Sound Radiation Properties of Complex Modes in Rectangular Plates: A Numerical Study

The sound radiation properties of real normal modes are often used to characterise acoustic sources such as vibrating plates. The assumption of homogeneously distributed structural damping is usually made and in consequence the eigenmodes are real. With the increasing use of high-performance composite structures and the demanding requirements for acoustic comfort, damping treatments such as constrained layer damping or embedded elastomer layers may be distributed locally at some critical locations of the vibrating structure. This violates the assumption of homogeneously distributed structural damping and results in complex. mode shapes. In this case, dynamics of the vibrating systems within the resonances is no longer dominated by pure standing waves, but also by a superposition with travelling waves. This paper presents the results of a numerical study on sound radiation properties of this phenomenon, generally known as complex modes of vibration. The finite element model of an inhomogeneously damped plate is used to generate and investigate complex vibration patterns. The level of modal complexity of the generated complex modes is characterized by the modal collinearity index and the spatial distribution of the standing wave ratio. The fluid structure interaction is implemented by a elemental radiator approach and used for the acoustic characterisation of vibration patterns in terms of far-field radiation efficiencies and spatial distributions of sound intensity. It is shown that the eigenvector complexity can seriously affect the sound radiation properties of structural modes.