Compatibility and modal coupling, using Lagrangian multipliers as coupling mechanisms, establishes the dynamic influence of isotropic flat plates on spatial vibratory structures containing arbitrary shaped rigid bodies. The elastodynamic Euler-Lagrange equations of equilibrium and compatibility are developed and resolved into matrix form to provide a convenient format for describing deterministic and nondeterministic response characteristics of the coupled system. The resulting vibration problem is solved by classical transform methods for free and forced vibration excitations. Special cases of randomly excited systems round out the nondeterministic statistical applications. A particular example illustrates the application of analysis.

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