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1.
In this brief communication, Melnikov's method is adopted to study the chaotic behaviors of a two-dimensional thin panel subjected to subsonic flow and external excitation. The nonlinear governing equations of the subsonic panel system are reduced to a series of ordinary differential equations by using Galerkin method. The critical parameters for chaos are obtained. It is found that the critical parameters obtained by the theoretical analysis are in agreement with the numerical simulations. The method suggested in this paper can also be extended for other fluid-structure dynamic systems, such as the fluid-conveying system. 相似文献
2.
大型网架式可展开空间结构的非线性动力学与控制 总被引:5,自引:0,他引:5
我国航天工业迫切需要掌握可入轨后展开的大型网架式空间结构技术,以便研制口径十几米、乃至数十米的大型星载天线。该技术的主要科学基础是这类空间结构展开和服役过程的非线性动力学建模、分析和控制。本文综述了与上述科学基础相关的研究进展,提出应重点关注的三个科学问题:一是大型网架式空间结构展开过程的多柔体系统动力学,尤其是如何对微重力环境下索网的接触和缠绕、运动副内碰撞、结构展开与航天器本体间的耦合等导致的非线性动力学进行建模和分析;二是大型网架式空间结构展开锁定后服役的动力学分析,尤其是如何揭示结构柔性、众多运动副间隙、交变热载荷等因素引起的复杂非线性振动机理;三是大型网架式空间结构展开锁定后服役的动力学控制,尤其是如何在欠驱动、低能耗条件下对非线性振动和波动传播提出有效的控制方法。 相似文献
3.
Based on the potential theory of incompressible flow and the energy method, a two-dimensional simply supported thin panel
subjected to external forcing and uniform incompressible subsonic flow is theoretically modeled. The nonlinear cubic stiffness
and viscous damper in the middle of the panel is considered. Transformation of the governing partial differential equation
to a set of ordinary differential equations is performed through the Galerkin method. The stability of the fixed points of
the panel system is analyzed. The regions of different motion types of the panel system are investigated in different parameter
spaces. The rich dynamic behaviors are presented as bifurcation diagrams, phase-plane portraits, Poincaré maps and maximum
Lyapunov exponents based on carefully numerical simulations. 相似文献
4.
It is well known that many nonlinear phenomena such as bifurcations and chaotic behavior occur in DC–DC converters mainly due to the switching action among all the different topologies of the circuit. Such behavior has been described with detail numerically, and also mathematical reasoning has been provided. In this paper we focuss on the experimental side of a DC–DC Buck converter controlled with two different strategies: classical Pulse Width Modulation (PWM) with a ramp and a more recently described Zero Average Dynamics (ZAD). We show some nonsmooth events and we explain with detail the experimental set-ups. In one of them, we use a FPGA card to obtain on-line results. In the other we use Virtual Instrumentation to generate an experimental two-dimensional bifurcation diagram, which will be compared to the numerical data. After the data acquisition of the system state variables some elaborated post-processing must be made. This is done through LabView. Although the main application of these results is centered in avoiding non-periodic or high-amplitude periodic behavior, they can also be applied to reducing the generated electro-magnetic interference and to the information transmission.Partially funded by SICONOS. 相似文献
5.
Nonlinear dynamics of flexible tethered satellite system subject to space environment 总被引:1,自引:0,他引:1
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J 2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multidegree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions. 相似文献
6.
Nonlinear response of a parametrically excited buckled beam 总被引:6,自引:0,他引:6
A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented. 相似文献
7.
8.
Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity. 相似文献
9.
In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthotropic surfaces. The critical point is determined and the postbuckling behaviour of the panel is studied. 相似文献
10.
In the present part of the paper various problems of non-linear dynamics of nano-beams within the modified couple stress theory as well as the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson models are studied taking into account the geometric non-linearity. Different characteristics of the vibrational process, including Fourier spectra, wavelet spectra, phase portraits, Poincaré maps as well as the largest Lyapunov exponents, are studied for the same physical-geometric parameter with and without consideration of the size-dependent behaviour. Vibration graphs are constructed and analysed, and scenarios of transition from regular to chaotic vibrations are illustrated and discussed. 相似文献
11.
Guoyong Zheng 《Acta Mechanica Sinica》2010,26(3):401-407
Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results. 相似文献
12.
13.
Fotios Georgiades 《Nonlinear dynamics》2018,93(1):89-118
Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in first-order approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational ‘modes’ of rotating structures bypassing critical situations, and also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures. 相似文献
14.
《International Journal of Solids and Structures》2005,42(18-19):5274-5306
This study presents a solution method to analyze the geometrically nonlinear response of a patch-repaired flat panel (skin) with a cutout under general loading conditions. The effect of induced stiffening due to tensile loading on the in-plane and, particularly, the out-of-plane behaviors of the patch-repaired skin are investigated. The damage to the skin is represented in the form of a cutout under the patch. The patch with tapered edges is free of external tractions. The skin is subjected to general boundary and loading conditions along its external edge. The solution method provides the transverse shear and normal stresses in the adhesive between the skin and the patch, and in-plane and bending stresses in the patch and skin. Both the patch and skin are made of linearly elastic composite laminates, and the adhesive between them is homogeneous and isotropic, exhibiting a bi-linear elastic behavior. Modified Green’s strain–displacement relations in conjunction with von Karman assumptions are employed in determining the in-plane strains in the skin and patch; however, the transverse shear strains in the adhesive are determined based on the shear-lag theory. The present solution method utilizes the principle of virtual work in conjunction with complex potential functions. 相似文献
15.
The aeroelastic system of an airfoil-store configuration with a pitch freeplay is investigated using the precise integration method (PIM). According to the piecewise feature, the system is divided into three linear sub-systems. The sub-systems are separated by switching points related to the freeplay nonlinearity. The PIM is then employed to solve the sub-systems one by one. During the solution procedures, one challenge arises when determining the vibration state passing the switching points. A predictor-corrector algorithm is proposed based on the PIM to tackle this computational obstacle. Compared with exact solutions, the PIM can provide solutions to the precision in the order of magnitude of 10−12. Given the same step length, the PIM results are much more accurate than those of the Runge–Kutta (RK) method. Moreover, the RK method might falsely track limit cycle oscillations (LCOs), bifurcation charts or chaotic attractors; even the step length is chosen much smaller than that for the PIM. Bifurcations and LCOs are obtained and analyzed by the PIM in detail. Interestingly, it is found that multiple LCOs and chaotic attractors can exist simultaneously. With this magnitude of precision and efficiency, the PIM could become a solution technique with excellent potential for piecewise nonlinear aeroelastic systems. 相似文献
16.
Summary The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according
to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure
for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical
solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are
compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied
directly to the design of bellows.
Received 13 November 1997; accepted for publication 6 July 1999 相似文献
17.
Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate 总被引:1,自引:0,他引:1
The nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based
on the Von Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, the dimensionless nonlinear
equations of motion are analyzed and solved. The solvability condition of nonlinear equations is obtained by eliminating secular
terms and, finally, nonlinear natural frequencies and mode-shapes are obtained. Knowing that the linear vibration of this
type of plate does not have exact solution, Ritz method is employed to obtain semi-analytical nonlinear mode-shapes of transverse
vibration of this plate. Airy stress function and Galerkin method are employed to reduce nonlinear PDEs into an ODE of duffing
type. Stability of plate and chaotic behavior are investigated by Runge–Kutta method. Poincare section diagrams are in good
agreement with results of Lyapunov criteria. 相似文献
18.
Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models. 相似文献
19.
Nonlinear Dynamics - This paper presents a stochastic model for performing the uncertainty and sensitivity analysis of a Jeffcott rotor system with fixed-point rub-impact and multiple uncertain... 相似文献
20.
This paper first demonstrates that the accuracy and efficiency of the method of numerical simulation often used is not very high in predicting the slow drift surge extreme responses of a compliant offshore structure. Next, the slow drift surge extreme responses of the structure are analyzed via the path integral solution racy and efficiency of the PIS (PIS) method, and the accumethod is found to be higher than those of the numerical simulation method. A compound PIS (CPIS) method is first proposed in this article to further improve the efficiency of the path integral solution method, and the accuracy and efficiency of the CPIS method is validated. 相似文献