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1.
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
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.
Yury M. Vetyukov 《Journal of Elasticity》2010,98(2):141-158
A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static
deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate.
A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell
strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions
of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements.
The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods
using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the
shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis
to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses
in the cross-section. 相似文献
4.
We prove, among other things, that if the acoustic tensor satisfies a suitable growth condition at infinity (the hyperbolicity condition) and the total initial energy is summable with a suitable weight, then the solution to the initial boundary value problem of linear elastodynamics in unbounded domains decays at infinity, at every instant, with a rate depending on the weight. Moreover, we show that the hyperbolicity condition is necessary and sufficient for the equipartition in mean of the total energy. 相似文献
5.
In this paper, a non-autonomous two species competitive allelopathic phytoplankton model in presence of a discrete time delay
is considered. We have obtained the sufficient conditions for permanence along with existence-uniqueness of an almost periodic
solution. Sufficient conditions are derived for the existence of unique almost periodic solution. Analytical findings are
supported through exhaustive numerical simulations. With the help of the numerical example, we have demonstrated that initial
density dependent almost periodic co-existence is possible in some situations when parameter values fail to satisfy all the
conditions of permanence. 相似文献
6.
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
7.
The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function W(ω), depending on the frequency ω, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and
sufficient conditions for a given function W(ω) to be the response function of an elastodynamic network, assuming there is no damping. In particular we construct an elastodynamic
network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks in
three dimensions and also for planar networks, which are networks where all the elements, displacements and forces are in
a plane. The network we design can fit within an arbitrarily small neighborhood of the convex hull of the terminal nodes,
provided the springs and masses occupy an arbitrarily small volume. Additionally, we prove stability of the network response
to small changes in the spring constants and/or addition of springs with small spring constants. 相似文献
8.
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
9.
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
10.
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
11.
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
12.
Kadry Zakaria 《Nonlinear dynamics》2011,66(4):457-477
The aim of this work is to study the instability of interacting waves between two immiscible magnetic liquids. The effects
of gravitation and a uniform normal magnetic field are taken into account. The method of multiple scales is used to determine
the stability criteria of the considered problem. The various stability criteria are discussed both analytically and graphically.
According to the numerical examples, we have remarked that the increase of the ratio of the permeability of the liquids appears
to be the destabilizing effect of the magnetic field. The short waves below the critical wavenumbers are stable whereas a
number of long waves are unstable. The viscosity effect on the stability criteria is a dual-role one, depending on the strength
of the applied magnetic field. 相似文献
13.
Karl-Hans Laermann 《Meccanica》2010,45(2):167-174
The necessity of health-monitoring and supervising structures will be justified under aspects of reliability and safety as
well as with regard to economical reasons. Considering the achievements in measurement techniques combined with computer techniques,
the requirements on the evolution of efficient monitoring systems will be indicated. The prerequisite will be pointed out,
to conceive such systems in close co-ordination with the mathematical modelling of the structure. This is inalienable with
concern to system-identification, as generally the control-parameters cannot be measured directly; they are to calculate on
the basis of the mathematical model and the measurable structural response symptoms. This requires mathematical complicate
solution of inverse problems. During service/operation many effects give rise for degradation of the structural resistance,
reducing the safety and the life-time as well. The results of system identification enable the determination of damage indicators,
which provide information on the scale of degradation in the course of time to estimate the limit of service-life and the
residual life-time. 相似文献
14.
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
15.
The paper considers the application of the method of direct separation of motions to the investigation of distributed systems.
An approach is proposed which allows one to apply the method directly to the initial equation of motion and to satisfy all
boundary conditions, arising for both slow and fast components of motion. The methodology is demonstrated by means of a classical
problem concerning the so-called Indian magic rope trick (Blekhman et al. in Selected topics in vibrational mechanics, vol.
11, pp. 139–149, [2004]; Champneys and Fraser in Proc. R. Soc. Lond. A 456:553–570, [2000]; in SIAM J. Appl. Math. 65(1):267–298, [2004]; Fraser and Champneys in Proc. R. Soc. Lond. A 458:1353–1373, [2002]; Galan et al. in J. Sound Vib. 280:359–377, [2005]), in which a wire with an unstable upper vertical position is stabilized due to vertical vibration of its bottom support
point. The wire is modeled as a heavy Bernoulli–Euler beam with a vertically vibrating lower end. As a result of the treatment,
an explicit formula is obtained for the vibrational correction to the critical flexural stiffness of the nonexcited system. 相似文献
16.
This paper presents a detailed analysis on the dynamics of a ring network with small world connection. On the basis of Lyapunov stability approach, the asymptotic stability of the trivial equilibrium is first investigated and the delay-dependent criteria ensuring global stability are obtained. The existence of Hopf bifurcation and the stability of periodic solutions bifurcating from the trivial equilibrium are then analyzed. Further studies are paid to the effects of small world connection on the stability interval and the stability of periodic solution. In particular, some complex dynamical phenomena due to short-cut strength are observed numerically, such as: period-doubling bifurcation and torus breaking to chaos, the coexistence of multiple periodic solutions, multiple quasi-periodic solutions, and multiple chaotic attractors. The studies show that small world connection may be used as a simple but efficient “switch” to control the dynamics of a system. 相似文献
17.
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
18.
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
19.
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
20.
Prior studies have indicated that heavy alcohol drinkers are likely to engage in risky sexual behaviours and thus, more likely
to get sexually transmitted infections (STIs) than social drinkers. Here, we formulate a deterministic model for evaluating
the impact of heavy alcohol drinking on the reemerging gonorrhea epidemic. The model is rigorously analysed, showing the existence
of a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less than unity. If the disease
threshold number is greater than unity, a unique endemic equilibrium exists and is globally asymptotically stable in the interior
of the feasible region and the disease persists at endemic proportions if it is initially present. Both analytical and numerical
results are provided to ascertain whether heavy alcohol drinking has an impact on the transmission dynamics of gonorrhea. 相似文献