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1.
M. S. Matbuly 《Meccanica》2009,44(5):547-554
The present work concerns with the multiple crack propagation along the interface of two bonded dissimilar strips. The crack
faces are subjected to anti-plane shear traction. Galilean transformation is employed to reduce the problem to a quasi-static
one. Then, using Fourier transforms and asymptotic analysis, the quasi-static problem is reduced to a pair of singular integral
equations. That are solved numerically, using Gauss-Chebyshev integration formulae. The values of the dynamic stress intensity
factors are obtained and compared with the previous similar works. Further, a parametric study is introduced to investigate
the effect of crack growth rate, geometric and elastic characteristics of the composite on the values of dynamic stress intensity
factors. 相似文献
2.
We address an iterative procedure that can be used to detect coarse-grained hyperbolic unstable equilibria (saddle points)
of microscopic simulators when no equations at the macroscopic level are available. The scheme is based on the concept of coarse timestepping (Kevrekidis et al. in Commun. Math. Sci. 1(4):715–762, 2003) incorporating an adaptive mechanism based on the chord method allowing the location of coarse-grained saddle points directly.
Ultimately, it can be used in a consecutive manner to trace the coarse-grained open-loop saddle-node bifurcation diagrams
of complex dynamical systems and large-scale systems of ordinary and/or partial differential equations. We illustrate the
procedure through two indicative examples including (i) a kinetic Monte Carlo simulation (kMC) of simple surface catalytic
reactions and (ii) a simple agent-based model, a financial caricature which is used to simulate the dynamics of buying and
selling of a large population of interacting individuals in the presence of mimesis. Both models exhibit coarse-grained regular
turning points which give rise to branches of saddle points. 相似文献
3.
Bifurcations and route to chaos of the Mathieu–Duffing oscillator are investigated by the incremental harmonic balance (IHB)
procedure. A new scheme for selecting the initial value conditions is presented for predicting the higher order periodic solutions.
A series of period-doubling bifurcation points and the threshold value of the control parameter at the onset of chaos can
be calculated by the present procedure. A sequence of period-doubling bifurcation points of the oscillator are identified
and found to obey the universal scale law approximately. The bifurcation diagram and phase portraits obtained by the IHB method
are presented to confirm the period-doubling route-to-chaos qualitatively. It can also be noted that the phase portraits and
bifurcation points agree well with those obtained by numerical time-integration. 相似文献
4.
The exact linear three-dimensional equations for a elastically monoclinic (13 constant) plate of constant thickness are reduced
without approximation to a single 4th order differential equation for a thickness-weighted normal displacement plus two auxiliary equations for
weighted thickness integrals of a stress function and the normal strain. The 4th order equation is of the same form as in
classical (Kirchhoff) theory except the unknown is not the midsurface normal displacement. Assuming a solution of these plate
equations, we construct so-called modified Saint-Venant solutions—“modified” because they involve non-zero body and surface
loads. That is, solutions of the exact three-dimensional elasticity equations that exhibit no boundary layers and that are
subject to a special set of body and surface loads that leave the analogous plate loads arbitrary. 相似文献
5.
Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction
of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction
is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking
error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero
of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller
is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the
control performances of the proposed controller are compared with the results of the augmented PD (APD) controller. 相似文献
6.
Dimitris Sfyris 《Journal of Elasticity》2011,103(2):281-287
In this note we study the condition of strong ellipticity under changes in the current and reference configuration for the
finite hyperelastostatic case. The outcome is that strong ellipticity is preserved provided one adjusts the vectors used in
the definition of this condition accordingly. 相似文献
7.
The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in
this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions
for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations
are given to show the effectiveness of the proposed method. 相似文献
8.
Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine
or piecewise self-affine in R
2 or R
3 (R is the set of real numbers). In this paper, the piecewise hidden-variable fractal model is extended from R
3 to R
n
(n is an integer greater than 3), which is called the multi-dimensional piecewise hidden variable fractal model. This new model
uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values
depend continuously on all the hidden variables. Therefore the result is very general. Moreover, the piecewise hidden-variable
fractal model in tensor form is more terse than in the usual matrix form. 相似文献
9.
The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler
beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end
of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter
rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of
solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for
a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping
parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement
is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the
tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that
they have to be included in the modeling process. 相似文献
10.
It is a significant issue to control bifurcation because many neuronal diseases have close relevance to bifurcation of neuron system. Some studies have been done on bifurcation control in the Hodgkin–Huxley (HH) model, but there is no clear mathematical criterion for bifurcation stabilization. In this paper, according to Routh–Hurwitz stability criterion, we employ linear control term of washout filter-aided dynamic feedback controller to stabilize bifurcation of the HH model. As a result, we can deduce linear control gain based on the criterion, and simulation shows the method is effective for making the HH model stable. The controller designs described here are achieved by electrical stimulus, so it may have potential applications in the diagnosis and therapy of dynamical diseases. 相似文献
11.
This paper considers the stabilization problem of nonlinear systems with center manifold (center systems). A new method based
on (system) immersion and (manifold) invariance (I&I) is introduced to stabilize the center systems. One of the key steps
is to define a target dynamics whose order should be strictly smaller than that of the system to be controlled. For the center
systems, we prove that the order of the target dynamics can be equal to that of the corresponding reduced dynamics on their
center manifolds. Constructing solution is given for the target dynamics of the quadratic center system with a transcritical
or a Hopf control bifurcation. Illustrating examples with simulations are respectively presented to validate the proposed
stabilization scheme.
Supported by the National Natural Science Foundation of China (Grant No. 60674024). 相似文献
12.
A mathematical model will be analyzed in order to study the effects of variables viscosity and thermal conductivity on unsteady
heat and mass transfer over a vertical wavy surface in the presence of magnetic field numerically by using a simple coordinate
transformation to transform the complex wavy surface into a flat plate. The fluid viscosity is assumed to vary as a exponential
function of temperature and thermal conductivity is assumed to vary linearly with temperature. An implicit marching Chebyshev
collocation scheme is employed for the analysis. Numerical solutions are obtained for different values of variable viscosity,
variable thermal conductivity and MHD variation parameter. Numerical results show that, variable viscosity, variable thermal
conductivity and MHD variation parameter have significant influences on the velocity, temperature and concentration profiles
as well as for the local skin friction, Nusselt number and Sherwood number. 相似文献
13.
The (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation of B-type (BKP) is hereby investigated. New soliton solutions and soliton-like similarity solutions are constructed for the (2+1)-dimensional BKP equation. The similarity solutions are not travelling wave solutions when the arbitrary functions involved are chosen appropriately. Painlevé test shows that there are two solution branches, one of which has the resonance ?2. And four similarity reductions for the BKP equation are given out through nontrivial variable transformations. Moreover, abundant soliton behaviour modes of the solutions, such as soliton fusion and soliton reflection, are discussed in detail. 相似文献
14.
We study the problem of an elastic shell-like inclusion with high rigidity in a three-dimensional domain by means of the asymptotic
expansion method. The analysis is carried out in a general framework of curvilinear coordinates. After defining a small real
adimensional parameter ε, we characterize the limit problems when the rigidity of the inclusion has order of magnitude
\frac1e\frac{1}{\varepsilon } and
\frac1e3\frac{1}{\varepsilon^{3}} with respect to the rigidities of the surrounding bodies. Moreover, we prove the strong convergence of the solution of the
initial three-dimensional problem towards the solution of the simplified limit problem. 相似文献
15.
In this paper, we consider a materially uniform but inhomogeneous body and we are interested in three particular cases of
inhomogeneities corresponding to three distinct distributions of dislocations. The field of defects enters the equilibrium
equations through the components of the tensor field describing the relaxation procedure. We examine what form should these
components take in order for the material to admit states of anti-plane shear. The results obtained in this paper hold for
a class of materials that obey a specific form for the stored energy function. In the special case of no dislocations, this
class falls under the well known class of Neo-Hookean materials.
相似文献
16.
Second-order approximation of primary resonance of a disk-type piezoelectric stator for traveling wave vibration 总被引:1,自引:0,他引:1
Considering the quadratic nonlinear constitutive relations of piezoelectric materials, a traveling wave dynamic model for
a lead zirconate titanate stator of a traveling wave ultrasonic motor is established using Hamilton’s principle and the Rayleigh–Ritz
method. Applying the method of multiple scales, the second-order approximation of the primary resonance for traveling wave
vibration of the stator is investigated. The second harmonic component is found in the primary response of the stator, which
arises from the quadratic stiffness in the condition of weak excitation. In the region of the resonance, the two coupled modals
are split and the lower-order peak bends to the left, hence a jump and delay exist in the response. In this way numerical
results are given to verify the feasibility of the analytical approach. The results provide a theoretical foundation for further
nonlinear dynamic analysis and design of the traveling wave ultrasonic motor. 相似文献
17.
Generalized projective synchronization of the fractional-order Chen hyperchaotic system 总被引:2,自引:0,他引:2
In this paper, we numerically investigate the hyperchaotic behaviors in the fractional-order Chen hyperchaotic systems. By utilizing the fractional calculus techniques, we find that hyperchaos exists in the fractional-order Chen hyperchaotic system with the order less than 4. We found that the lowest order for hyperchaos to have in this system is 3.72. Our results are validated by the existence of two positive Lyapunov exponents. The generalized projective synchronization method is also presented for synchronizing the fractional-order Chen hyperchaotic systems. The present technique is based on the Laplace transform theory. This simple and theoretically rigorous synchronization approach enables synchronization of fractional-order hyperchaotic systems to be achieved and does not require the computation of the conditional Lyapunov exponents. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme. 相似文献
18.
Takashi Ikeda 《Nonlinear dynamics》2010,60(3):425-441
Autoparametric interaction of a liquid free surface in a rectangular tank with an elastic support structure, which is subjected
to vertical excitation, is investigated. When the natural frequency of the structure is equal to the lowest natural frequency
of liquid sloshing, this system is categorized as an autoparametric system with an internal resonance ratio 1:1. The structure
is elastically supported so there is a higher possibility that the 1:1 internal resonance can be observed. The nonlinear theoretical
analysis is conducted for a fluid assumed to be perfect in a tank with a finite liquid depth. The equations of motion for
the first three sloshing modes are derived employing Galerkin’s technique and considering both the nonlinearity of the fluid
motion, and the viscous damping effect. Then the theoretical frequency response curves for the harmonic oscillations of the
structure and sloshing are determined using van der Pol’s method. The frequency response curves show that high amplitudes
of the structure’s vibrations facilitate the liquid sloshing. Furthermore, the influence of the internal detuning parameter
is investigated by showing the frequency response curves and bifurcation sets. Hopf bifurcations may occur followed by amplitude-modulated
motions. The theoretical results are in quantitative agreement with the experimental data. 相似文献
19.
This paper aims to study a class of differential equations with parametric Gaussian colored noise. We present the general
framework to get the solvability conditions of the approximate stationary probability density function, which is determined
by the Fokker-Planck-Kolmogorov (FPK) equations. These equations are derived using the stochastic averaging method and the
operator theory with the perturbation technique. An illustrative example is proposed to demonstrate the procedure of our proposed
method. The analytical expression of approximate stationary probability density function is obtained. Numerical simulation
is carried out to verify the analytical results and excellent agreement can be easily found. The FPK equation for the probability
density function of order ε
0 is used to examine the almost-sure stability for the amplitude process. Finally, the stability in probability of the amplitude
process is investigated by Lin and Cai’s method. 相似文献
20.
In this paper, a fractional 3-dimensional (3-D) 4-wing quadratic autonomous system (Qi system) is analyzed. Time domain approximation method (Grunwald–Letnikov method) and frequency domain approximation method are used together to analyze the behavior of this fractional order chaotic system. It is found that the decreasing of the system order has great effect on the dynamics of this nonlinear system. The fractional Qi system can exhibit chaos when the total order less than 3, although the regular one always shows periodic orbits in the same range of parameters. In some fractional order, the 4 wings are decayed to a scroll using the frequency domain approximation method which is different from the result using time domain approximation method. A surprising finding is that the phase diagrams display a character of local self-similar in the 4-wing attractors of this fractional Qi system using the frequency approximation method even though the number and the characteristics of equilibria are not changed. The frequency spectrums show that there is some shrinking tendency of the bandwidth with the falling of the system states order. However, the change of fractional order has little effect on the bandwidth of frequency spectrum using the time domain approximation method. According to the bifurcation analysis, the fractional order Qi system attractors start from sink, then period bifurcation to some simple periodic orbits, and chaotic attractors, finally escape from chaotic attractor to periodic orbits with the increasing of fractional order α in the interval [0.8,1]. The simulation results revealed that the time domain approximation method is more accurate and reliable than the frequency domain approximation method. 相似文献