Coupling effects between a lumped vibrational source of finite impedance and a plane radiator

Abstract

A typical situation in structural acoustics and vibrations is the case of a mechanical source of vibrations attached to a large, thin structure (radiator). In general, the force input into the structure, responsible for undesired vibrations of, and radiation from, the structure, is the resultant of both the output impedance of the source and the input impedance of the structure. A theoretical analysis of the problem is presented in the case of a lumped mechanical source composed of masses, springs, and dampers, with one single attachment point to a baffled, thin, rectangular, plane structure. The coupling assumes only pure transverse force transmission into the structure. A quadrupole approach for the source assembly and a variational approach for the motion of the structure allow, respectively, the source output impedance and the structure input impedance to be calculated in a variety of configurations. The force input into the structure, kinetic energy of the structure, and radiation of sound from the structure can then be derived. It is shown how the natural frequencies of the combined system can be found from the natural frequencies of the source and structure decoupled. Numerical results are presented for the particular application of optimal suspension design of mass‐type source. [Dr. I. Michaluk is acknowledged for fruitful discussions.]