共查询到20条相似文献,搜索用时 15 毫秒
1.
N. BanichukJ. Jeronen P. NeittaanmäkiT. Tuovinen 《Journal of Fluids and Structures》2011,27(7):986-1005
The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity. 相似文献
2.
In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes. 相似文献
3.
Approximate solutions of axially moving viscoelastic beams subject to multi-frequency excitations are presented. A non-linear partial-differential equation governing the transverse vibration of the beams is derived from Newton's second law, the Kelvin constitutive relationship, and the Lagrangian strain. Based on 1-term Galerkin's truncation, the governing equation is reduced to an ordinary differential equation. Three cases, including superharmonic resonance case, subharmonic resonance, and combination resonance are studied. The approximate solutions of the transverse vibration of the beams are obtained. Numerical results show that the approximate solutions are in good agreement with numerical results. 相似文献
4.
The paper is devoted to a stability and out-of-plane deformation analysis of an axially moving elastic web modelled as a panel (a plate undergoing cylindrical deformation). The panel is under homogeneous pure mechanical in-plane tension and thermal strains corresponding to the thermal tension and bending. In accordance with the static approach of stability analysis the problem of out-of-plane thermomechanical divergence (buckling) is reduced to an eigenvalue problem which is analytically solved. This problem corresponds to the case of in-plane thermomechanical tension and zero thermal bending. The general case of deformations induced by combined thermomechanical bending and tension is reduced to nonhomogeneous boundary-value problem and analyzed with the help of Fourier series. 相似文献
5.
K. Marynowski 《International Journal of Non》2007,42(1):118-131
Non-linear vibrations of axially moving beam with time-dependent tension are investigated in this paper. The beam material is modelled as three-parameter Zener element. The Galerkin method and the fourth order Runge-Kutta method are used to solve the governing non-linear partial-differential equation. The effects of the transport speed, the tension perturbation amplitude and the internal damping on the dynamic behaviour of the system are numerically investigated. The Poincare maps and bifurcation diagrams are constructed to classify the vibrations. For small values of the transport speed and the amplitude of periodic perturbation the system is asymptotically stable with its response tending to zero. With the increase of parameters one can observe the coexistence of attractors. Regular and chaotic motion occur when the internal damping increases. 相似文献
6.
Vibration and stability of an axially moving viscoelastic beam with hybrid supports 总被引:11,自引:0,他引:11
Vibration and stability are investigated for an axially moving beam constrained by simple supports with torsion springs. A scheme is proposed to derive natural frequencies and modal functions from given boundary conditions of an elastic beam moving at a constant speed. For a beam constituted by the Kelvin model, effects of viscoelasticity on the free vibration are analyzed via the method of multiple scales and demonstrated via numerical simulations. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams in parametric resonance. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity. 相似文献
7.
The dynamic characteristics and stability of axially moving viscoelastic rect- angular thin plate are investigated.Based on the two dimensional viscoelastic differential constitutive relation,the differential equations of motion of the axially moving viscoelastic plate are established.Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method.The effects of the aspect ratio,moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed. 相似文献
8.
In this paper, the forced response of a non-linear axially moving strip with coupled transverse and longitudinal motions is studied. In particular, the response of the system is examined in the neighborhood of a 3 : 1 internal resonance between the first two transverse modes. The equations of motion are derived using the Hamilton's Principle and discretized by the Galerkin's method. First, with the longitudinal motion neglected, the forced transverse response is investigated by applying the method of multiple scales to assess the effects of speed and the internal resonance. In general, the speed is shown to affect each mode differently. The internal resonance results in the constant solutions having transition to instability of both a saddle-node type and a Hopf bifurcation. In the region where the Hopf bifurcation occurs, steady-state periodic motion does not exist. Instead the stable motion is amplitude- and phase-modulated. When the coupled system with longitudinal motion is examined with internal resonance, results reveal that the modulated motions disappear. Thus, the presence of the longitudinal motion has a stabilizing effect on the transverse modes in the Hopf bifurcation region. The second longitudinal mode is shown to drift due primarily to a direct excitation of the first transverse mode. Effects of the longitudinal motion on the transverse response are shown to be significant for speeds both away from and close to the critical speed. 相似文献
9.
In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed. 相似文献
10.
The Hamiltonian dynamics is adopted to solve the eigenvalue problem for transverse vibrations of axially moving strings. With
the explicit Hamiltonian function the canonical equation of the free vibration is derived. Non-singular modal functions are
obtained through a linear, symplectic eigenvalue analysis, and the symplectic-type orthogonality conditions of modes are derived.
Stability of the transverse motion is examined by means of analyzing the eigenvalues and their bifurcation, especially for
strings transporting with the critical speed. It is pointed out that the motion of the string does not possess divergence
instability at the critical speed due to the weak interaction between eigenvalue pairs. The expansion theorem is applied with
the non-singular modal functions to solve the displacement response to free and forced vibrations. It is demonstrated that
the modal functions can be used as the base functions for solving linear and nonlinear vibration problems.
The project supported by the National Natural Science Foundation of China (10472021, 10421002 and 10032030), the NSFC-RFBR
Collaboration Project (1031120166/10411120494) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars,
State Education Ministry
The English text was polished by Keren Wang 相似文献
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12.
研究磁场环境中轴向运动导电薄板磁弹性动力学及分岔特性。考虑几何非线性因素,在给出薄板运动的动能、应变能及外力虚功的基础上,应用哈密顿变分原理,得到磁场中轴向运动薄板的非线性磁弹性振动方程,并给出洛伦兹电磁力的确定形式。针对横向磁场环境中条形板共振特性进行分析,应用多尺度法和奇异性理论,得到稳态运动下的分岔响应方程以及普适开折对应的转迁集。通过算例,分别得到以磁感应强度、轴向运动速度和激励力为分岔控制参数的分岔图、最大李雅普诺夫指数图和庞加莱映射图等计算结果,讨论不同分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,通过相应参数的改变可实现对系统复杂动力学行为的控制。 相似文献
13.
In this paper an initial-boundary value problem for a linear equation describing an axially moving string will be considered
for which the bending stiffness will be neglected. The velocity of the string is assumed to be time-varying and to be of the
same order of magnitude as the wave speed. A two time-scales perturbation method and the Laplace transform method will be
used to construct formal asymptotic approximations of the solutions. It will be shown that the linear axially moving string
model already has complicated dynamical behavior and that the truncation method can not be applied to this problem in order
to obtain approximations which are valid on long time-scales. 相似文献
14.
Xiao-Dong Yang You-Qi Tang Li-Qun Chen C.W. Lim 《European Journal of Mechanics - A/Solids》2010,29(1):81-90
This study investigates dynamic stability in transverse parametric vibrations of an axially accelerating tensioned beam of Timoshenko model on simple supports. The axial speed is assumed as a harmonic fluctuation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a finite set of ordinary differential equations. The method of averaging is applied to analyze the instability phenomena caused by subharmonic and combination resonance. Numerical examples demonstrate the effects of the mean axial speed, bending stiffness, rotary inertia and shear modulus on the instability boundaries. 相似文献
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16.
不确定性移动载荷激励下的弹性梁振动是土木、机械和航空航天等工程领域普遍存在的一类重要问题。在许多实际工程中,不确定移动载荷的样本测试数据有限或测试成本较高,本文引入区间过程模型对此类动态不确定性参数进行描述,提出了一种求解不确定移动载荷激励下弹性梁振动响应边界的非随机振动分析方法。首先,介绍了确定性移动载荷激励下弹性梁的振动微分方程及其解析求解方法;其次,引入区间过程模型,以上下边界函数的形式对不确定性移动载荷进行度量,进而基于模态叠加法发展出弹性梁振动响应边界求解的非随机振动分析方法;最后,将上述非随机振动分析方法应用于车桥耦合振动问题。 相似文献
17.
In this paper supercritical equilibria and critical speeds of axially moving beams constrained by sleeves with torsion springs are deduced. Transverse vibration of the beams is governed by a nonlinear integro-partial-differential equation. In the supercritical regime, the corresponding static equilibrium equation for the hybrid boundary conditions is analytically solved for the equilibria and the critical speeds. In the view of the non-trivial equilibrium, comparisons are made among the integro-partial-differential equation, a nonlinear partial-differential equation for transverse vibration, and coupled equations for planar motion under the hybrid boundary conditions. 相似文献
18.
Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams 总被引:1,自引:0,他引:1
Hu Ding · Li-Qun Chen Shanghai Institute of Applied Mathematics Mechanics Shanghai University Shanghai China Department of Mechanics Shanghai China 《Acta Mechanica Sinica》2011,27(3):426-437
Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales. 相似文献
19.
The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams. 相似文献
20.
Cheng Li 《基于设计的结构力学与机械力学》2017,45(4):463-478
This work is concerned with the thermo-electro-mechanical coupling transverse vibrations of axially moving piezoelectric nanobeams which reveal potential applications in self-powered components of biomedical nano-robot. The nonlocal theory and Euler piezoelectric beam model are employed to develop the governing partial differential equations of the mathematical model for axially moving piezoelectric nanobeams. The natural frequencies of nanobeams under simply supported and fully clamped boundary constraints are numerically determined based on the eigenvalue method. Subsequently, some detailed parametric studies are presented and it is shown that the nonlocal nanoscale effect and axial motion effect contribute to reduce the bending rigidity of axially moving piezoelectric nanobeam and hence its natural frequency decreases within the framework of nonlocal elasticity. Moreover, the natural frequency decreases with increasing the positive external voltage, axial compressive force and change of temperature, while increases with increasing the axial tensile force. The critical speed and critical axial compressive force are determined and the dynamical buckling behaviors of axially moving piezoelectric nanobeams are indicated. It is concluded the nonlocal nanoscale parameter plays a remarkable role in the size-dependent natural frequency, critical speed and critical axial compressive force. 相似文献