using the mobility power flow ͑MPF͒ approach, for both in-plane ͑longitudinal and shear͒ and out-of-plane ͑bending͒ waves' propagation. Power flow by both types of waves is included by considering the junction edge between the two plates, when uncoupled, to be free. Mobility expressions are then derived for both in-plane and out-of-plane degrees of freedom forces and responses. The results of the analysis show that the in-plane waves do not significantly contribute to the structural power flow at relatively low frequencies, that is, for frequencies below a bending wave number and plate thickness product of approximately 0.1. In this case, the power flow results are not different from those obtained if the junction is assumed to be pinned, and power is transmitted by only the out-of-plane waves. However, as the frequency increases, the significance of the in-plane waves' contribution increases, and for a bending wave number and plate thickness product greater than approximately 1.0, the contribution from the in-plane waves dominates. This condition is different from the well-known result that if the thickness is greater than approximately 10% of the bending wavelength, simple bending theory does not apply. This condition deals with the significance of the in-plane waves. In the frequency region where the in-plane waves dominate, the in-plane longitudinal waves are more significant than the in-plane shear waves, although this has some dependence on the selected L-shaped configuration. The in-plane longitudinal waves couple directly to the out-of-plane waves because of the 90 degree junction.

In the analysis of the power transmission through junctions between thick plate structures, it is necessary to consider not only the transverse bending motion of the plates but also the in-plane wave motion. That is, for these types of structures both the shear and rotary inertia effects and the in-plane wave effects must be considered simultaneously in order to obtain a complete solution to the problem. In this paper, a statistical energy analysis approach is developed to evaluate the power transmission through the junction between two plates in an L-shaped configuration, where the solution includes the shear and rotary inertia effects (Mindlin bending) and the in-plane waves effects. Analytical results are presented for the absorption (or transmissibility) of the junction and the ratio between the incident bending wave power and the transmitted waves (bending and in-plane) power. Results for pure (classical) bending are also presented for comparison with the Mindlin bending results.

The mobility power flow (MPF) approach is used in this paper to describe the flexural behavior of an L-shaped plate structure consisting of thick plates with rotary inertia and shear deformation effects included in the analysis. The introduction of the thick plate effects significantly increases the complexity of the structural mobility functions used in the definitions of the power flow terms; however, because of the substructuring that is used in the MPF approach, the complexity of the problem is significantly reduced as compared to solving for the global structure. Additionally, with the MPF approach the modal behavior is described. The MPF analysis of the L-shaped plate is performed for the case of point force excitation on one plate, with the two plates being identical in both size and thickness. The results of this analysis are compared to results from the finite-element analysis (FEA) and the statistical energy analysis (SEA) and show very good agreement in the low- and high-frequency regimes, respectively.

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One approach to modeling the resonant behavior of structures in a compressible fluid is to use finite elements to describe the structure and boundary elements to describe the fluid. The fluid loading is characterized by a complex, frequency-dependent influence matrix that is combined with the frequency-independent stiffness and mass matrices obtained from the finite element model. This approach works well for determining the fluid-loaded harmonic response of the structure over a specified frequency range, if one knows the appropriate frequency range over which to perform the analysis. Since the in-fluid resonance frequency is usually not known, the designer must choose successive frequency sets until the resonance peak is found. This paper describes a method that eliminates this guesswork by computing the in-fluid eigenfrequency of the mode of interest using boundary elements to model the fluid loading. The procedure is iterative, beginning with the in vacuo eigenfrequency and continuing until the in-fluid eigenvalue converges. The designer may then perform a harmonic analysis in a narrow band about the computed eigenfrequency to obtain the structural and/or acoustic response levels. The accuracy and efficiency of the technique is demonstrated with two examples: a spherical shell and a low-frequency projector, both in water.