Diffuse transmission of structure-borne sound at periodic junctions of semi-infinite plates

Abstract

Vibration attenuation at junctions of point connected plates is an important aspect of structure-borne sound transmission in many realistic structures. The vibrational response of point connected plates can be predicted using statistical energy analysis (SEA), where coupling loss factors are calculated based on mobility formulations. However, in the process of deriving the coupling loss factors for point connected systems, a number of assumptions and simplifications were introduced. In this paper, a more advanced calculation model, based on a wave approach for elastically coupled semi-infinite plates, is presented. Local rigid connections are modeled using an elastic interlayer characterized by a space-dependent stiffness. Periodic boundary conditions are assumed at the junction and the plate response is described using a Fourier decomposition technique. Calculation results obtained for two different junction geometries demonstrate the influence of the distance between the point connections on the structure-borne sound transmission. Finally, a comparison between a number of numerical and experimental results illustrates the ability of the model to predict the influence of the density and the width of the point connections with good accuracy.

Modeling vibrational energy transmission at bolted junctions between a plate and a stiffening rib

“…17. Since the remaining bending wave parameters (α zp ,F yp ,M zp ) can be expressed in terms of the transverse displacement η p , they can be written in a form very similar to Eq.…”

“…Both aspects are discussed in the following paragraphs. 17. In this paper, the bolted connection is modelled by a step-wise variation of the spring stiffness, leading to a periodic boundary condition.…”

“…The periodic boundary condition at the junction, characterized by a spatial period L, causes diffuse reflection and transmission of structure-borne sound waves on the source and receiving plates. 17 The forces and displacements at the edges of the coupled plates are expressed in terms of the unknown amplitudes of the waves in the resulting scattered wavefields. The wave amplitudes are calculated as the solution of a system of equations consisting of equilibrium and continuity conditions at the junction.…”

“…17 For local connections with a finite width, the spring stiffness is constant over the width of each connection, and zero elsewhere. For idealized point connections, the spring stiffness is expressed in terms of a dirac function.…”

“…Craik et al 16 used the modal approach to model point connections between a beam and two parallel plates. Bosmans and Vermeir 17 presented a more complete theory where a point connected plate junction is modelled using an interlayer with a spatially dependent stiffness. The spatial variation is assumed to be periodic and the plate response is described by a scattered wavefield.…”