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1.
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
2.
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
3.
We analyze the quasiperiodic damped Mathieu equation
[(x)\ddot]+ g[(x)\dot]+ x ( 1 + d+ eq(t) )=0 ,\ddot{x}+ \gamma\dot{x}+ x \bigl( 1 + \delta+ \epsilon q(t) \bigr )=0 , 相似文献
4.
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
5.
The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable
defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic
obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected,
having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to
establish sufficient conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong
to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the
mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that
(i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle
and the background solid are heterogeneous, and (ii) they are dimensionally consistent, i.e., invariant under the choice of
physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier
studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective
of the vibration frequency. When applied to the situation where both the scatterer and the background medium are viscoelastic, i.e., dissipative, on the other hand, the same type of analysis
shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the “viscoelastic-viscoelastic”
case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically
insulated from its surroundings—a feature that is particularly cloaked in situations when either the background medium or
the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions
for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results
indicate that the set of transmission values is indeed empty in the “elastic-viscoelastic” case, and countable for “elastic-elastic”
and “viscoelastic-viscoelastic” configurations. 相似文献
6.
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
7.
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
8.
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
9.
To overcome the shortcomings of extreme time-consuming in solving the Reynolds equation, two efficient calculation methods,
based on the free boundary theory and variational principles for the unsteady nonlinear Reynolds equation in the condition
of Reynolds boundary, are presented in the paper. By employing the two mentioned methods, the nonlinear dynamic forces as
well as their Jacobians of the journal bearing can be calculated saving time but with the same accuracy. Of these two methods,
the one is called a Ritz model which manipulates the cavitation region by simply introducing a parameter to match the free
boundary condition and, as a result, a very simple approximate formulae of oil-film pressure is being obtained. The other
one is a one-dimensional FEM method which reduces the two-dimensional variational inequality to the one-dimensional algebraic
complementary equations, and then a direct method is being used to solve these complementary equations, without the need of
iterations, and the free boundary condition can be automatically satisfied. Meanwhile, a new order reduction method is contributed
to reduce the degrees of freedom of a complex rotor-bearing system. Thus the nonlinear behavior analysis of the rotor-bearing
system can be studied time-sparingly. The results in the paper show the high efficiency of the two methods as well as the
abundant nonlinear phenomenon of the system, compared with the results obtained by the usual numerical solution of the Reynolds
equation. 相似文献
10.
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
11.
In this paper we justify a two-dimensional evolution and eigenvalue model for micropolar plates starting from three-dimensional
linearly micropolar elasticity. A small parameter representing the thickness of the plate-like body is introduced in the problem.
The asymptotics of the evolution and eigenvalue problems is then developed as this small parameter tends to zero. First the
appropriate convergences of the eigenpairs of the three-dimensional problem to the eigenpairs of the two-dimensional eigenvalue
problem for micropolar plates is shown. Then these convergences are used in the Fourier method to obtain the convergences
of the solution of the three-dimensional evolution problem to the solution of the two-dimensional evolution plate model.
相似文献
12.
The polar method is a minimal invariant representation in plane elasticity. A plane orthotropic elastic behaviour is expressed
by five polar invariants related to the elastic symmetries. In this paper, considering the orthotropy orientation and the
polar invariants as optimisation parameters, we discuss the problem of minimising the elastic energy for a given state of
stress. The minimisation with respect to the orientation is solved in order to find the associated optimal elastic energy
for given polar invariants. Then, this quantity is minimised with respect to the polar invariants which characterise the magnitude
of the anisotropic components of the elastic stiffness tensor. Optimal uncoupled composite laminates corresponding to this
optimum are presented for membrane and bending loadings. 相似文献
13.
A visco-elastoplastic model for the impact between a compact body and a composite target is presented. The model is a combination
of a nonlinear contact law that includes energy loss due to plastic deformation and a viscous element that accounts for energy
losses due to wave propagation and/or damping. The governing nonlinear equations are solved numerically to obtain the response.
A piecewise linear version of the model is also presented, which facilitates analytical solution. The model predictions are
compared to those of the well-known and commonly used Hunt–Crossley model. The effects of the various impact parameters, such
as impactor mass, velocity, plasticity, and damping, on the impact response and coefficient of restitution are investigated.
The model appears to be suitable for a wide range of impact situations, with parameters that are well defined and easily calculated
or measured. Furthermore, the resulting coefficient of restitution is shown to be a function of impact velocity and damping,
as confirmed by published experimental data. 相似文献
14.
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
15.
The paper deals with the problem of existence of the minimum path for movable end-points in the one-of-degree-of-freedom mechanical
system. The criteria for obtaining of extremum path for movable end-points is extended with new criteria for minimum. The
nonsimultaneous variational calculus is applied. It is assumed that the actual path belongs to sub-set C
2 of admissible curves. The series expansion up to the second order small values is applied and the first and the second variation
of functional are calculated. It is proved that the necessary and sufficient conditions for the minimum path are that the
first order variation is zero and the second order variation is positive. The second conditions are based on the arbitrary
solution of Riccati’s differential equation and also the known Legender’s and Jacobi criteria for minimum for the case of
fixed end-points. Two examples are solved: the problem of the minimal length of a curve joining two fixed boundary curves
and problem of motion of a particle between variable boundaries for which the Hamilton action integral is minimal. 相似文献
16.
Emrullah Yaşar 《Nonlinear dynamics》2008,54(4):307-312
We generate conservation laws for the Burridge–Knopoff equation which model nonlinear dynamics of earthquake faults by a new
conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation
(or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined
by the adjoint equations to the Burridge–Knopoff equation. 相似文献
17.
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
18.
In this paper the physically-based approach to non-local elasticity theory is introduced. It is formulated by reverting the
continuum to an ensemble of interacting volume elements. Interactions between adjacent elements are classical contact forces
while long-range interactions between non-adjacent elements are modelled as distance-decaying central body forces. The latter
are proportional to the relative displacements rather than to the strain field as in the Eringen model and subsequent developments.
At the limit the displacement field is found to be governed by an integro-differential equation, solved by a simple discretization
procedure suggested by the underlying mechanical model itself, with corresponding static boundary conditions enforced in a
quite simple form. It is then shown that the constitutive law of the proposed model coalesces with the Eringen constitutive
law for an unbounded domain under suitable assumptions, whereas it remains substantially different for a bounded domain. Thermodynamic
consistency of the model also has been investigated in detail and some numerical applications are presented for different
parameters and different functional forms for the decay of the long range forces. For simplicity, the problem is formulated
for a 1D continuum while the general formulation for a 3D elastic solid has been reported in the appendix. 相似文献
19.
Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations 总被引:1,自引:0,他引:1
This investigation is concerned with the use of an implicit integration method with adjustable numerical damping properties
in the simulation of flexible multibody systems. The flexible bodies in the system are modeled using the finite element absolute nodal coordinate formulation (ANCF), which can be used in the simulation of large deformations and rotations of flexible bodies. This formulation, when
used with the general continuum mechanics theory, leads to displacement modes, such as Poisson modes, that couple the cross section deformations, and bending and extension of structural elements such as beams. While these
modes can be significant in the case of large deformations, and they have no significant effect on the CPU time for very flexible
bodies; in the case of thin and stiff structures, the ANCF coupled deformation modes can be associated with very high frequencies that can be a source of numerical problems when explicit integration methods
are used. The implicit integration method used in this investigation is the Hilber–Hughes–Taylor method applied in the context of Index 3 differential-algebraic equations (HHT-I3). The results obtained using this integration method are compared with the results obtained using an explicit Adams-predictor-corrector method, which has no adjustable numerical damping. Numerical examples that include bodies with different degrees of flexibility
are solved in order to examine the performance of the HHT-I3 implicit integration method when the finite element absolute
nodal coordinate formulation is used. The results obtained in this study show that for very flexible structures there is no
significant difference in accuracy and CPU time between the solutions obtained using the implicit and explicit integrators.
As the stiffness increases, the effect of some ANCF coupled deformation modes becomes more significant, leading to a stiff
system of equations. The resulting high frequencies are filtered out when the HHT-I3 integrator is used due to its numerical
damping properties. The results of this study also show that the CPU time associated with the HHT-I3 integrator does not change
significantly when the stiffness of the bodies increases, while in the case of the explicit Adams method the CPU time increases
exponentially. The fundamental differences between the solution procedures used with the implicit and explicit integrations
are also discussed in this paper. 相似文献
20.
E. R. Viana R. M. Rubinger H. A. Albuquerque F. O. Dias A. G. de Oliveira G. M. Ribeiro 《Nonlinear dynamics》2012,67(1):385-392
We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim
to build the Periodicity-parameter-space (P-parameter-space). As results of the P-parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of
accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results
agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work. 相似文献
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