On energy and complementary energy formulations of acoustic and structural vibration problems

Abstract This paper concerns the variational formulation of the equations governing the harmonic vibration of structural and acoustic systems. It is shown that there are two possible formulations for such problems, one involving displacements only and the other involving force-like quantities only, and that these are very close duals of one another. The two principles are applied to the vibration of membranes and plates, to coupled air-membrane and air-plate vibrations, and to the vibration of an isotropic elastic solid. The paper describes the first stage in the development of a general method, of the “matrix displacement” type, for the approximate solution of coupled acousto-structural vibration problems.