In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical-energy analysis (SEA) or finite-element analysis (FEA) are generally used. However, an alternative method is to use vibrational power-flow techniques that can be especially useful in the midfrequencies between the optimum frequency regimes for FEA and SEA. Mobility power-flow analysis has, in general, been used for one-dimensional beamlike coupled structures or for point-coupled structures. In this paper, the power-flow technique is extended to two-dimensional platelike coupled structures joined along a common edge. Because of the inherent advantages in using this power-flow approach, frequency or spatial averaging is not required, and thus the resonant modal response of the coupled structure is determined. The mobility power-flow results are compared to results obtained using FEA and SEA. The agreement with FEA results is good at low frequencies. However, the power-flow technique has an improved computational efficiency as the frequency increases. Compared to the SEA results, the power-flow results show a closer representation of the actual modal response of the coupled structure.

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.

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The scattering of a plane acoustic wave by a fluid-loaded, thin, elastic plate, of infinite extent, with a distributed mass inhomogeneity is investigated. Two approaches are presented, an iterative approach valid when a measure of the distributed impedance is much lower than that of the uniform fluid-loaded plate, and a full numerical solution which while having no restricting assumptions is somewhat demanding computationally. For the iterative solution a set of correction terms is evaluated and applied to the response of the uniform plate with no inhomogeneities. The number of correction terms required is dependent on the relative magnitude of the inhomogeneity. In the full numerical solution, the presence of the distributed inhomogeneity in the equation of motion, when expressed in the wave-number domain, results in a Fredholm integral equation of the third kind. By substituting for the product of the response and the plate characteristic equation (impedance), the Fredholm integral of the third kind is reduced to a Fredholm integral of the second kind. The plate response in the spectral wave-number domain is obtained from the solution of the Fredholm integral. Inverse Fourier transforming the wave-number domain response function gives the spatial domain solution for the response. The hybrid numerical analytical approach [J. Acoust. Soc. Am. 95, 1998–2005 (1994)] is used to perform the inverse Fourier transform. The far-field scattered pressure is obtained from the spectral domain solution of the response. Response and scattered pressure results for distributed mass inhomogeneities, with different distribution functions, are presented and compared to the results for a line inhomogeneity.