Vibrational Power Flow Analysis of a Generally Restrained Double-Beam Structure Coupled via a Spring-Mass System

Double-beam structure is frequently encountered in various engineering occasions, and investigation on its dynamic behavior has been attracting more and more research attention. Most of the existing studies mainly focus on the modal characteristics and forced response of the double-beam structure. Motivated by such a limitation in the literature, a vibrational power flow model of an elastically restrained double-beam coupled via a spring-mass oscillator is proposed for the first time. Structural coupling springs are introduced to simulate the discontinuity phenomenon of shear force and bending moment at the interaction position of the double-beam structure. Flexural displacement fields of double-beam structure are constructed as the superposition of standard Fourier series and boundary-smoothed auxiliary terms. Then, the system characteristic matrix is derived via the energy principle in conjunction with the Rayleigh–Ritz procedure. Dynamic information, including modal frequencies, modal loss factors, and energy flows of a double-beam structure, can be obtained by solving such a standard system matrix problem. The proposed model is validated through the comparison of results with those from other approaches and FEM. The transmission path of vibrational energy flows under various excitation frequencies is investigated. Results show that the current model can effectively overcome the numerical instability in comparison with the traditional model. Moreover, the influence of coupling restraining spring types as well as stiffness coefficients on vibrational energy flows of the double-beam structure is revealed, and the vibrational energy transmission pattern of the double-beam structure can be adjusted or controlled effectively through the appropriate design of coupling parameters in the sensitive regions.