Dynamic response and power flow in two-dimensional coupled beam structures under in-plane loading

Abstract

This paper is concerned with the prediction of dynamic response of planar coupled beam structures in the low and medium frequency ranges. Based on the receptance concept, the modal properties of the components of the coupled systems with specific boundary conditions are used to form the receptance matrix for the determination of the internal force and displacement response of the coupled structures. Only in-plane loading is considered here and so the structural response will include the longitudinal and in-plane flexural waves only and the torsional and out-of-plane flexural vibrations are not considered here. The mechanism of power flow through the joint boundaries of the in-plane coupled beam structures is investigated by calculating the power flow components of different wave types. The results from the receptance model are compared with that from the finite element analysis and the traveling wave solutions. Good agreement was found. Examples of connected beams are presented, and the characteristics of the power flow and wave interaction are highlighted.

Power Flow Analysis of Complex Coupled Systems by Progressive Approaches

“…Cuschieri [13,14] used a mobility approach to analyze the power #ow in periodically connected beams and¸-plates subject to a single excitation. Farag and Pan [15] extended Cuschieri's work to coupled two-dimensional beam structures with multiple joints under in-plane loading. The mobility functions of vacuous elastic cylindrical shells were numerically studied by Ming et al [16] and applied to estimate both the input power and the power #ow in coupled "nite cylindrical shell systems.…”

Energy Flow Theory of Nonlinear Dynamical Systems with Applications

“…The former method chooses the coupling forces at the interfaces as the variables while the latter chooses the coupling interface displacements. This approach was employed to investigate the amount of power flows at joints of beams and plates (Clarkson 1991) and at the interface of two coupled rectangular plates (see, Dimitriadis & Pierce 1988;Farag & Pan 1996;Beshara & Keane 1998).…”

“…The vibrational power flow into a sub-member and between them is expressed in terms of input and transfer structural mobility functions to explore the power flow behaviour of dynamic structures. Petersson & Plunt (1982) proposed an effective point mobility method in the prediction of structure-borne sound transmission between a source and a receiver structure, which was used to model the vibration power flow transmission through periodic structures by Cuschieri (1990ab), multiple beams, coupled beam structures under in-plane loading by Farag & Pan (1996). The mobility functions of vacuous elastic cylindrical shells were numerically studied by Ming, Pan & Norton (1999) and applied to estimate both the input power and the power flow in coupled finite cylindrical shell systems.…”