Abstract
Energy flow analysis (EFA) is developed to predict the vibrational energy density of beam structures with both full free layer damping (FFLD) and partial free layer damping (PFLD) treatments in the high frequency range. Both equivalent flexural stiffness and structural damping loss factor of a beam with free layer damping are obtained using the equivalent complex stiffness method. Then the energy density governing equation considering high damping effect is derived for a beam with FFLD treatment. Following obtainment of the energy transfer coefficients at both ends of free damping layer, the energy density within a beam with PFLD treatment is evaluated by solving the presented energy governing equation. To verify the proposed formulation, numerical simulations are performed for the pinned-pinned beams with FFLD and PFLD treatments. The EFA results are compared with the exact solutions from wave analysis at various frequencies, and good correlations are observed between the developed EFA results and the exact solutions.
Highlights
As one of typical structural components, lightweight beams are extensively used in mechanical and aerospace engineering in recent years
Unlike the traditional energy model for the coupled beam, the energy transfer coefficients is derived from exact wavenumber without linear approximation because the influence of high damping is not neglected for a beam with partial free layer damping (PFLD) treatment
Due to high structural damping loss factor, the energy density governing equation of a beam with full free layer damping (FFLD) is derived by using the exact wavenumber obtained without linear in good agreement with time and space averaged wave solution
Summary
As one of typical structural components, lightweight beams are extensively used in mechanical and aerospace engineering in recent years. For a beam with FFDL treatment, excited by a transverse harmonic load Fðx0Þejvt at point x = x0, as where kf[01] and kf[02] are the real and imaginary terms of wavenumber kf[0], h0 is the structural damping loss factor, m0 is the mass of per unit length and D0 is the complex flexural rigidity for the homogeneous beam. Unlike the traditional energy flow model which is only suitable for lightly damped systems, the developed energy density equation is deduced by using the exact wavenumber to evaluate the time and space averaged energy density and intensity due to high damping effect of the laminated beam. Unlike the traditional energy model for the coupled beam, the energy transfer coefficients is derived from exact wavenumber without linear approximation because the influence of high damping is not neglected for a beam with PFLD treatment. Substituting equations (49);(56) to equations (46);(48), the energy densities for the coupled beam can be predicted
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