共查询到20条相似文献,搜索用时 46 毫秒
1.
This paper deals with simplified mathematical models of the dynamic systems with weak non-linearities and described by complex continuous transfer functions without jumping. We consider only the first approximation of the steady state forced vibration where the complex amplitude corresponds to the same frequency as the harmonic excitation. The iterative smoothing of the above system from the measured transfer function at discrete frequency points and especially from their moduli is proposed. The aim of this method is to determine the complex eigenvalues of the systems with Duffing-type stiffness behaviour (only their imaginary parts depend on the squares of the absolute values of the amplitudes) and real modal parameters in situations when no-phase difference between output and input is known. If the complex transfer function is completely known, the identified complex eigenvalues are assumed to be linear and quadratic functions of absolute values of amplitudes and the modal parameters are complex. 相似文献
2.
A class of hyperchaotic systems has strong noise robustness. When conventional synchronization algorithms are used in this
system, however, the convergence rate of synchronization is slow, and the synchronization performances are very sensitive
to the parameters of response system. To resolve the problems, synchronization using nonlinear feedback control is proposed.
According to Hurwitz stability theory, designing a nonlinear controller can make the real parts of the eigenvalues of the
error equation’s Jacobian matrix negative. And the absolute values of the eigenvalues are larger, the convergence rate of
synchronization is faster. Besides, the theoretical results of parameters insensitivity are given. Finally, numerical simulations
are given to verify and test the correctness and effectiveness of the methods we proposed. 相似文献
3.
黄蔚章 《应用数学和力学(英文版)》1997,18(6):575-584
I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit… 相似文献
4.
连续时间系统的混沌同步 总被引:2,自引:0,他引:2
本文讨论混沌连续时间系统的完全同步问题,提出一个构造混沌同步系统的新方法。这个方法基于线性系统的稳定性分析准则。通过对系统线性项与非线性项的适当分离,当系统的雅可比矩阵的所有特征值都具有负实部时,同步误差e(t)的线性系统是渐进稳定的,即可实现新系统和原系统的完全同步。新方法不需计算条件Lyapunov指数以作为判定同步的条件,因而比通用方法更为简单有效。新方法适用于自治或非自治系统,尤其适用于具有多于两个正Lyapunov指数的超混沌系统。甚至当初始同步误差极大时,也能实现理想的混沌同步。以Lorenz系统,耦合Duffing振子系统和超混沌Roessler系统作为算例。数值计算结果证实所提出方法的有效性和鲁棒性。 相似文献
5.
Longwave Approximation in Film Flow Theory 总被引:1,自引:0,他引:1
An asymptotic longwave model which takes dispersive terms into account is constructed for describing the motion of thin films with finite deviations from the middle surface. An exact periodic solution describing a nonlinear capillary wave is constructed within the framework of the model. Small deviations from the nonlinear capillary wave are described by a linear system with periodic coefficients. It is shown that for wave perturbation periods greater than a certain critical value the monodromy matrix of this system has eigenvalues whose absolute values are equal to unity. For perturbation periods less than the critical period the absolute value of one of the eigenvalues becomes greater than unity. 相似文献
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7.
Cong Nguyen Dinh Duc Luu Hoang Hong Phan Thanh 《Journal of Dynamics and Differential Equations》2022,34(1):605-636
We study the asymptotic dynamics of stochastic Young differential delay equations under the regular assumptions on Lipschitz continuity of the coefficient functions. Our main results show that, if there is a linear part in the drift term which has no delay factor and has eigenvalues of negative real parts, then the generated random dynamical system possesses a random pullback attractor provided that the Lipschitz coefficients of the remaining parts are small.
相似文献8.
In this paper, stability and local bifurcation behaviors for the nonlinear aeroelastic model of an airfoil with external store are investigated using both analytical and numerical methods. Three kinds of degenerated equilibrium points of bifurcation response equations are considered. They are characterized as (1) one pair of purely imaginary eigenvalues and two pairs of conjugate complex roots with negative real parts; (2) two pairs of purely imaginary eigenvalues in nonresonant case and one pair of conjugate complex roots with negative real parts; (3) three pairs of purely imaginary eigenvalues in nonresonant case. With the aid of Maple software and normal form theory, the stability regions of the initial equilibrium point and the explicit expressions of the critical bifurcation curves are obtained, which can lead to static bifurcation and Hopf bifurcation. Under certain conditions, 2-D tori motion may occur. The complex dynamical motions are considered in this paper. Finally, the numerical solutions achieved by the fourth-order Runge–Kutta method agree with the analytic results. 相似文献
9.
A study is made of a nonlinear dynamic system in which the two of the eigenvalues of the matrix of equations of the linear
approximation have negative parts and two other eigenvalues have purely imaginary parts. The nonlinearities are of the third
order. The Poincare-Lyapunov-Malkin method is used to show that the motion of such systems is generally aperiodic. Periodic
motions can occur only in isolated cases.
Institute of Railroad Transport, Kiev; Highway Institute of Donetsk Technical University, Gorlovka, Ukraine. Translated from
Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 101–107, August, 1999. 相似文献
10.
D.W. Nicholson 《Mechanics Research Communications》1978,5(3):147-152
Lower bounds are obtained on the real and imaginary parts of the eigenvalues of a damped linear system in free vibration. A condition for subcritical damping in all modes is obtained. The bounds have a close relation to the eigenvalue of a one degree-of-freedom system. 相似文献
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12.
This paper presents an approach for determining the linear stability of steady states of partial differential equations (PDEs) on massively parallel computers. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem. The eigenvalues with the largest real part are calculated using Arnoldi's iteration driven by a novel implementation of the Cayley transformation. The Cayley transformation requires the solution of a linear system at each Arnoldi iteration. This is done iteratively so that the algorithm scales with problem size. A representative model problem of three‐dimensional incompressible flow and heat transfer in a rotating disk reactor is used to analyze the effect of algorithmic parameters on the performance of the eigenvalue algorithm. Successful calculations of leading eigenvalues for matrix systems of order up to 4 million were performed, identifying the critical Grashof number for a Hopf bifurcation. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
13.
Coupled equations of thermoelasticity take into account the effect of nonuniform heating on the medium deformation and that
of the dilatation rate on the temperature distribution. As a rule, the coupling coefficients are small and it is assumed,
sometimes without proper justification, that the effect of the dilatation rate on the heat conduction process can be neglected.
The aim of the present paper is to construct analytical solutions of some model boundary-value problems for a thermoelastic
bounded body and to determine the body characteristic dimensions and the medium thermomechanical moduli forwhich it is necessary
to take into account that the temperature and displacement fields are coupled. We consider some models constructed on the
basis of the Fourier heat conduction law and the generalized Cattaneo-Jeffreys law in which the heat flux inertia is taken
into account. The solution is constructed as an expansion in a biorthogonal system of eigenfunctions of the nonself-adjoint
operator pencil generated by the coupled equations of motion and heat conduction. For the model problem, we choose a special
class of boundary conditions that allows us to exactly determine the pencil eigenvalues. 相似文献
14.
Joaquín Zueco 《Meccanica》2008,43(1):37-46
The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane
channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness,
Péclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation
parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference
scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model
that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary,
while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical
software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law
for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or
integrated transport variables at any point or section of the medium. 相似文献
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16.
M.R. Ayatollahi M. Dehghany M. Nejati 《International Journal of Solids and Structures》2011,48(10):1579-1589
The effect of the first non-singular stress term on the fracture behavior of notched structures was investigated under symmetric geometry and loading conditions. According to the Williams series expansion, for a large domain of notch angles the non-singular stress terms of sharp notches are functions of complex eigenvalues and their corresponding complex coefficients. Hence, a new representation of stress field near the notch tip was developed in which the higher order terms are expressed as several explicit functions of real and imaginary parts of both the complex eigenvalues and their complex coefficients. A critical stress criterion was then applied to the new stress formulations to assess the influence of the first non-singular stress term on the apparent fracture toughness. Several finite element analyses were also performed on two laboratory specimens in order to show the effects of first non-singular term on the near field stress distribution of notched specimens. The results demonstrated that neglecting the first non-singular stress term could lead to significant errors in predicting the apparent fracture toughness of notched components. 相似文献
17.
In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s
modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model,
an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work,
in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN
is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an
appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of
damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped
model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved
by repeating the identification process for several times. The validity of results is proved by comparing the results with
those identified in a previous work. 相似文献
18.
This paper presents a novel implementation of an adaptive robust second-order sliding mode control (ARSSMC) on a mobile robot with four Mecanum wheels. Each wheel of the mobile robot is actuated by separate motors. It is the first time that higher-order sliding mode control method is implemented for the trajectory tracking control of Mecanum-wheeled mobile robot. Kinematic and dynamic modeling of the robot is done to derive an equation of motion in the presence of friction, external force disturbance, and uncertainties. In order to make the system robust, second-order sliding mode control law is derived. Further, adaptive laws are defined for adaptive estimation of switching gains. To check the tracking performance of the proposed controller, simulations are performed and comparisons of the obtained results are made with adaptive robust sliding mode control (ARSMC) and PID controller. In addition, a new and low-cost experimental approach is proposed to implement the proposed control law on a real robot. Experimental results prove that without compromising on the dynamics of the robot real-time implementation is possible in less computational time. The simulation and experimental results obtained confirms the superiority of ARSSMC over ARSMC and PID controller in terms of integral square error (ISE), integral absolute error (IAE), and integral time-weighted absolute error (ITAE), control energy and total variance (TV). 相似文献
19.
The aim of this paper is to show that the Jacobi–Davidson (JD) method is an accurate and robust method for solving large generalized algebraic eigenvalue problems with a singular second matrix. Such problems are routinely encountered in linear hydrodynamic stability analysis of flows that arise in various areas of continuum mechanics. As we use the Chebyshev collocation as a discretization method, the first matrix in the pencil is nonsymmetric, full rank, and ill‐conditioned. Because of the singularity of the second matrix, QZ and Arnoldi‐type algorithms may produce spurious eigenvalues. As a systematic remedy of this situation, we use two JD methods, corresponding to real and complex situations, to compute specific parts of the spectrum of the eigenvalue problems. Both methods overcome potentially severe problems associated with spurious unstable eigenvalues and are fairly stable with respect to the order of discretization. The real JD outperforms the shift‐and‐invert Arnoldi method with respect to the CPU time for large discretizations. Three specific flows are analyzed to advocate our statements, namely a multicomponent convection–diffusion in a porous medium, a thermal convection in a variable gravity field, and the so‐called Hadley flow. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
20.
B. Peters 《Flow, Turbulence and Combustion》2005,73(3-4):217-229
The objective of this contribution is to investigate whether the mechanism of the thermal diffusion instability in gaseous
flames causing cellular flame structures also occurs during the combustion of porous solid fuel. Based on conservation for
mass and energy, the relevant set of differential equations was derived. Assuming thermal equilibrium between fuel and oxidiser,
a global energy equation was valid for both solid and gaseous phase. The resulting set of differential equations was discretised
by the Collocation method to arrive at a system of algebraic equations. In order to investigate into cellular flame structures,
an infinitesimal disturbance was superimposed onto the plane conversion front. Carrying out a linear instability analysis,
yielded eigenvalues dependent on the wave number of the disturbance. A critical wave number exists below which the real part
of the eigenvalues is positive, thus, indicating a regime of instability. Within this region, eigenvalues with a not-vanishing
imaginary part of the eigen value existed causing cellular flame structures. However, the growth rate of disturbances was
found to be small, which may explain the difficulty to investigate this phenomena experimentally. 相似文献