This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necess...This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.展开更多
This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic gover...This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic governing equations are employed to study this nonlinear problem. An elliptical integral method, which was recently developed for the nonlinear panel cavity problem, is introduced here to solve for the structural-acoustics responses. The present results agree reasonably well with those obtained from the classical harmonic balance method. Modal convergences of the nonlinear solutions are performed to verify the proposed method. The effects of vibration amplitude and leakage size are studied and discussed. It is found that （1） the edge leakages in a panel cavity system significantly affect the natural frequency properties, and （2） the edge leakages induce a low frequency acoustic resonance.展开更多
文摘This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.
基金Project supported by the City USRG Grant(No.7004701),China
文摘This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic governing equations are employed to study this nonlinear problem. An elliptical integral method, which was recently developed for the nonlinear panel cavity problem, is introduced here to solve for the structural-acoustics responses. The present results agree reasonably well with those obtained from the classical harmonic balance method. Modal convergences of the nonlinear solutions are performed to verify the proposed method. The effects of vibration amplitude and leakage size are studied and discussed. It is found that （1） the edge leakages in a panel cavity system significantly affect the natural frequency properties, and （2） the edge leakages induce a low frequency acoustic resonance.
