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1.
黏弹性环形板的临界载荷及动力稳定性 总被引:7,自引:0,他引:7
利用线性黏弹性力学的Boltzmann叠加原理,在考察位移单值性条件的基础上,给出黏弹性环形板非线性动力学分析的初边值问题。通过Galerkin方法和引进新的状态变量,将其化归为四维非线性非自治常微分方程组,从而得到黏弹性环形板的四种临界载荷,同时考察了几何缺陷对黏弹性薄板临界载荷的影响。根据Floquet理论,得出黏弹性形板在周期激励下的线性动力稳定性判据。综合使用非线性动力学中的数值分析方法,研究了参数对黏弹性环形板非线性动力稳定性的影响。 相似文献
2.
The bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances are investigated.
The combined effects of the nonlinear term due to the cable’s geometric and coupled behavior between the modes of the beam
and the cable are considered. The nonlinear partial-differential equations are derived by the Hamiltonian principle. The Galerkin
method is applied to truncate the governing equation into a set of ordinary differential equations. The bifurcation diagrams
in three separate loading cases, namely, excitation acting on the cable, on the beam and simultaneously on the beam and cable,
are analyzed with changing forcing amplitude. Based on careful numerical simulations, bifurcations and possible chaotic motions
are represented to reveal the combined effects of nonlinearities on the dynamics of the beam and the cable when they act as
an overall structure. 相似文献
3.
Ming Hai Wei Yi Qing Xiao Hai Tao Liu Kun Lin 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(2):173-185
This paper analytically investigates the nonlinear responses of a cable-beam coupled system under the combined effects of internal and external resonance. The cable is considered a geometric nonlinearity, and the beam is considered as Euler–Bernoulli model, but it is coupled by fixing it at one end. The coupled nonlinear differential equations are formulated by using the Hamilton principle. The spatial problem is solved by using Galerkin’s method to simplify the governing equations to a set of ordinary differential equations. Applying the multiple time scales method to the ordinary differential equations, the first approximate solutions and solvability condition are derived. The effects of the cable sag to span ratio, mass ratio, and stiffness ratio on the nonlinear responses are investigated. The results show good agreement between the analytical and numerical solutions especially near the external resonance frequency. 相似文献
4.
Fluid Flow-Induced Nonlinear Vibration of Suspended Cables 总被引:2,自引:0,他引:2
The nonlinear interaction of the first two in-plane modes of a suspended cable with a moving fluid along the plane of the cable is studied. The governing equations of motion for two-mode interaction are derived on the basis of a general continuum model. The interaction causes the modal differential equations of the cable to be non-self-adjoint. As the flow speed increases above a certain critical value, the cable experiences oscillatory motion similar to the flutter of aeroelastic structures. A co-ordinate transformation in terms of the transverse and stretching motions of the cable is introduced to reduce the two nonlinearly coupled differential equations into a linear ordinary differential equation governing the stretching motion, and a strongly nonlinear differential equation for the transverse motion. For small values of the gravity-to-stiffness ratio the dynamics of the cable is examined using a two-time-scale approach. Numerical integration of the modal equations shows that the cable experiences stretching oscillations only when the flow speed exceeds a certain level. Above this level both stretching and transverse motions take place. The influences of system parameters such as gravity-to-stiffness ratio and density ratio on the response characteristics are also reported. 相似文献
5.
Yong-Gang Wang Xiao-Meng Li Dan Li Xin-Zhi Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(12):1925-1933
An integrated mathematic model and an efficient algorithm on the dynamical behavior of homogeneous viscoelastic corrugated
circular plates with shallow sinusoidal corrugations are suggested. Based on the nonlinear bending theory of thin shallow
shells, a set of integro-partial differential equations governing the motion of the plates is established from extended Hamilton’s
principle. The material behavior is given in terms of the Boltzmann superposition principle. The variational method is applied
following an assumed spatial mode to simplify the governing equations to a nonlinear integro-differential variation of the
Duffing equation in the temporal domain, which is further reduced to an autonomic system with four coupled first-order ordinary
differential equation by introducing an auxiliary variable. These measurements make the numerical simulation performs easily.
The classical tools of nonlinear dynamics, such as Poincaré map, phase portrait, Lyapunov exponent, and bifurcation diagrams,
are illustrated. The influences of geometric and physical parameters of the plate on its dynamic characteristics are examined.
The present mathematic model can easily be used to the similar problems related to other dynamical system for viscoelastic
thin plates and shallow shells. 相似文献
6.
In this study the momentum and heat transfer characteristics in an incompressible electrically conducting viscoelastic boundary
layer fluid flow over a linear stretching sheet are considered. Highly non-linear momentum and thermal boundary layer equations
are reduced to set of nonlinear ordinary differential equations by appropriate transformation. 相似文献
7.
This paper investigates longtime dynamical behaviors of an axially accelerating viscoelastic string with geometric nonlinearity.
Application of Newton's second law leads to a nonlinear partial-differential equation governing transverse motion of the string.
The Galerkin method is applied to truncate the partial-differential equation into a set of ordinary differential equations.
By use of the Poincare maps, the dynamical behaviors are presented based on the numerical solutions of the ordinary differential
equations. The bifurcation diagrams are presented for varying one of the following parameter: the mean transport speed, the
amplitude and the frequency of transport speed fluctuation, the string stiffness or the string dynamic viscosity, while other
parameters are fixed. 相似文献
8.
Nonlinear oscillations of viscoelastic simply supported rectangular plates are studied by assuming the Voigt–Kelvin constitutive model. Using Hamilton's principle in conjunction with the kinematics associated with Kirchhoff's plate model, the governing equations of motion including the effect of damping are represented in terms of the transversal deflection and a stress function. Utilizing the Bubnov–Galerkin method, the nonlinear partial differential equations are reduced to an ordinary differential equation which is studied geometrically by approximate construction of the Poincaré maps. Explicit expressions are given for periodic solutions. 相似文献
9.
In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion. 相似文献
10.
A system of nonlinear equations for describing the perturbations of the pressure and radius in fluid flow through a viscoelastic tube is derived. A differential relation between the pressure and the radius of a viscoelastic tube through which fluid flows is obtained. Nonlinear evolutionary equations for describing perturbations of the pressure and radius in fluid flow are derived. It is shown that the Burgers equation, the Korteweg-de Vries equation, and the nonlinear fourth-order evolutionary equation can be used for describing the pressure pulses on various scales. Exact solutions of the equations obtained are discussed. The numerical solutions described by the Burgers equation and the nonlinear fourth-order evolutionary equation are compared. 相似文献
11.
The integro-partial differential equations governing the dynamic behavior of viscoelastic plates taking account of higher-order shear effects and finite deformations are presented. From the matrix formulas of differential quadrature, the special matrix product and the domain decoupled technique presented in this work, the nonlinear governing equations are converted into an explicit matrix form in the spatial domain. The dynamic behaviors of viscoelastic plates are numerically analyzed by introducing new variables in the time domain. The methods in nonlinear dynamics are synthetically applied to reveal plenty and complex dynamical phenomena of viscoelastic plates. The numerical convergence and comparison studies are carried out to validate the present solutions. At the same time, the influences of load and material parameters on dynamic behaviors are investigated. One can see that the system will enter into the chaotic state with a paroxysm form or quasi-periodic bifurcation with changing of parameters. 相似文献
12.
The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ- ential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thor- oughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter in- crease. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase. 相似文献
13.
14.
The effect of the narrow-band random excitation on the non-linear response of sandwich plates with an incompressible viscoelastic core is investigated. To model the core, both the transverse shear strains and rotations are assumed to be moderate and the displacement field in the thickness direction is assumed to be linear for the in-plane components and quadratic for the out-of-plane components. In connection to the moderate shear strains considered for the core, a non-linear single-integral viscoelastic model is also used for constitutive modeling of the core. The fifth-order perturbation method is used together with the Galerkin method to transform the nine partial differential equations to a single ordinary integro-differential equation. Converting the lower-order viscoelastic integral term to the differential form, the fifth-order method of multiple scale is applied together with the method of reconstitution to obtain the stochastic phase-amplitude equations. The Fokker–Planck–Kolmogorov equation corresponding to these equations is then solved by the finite difference method, to determine the probability density of the response. The variation of root mean square and marginal probability density of the response amplitude with excitation deterministic frequency and magnitudes are investigated and the bimodal distribution is recognized in narrow ranges of excitation frequency and magnitude. 相似文献
15.
层状层电介质空间轴对称问题的状态空间解 总被引:15,自引:0,他引:15
从横观各向同性压电介质空间轴对称问题的基本方程出发,建立了压电介质空间轴对称问题的状态变量方程,对状态变量方程进行Hankel变换,得到以状态变量表示的单层压电介质在Hankel变换空间中的解,讨论了3种不同特征根的情况,利用提出的解得到了半无限压电体在垂直集中载荷和点电荷作出下的Boussinesq解。利用传递矩阵方法导出了多层压电介质空间轴对称问题解一般解析式。 相似文献
16.
17.
本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。 相似文献
18.
In this paper an inclined nearly taut stay, belonging to a cable-stayed bridge, is considered. It is subject to a prescribed
motion at one end, caused by traveling vehicles, and embedded in a wind flow blowing simultaneously with rain. The cable is
modeled as a non-planar, nonlinear, one-dimensional continuum, possessing torsional and flexural stiffness. The lower end
of the cable is assumed to undergo a vertical sinusoidal motion of given amplitude and frequency. The wind flow is assumed
uniform in space and constant in time, acting on the cable along which flows a rain rivulet. The imposed motion is responsible
for both external and parametric excitations, while the wind flow produces aeroelastic instability. The relevant equations
of motion are discretized via the Galerkin method, by taking one in-plane and one out-of-plane symmetric modes as trial functions.
The two resulting second-order, non-homogeneous, time-periodic, ordinary differential equations are coupled and contain quadratic
and cubic nonlinearities, both in the displacements and velocities. They are tackled by the Multiple Scale perturbation method,
which leads to first-order amplitude-phase modulation equations, governing the slow dynamics of the cable. The wind speed,
the amplitude of the support motion and the internal and external frequency detunings are set as control parameters. Numerical
path-following techniques provide bifurcation diagrams as functions of the control parameters, able to highlight the interactions
between in-plane and out-of-plane motions, as well as the effects of the simultaneous presence of the three sources of excitation. 相似文献
19.
Dynamical behavior of nonlinear viscoelastic beams 总被引:2,自引:0,他引:2
IntroductionTheGalerkintruncationiswidelyusedtostudythedynamicalbehavior(especiallythenonlineardynamicalbehavior)ofstructures[1].However,asfarthereisnodirectevidencetoprovetheplausibilityoftheloworderGalerkintruncation,althoughitcanbeinferredfromcertaini… 相似文献
20.
This paper describes a new stochastic control methodology for nonlinear affine systems subject to bounded parametric and functional
uncertainties. The primary objective of this method is to control the statistical nature of the state of a nonlinear system
to designed (attainable) statistical properties (e.g., moments). This methodology involves a constrained optimization problem
for obtaining the undetermined control parameters, where the norm of the error between the desired and actual stationary moments
of state responses is minimized subject to constraints on moments corresponding to a stationary distribution. To overcome
the difficulties in solving the associated Fokker–Planck equation, generally experienced in nonlinear stochastic control and
filtering problems, an approximation using the direct quadrature method of moments is proposed. In this approach, the state
probability density function is expressed in terms of a finite collection of Dirac delta functions, and the partial differential
equation can be converted to a set of ordinary differential equations. In addition to the above mentioned advantages, the
state process can be non-Gaussian. The effectiveness of the method is demonstrated in an example including robustness with
respect to predefined uncertainties and able to achieve specified stationary moments of the state probability density function. 相似文献