A finite element formulation is presented for the analysis of the aeroelastic effect on the aerothermoacoustic response of metallic panels in supersonic flow. The first-order shear deformation theory(FSDT) and the von...A finite element formulation is presented for the analysis of the aeroelastic effect on the aerothermoacoustic response of metallic panels in supersonic flow. The first-order shear deformation theory(FSDT) and the von Karman nonlinear strain-displacement relationships are employed to consider the geometric nonlinearity induced by large deflections. The piston theory and the Gaussian white noise are used to simulate the mean flow aerodynamics and the turbulence from the boundary layer. The thermal loading is assumed to be steady and uniformly distributed, and the material properties are assumed to be temperature independent. The governing equations of motion are firstly formulated in structural node degrees of freedom by using the principle of virtual work,and then transformed and reduced to a set of coupled nonlinear Duffing oscillators in modal coordinates. The dynamic response of a panel is obtained by the Runge-Kutta integration method. The results indicate that the increasing aeroelastic effect can lead the panel vibration from a random motion to a highly ordered motion in the fashion of diffused limit cycle oscillations(LCOs), and remarkably alter the stochastic bifurcation and the spectrum of the aerothermoacoustic response.On the other hand there exists a counterbalance mechanism between the external random loading and the aeroelastic effect, which mainly functions through the nonlinear frequency-amplitude response. It is surmised that the aeroelastic effect must be considered in sonic fatigue analysis for panel structures in supersonic flow.展开更多
This paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive.The governing equation of motion of the objective system is developed by virtue of Lagrangian’s method.A complicated term is ...This paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive.The governing equation of motion of the objective system is developed by virtue of Lagrangian’s method.A complicated term is broached in the governing equation of the motion of the system owing to existence of multiplication of a quadratic function of velocity with a sinusoidal function of displacement in the kinetic energy of the system.The obtained equation is an example of a well-known category of nonlinear oscillators,namely,non-natural systems.Due to the complex terms in the governing equation,perturbation methods cannot directly extract any closed form expressions for the natural frequency.Unavoidably,different non-perturbative approaches are employed to solve the problem and to elicit a closed-form expression for the natural frequency.Energy balance method,modified energy balance method and variational approach are utilized for frequency analyzing of the system.Frequencyamplitude relationships are analytically obtained for nonlinear vibration of the elevator’s drum.In order to examine accuracy of the obtained results,exact solutions are numerically obtained and then compared with those obtained from approximate closed-form solutions for several cases.In a parametric study for different nonlinear parameters,variation of the natural frequencies against the initial amplitude is investigated.Accuracy of the three different approaches is then discussed for both small and large amplitudes of the oscillations.展开更多
基金supported by the National Natural Science Foundation of China (No. 11472216)support from China Scholarship Council (CSC)German Aerospace Center (DLR)
文摘A finite element formulation is presented for the analysis of the aeroelastic effect on the aerothermoacoustic response of metallic panels in supersonic flow. The first-order shear deformation theory(FSDT) and the von Karman nonlinear strain-displacement relationships are employed to consider the geometric nonlinearity induced by large deflections. The piston theory and the Gaussian white noise are used to simulate the mean flow aerodynamics and the turbulence from the boundary layer. The thermal loading is assumed to be steady and uniformly distributed, and the material properties are assumed to be temperature independent. The governing equations of motion are firstly formulated in structural node degrees of freedom by using the principle of virtual work,and then transformed and reduced to a set of coupled nonlinear Duffing oscillators in modal coordinates. The dynamic response of a panel is obtained by the Runge-Kutta integration method. The results indicate that the increasing aeroelastic effect can lead the panel vibration from a random motion to a highly ordered motion in the fashion of diffused limit cycle oscillations(LCOs), and remarkably alter the stochastic bifurcation and the spectrum of the aerothermoacoustic response.On the other hand there exists a counterbalance mechanism between the external random loading and the aeroelastic effect, which mainly functions through the nonlinear frequency-amplitude response. It is surmised that the aeroelastic effect must be considered in sonic fatigue analysis for panel structures in supersonic flow.
文摘This paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive.The governing equation of motion of the objective system is developed by virtue of Lagrangian’s method.A complicated term is broached in the governing equation of the motion of the system owing to existence of multiplication of a quadratic function of velocity with a sinusoidal function of displacement in the kinetic energy of the system.The obtained equation is an example of a well-known category of nonlinear oscillators,namely,non-natural systems.Due to the complex terms in the governing equation,perturbation methods cannot directly extract any closed form expressions for the natural frequency.Unavoidably,different non-perturbative approaches are employed to solve the problem and to elicit a closed-form expression for the natural frequency.Energy balance method,modified energy balance method and variational approach are utilized for frequency analyzing of the system.Frequencyamplitude relationships are analytically obtained for nonlinear vibration of the elevator’s drum.In order to examine accuracy of the obtained results,exact solutions are numerically obtained and then compared with those obtained from approximate closed-form solutions for several cases.In a parametric study for different nonlinear parameters,variation of the natural frequencies against the initial amplitude is investigated.Accuracy of the three different approaches is then discussed for both small and large amplitudes of the oscillations.
