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Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions
Compact analytical models for computing the effects of compressible SFD (Squeeze Film Damping) are developed using Green's function approach. The coupling is handled by applying the structural velocity distribution to the Reynolds equation as the forcing term. The nonlinear Reynolds equation is divided into the harmonics of the oscillation frequency of the structure. Then the solution to the Reynolds equation for each harmonic is presented in order to calculate the nonlinear pressure distribution, the nonlinear damping and stiffness forces, as well as the damping ratio and frequency shift for the linear case. The nonlinearity due to the deflection amplitude of the structure and the squeeze number are investigated. It is found that the nonlinearity is directly effected by the boundary conditions for a particular configuration. The presented method allows the rapid calculation of reaction forces using the infinite series which includes the expansion of approximate mode shapes on eigenfunctions. The truncation of infinite series to the first few terms can also be represented, which is useful for system simulations. Tabulated examples can be expandable to cover more complicated and higher mode shapes. In conclusion, the present analysis provides an efficient and rapid technique for investigating both linear and nonlinear effects of SFD on rectangular elastic plates. Further, it also provides a powerful, compact and convenient tool to identify the modal damping and frequency shift for linear cases as well as pressure distribution underneath plates in practice.
Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions
Compact analytical models for computing the effects of compressible SFD (Squeeze Film Damping) are developed using Green's function approach. The coupling is handled by applying the structural velocity distribution to the Reynolds equation as the forcing term. The nonlinear Reynolds equation is divided into the harmonics of the oscillation frequency of the structure. Then the solution to the Reynolds equation for each harmonic is presented in order to calculate the nonlinear pressure distribution, the nonlinear damping and stiffness forces, as well as the damping ratio and frequency shift for the linear case. The nonlinearity due to the deflection amplitude of the structure and the squeeze number are investigated. It is found that the nonlinearity is directly effected by the boundary conditions for a particular configuration. The presented method allows the rapid calculation of reaction forces using the infinite series which includes the expansion of approximate mode shapes on eigenfunctions. The truncation of infinite series to the first few terms can also be represented, which is useful for system simulations. Tabulated examples can be expandable to cover more complicated and higher mode shapes. In conclusion, the present analysis provides an efficient and rapid technique for investigating both linear and nonlinear effects of SFD on rectangular elastic plates. Further, it also provides a powerful, compact and convenient tool to identify the modal damping and frequency shift for linear cases as well as pressure distribution underneath plates in practice.
Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions
Analytische Modellierung der Quetschfilmdämpfung für elastische Rechteckplatten mit Hilfe von Green-Funktionen
Bicak, M.M. Altug (Autor:in) / Rao, M.D. (Autor:in)
Journal of Sound and Vibration ; 329 ; 4617-4633
2010
17 Seiten, 7 Bilder, 2 Tabellen, 28 Quellen
Aufsatz (Zeitschrift)
Englisch
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