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1.
The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator
with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition
and Monte–Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio
of safe initial points (RSIP) is presented in some given limited domain defined by the system’s Hamiltonian for various parameters
or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed
on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From
the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited
by harmonic or stochastic forces, which are different from the customary continuous ones in view of the first-passage problems.
In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external
harmonic excitation when the Gaussian white noise is also present in the system.
The project supported by the National Natural Science Foundation of China (10302025 and 10672140).
The English text was polished by Yunming Chen. 相似文献
2.
Sébastien Barré Christophe Bogey Christophe Bailly 《Theoretical and Computational Fluid Dynamics》2008,22(1):65-82
The aerodynamic evolution and the acoustic radiation of elliptic vortices with various aspect ratios and moderate Mach numbers
are investigated by solving numerically the full compressible Navier–Stokes equations. Three behaviours are observed according
to the aspect ratio σ = a/b where a and b are the major and minor semi-axes of the vortices. At the small aspect ratio σ = 1.2, the vortex rotates at a constant angular velocity and radiates like a rotating quadrupole. At the moderate aspect
ratio σ = 5, the vortex is initially unstable. However the growth of instability waves is inhibited by the return to axisymmetry
which decreases its aspect ratio. The noise level becomes lower with time and the radiation frequency increases. For vortices
with larger aspect ratios σ ≥ 6, the return to axisymmetry does not occur quickly enough to stop the growth of instabilities, which splits the vortices.
Various mergers are then found to occur. For instance in the case σ = 6, several successive switches between an elliptic state and a configuration of two co-rotating vortices are observed.
The present results show that the initial value of the aspect ratio yields the relative weight between the return to axisymmetry
which stabilizes the vortex and the growth of instabilities which tends to split it. Moreover the noise generated by the vortices
is also calculated using the analytical solution derived by Howe (J. Fluid Mech. 71:625–673, 1975) and is compared with the
reference solution provided by the direct computation. This solution is found to be valid for σ = 1.2. An extended solution is proposed for higher aspect ratios. Finally, the pressure field appears weakly affected by
the switches between the two unstable configurations in the case σ = 6, which underlines the difficulty to detect the split or the merger of vortices from the radiated pressure. This study
also shows that elliptic vortices can be used as a basic configuration of aerodynamic noise generation.
相似文献
3.
We investigate the steady-state rheological behaviour of the lamellar phase of a lyotropic system (CpCl, hexanol, brine)
and of a thermotropic system (8CB). Power laws characterize the behaviour of the imposed stress as a function of the measured
shear rate and similarities are observed for both systems; the same regime γ˙∼σ
m
with m≈1.7 is obtained at low shear stresses corresponding to a texture of oily streaks oriented in the direction of the flow, as
shown by microscopic observations. The “onion state” only exists in the case of dilute samples of the lyotropic lamellar phase;
the stress then varies as γ˙∼σ
m
with m≈4.8, as already observed by other groups with different systems. Rheological measurements at different temperatures allow
determination of different activation energies relating to the still badly understood processes involved in the different
rheological regimes. We propose a model which reproduces the experimental power laws and which is based on an analogy with
the theory of high-temperature creep in metals and alloys.
Received: 19 October 1999/Accepted: 1 November 1999 相似文献
4.
Fundamental experiments are carried out to examine the parameter that dominates the slip-band initiation in electroplated
copper foil under the condition where the mean stress as well as the stress amplitude varies. In the case of constant-amplitude
stressing, the relation between the critical stress for the slip-band initiation σ
p
and the number of cyclesN is well represented by σ
p
α
N=C. In other words, the slip bands appear when the total hysteresis energy applied to the copper foil attains a critical value.
In the case of variable stresses, the range-pair mainly dominates the occurrence of the slip bands, and Miner's linear cumulative
damage rule holds for the accumulation of the fatigue damage for the slip-band initiation. Accordingly, the parameter (Σσ
i
α
n
i/Σn
i)1/α is equivalent to the critical stress σ
p
under constant amplitude stressing, where σ
i
andn
i are the stress amplitude and the number of cycles counted by the range-pair method, respectively, and α is the exponent of
the σ
p
-N relation. Based on these results, the applicability of the copper foil to the fatigue gage that accumulates and indicates
a load experience is discussed. 相似文献
5.
A. M. Lokoshchenko 《Mechanics of Solids》2012,47(3):357-372
An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ e on the principal stresses. Statistical methods are used to obtain an expression for σ e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ e by using additional material constants are considered. 相似文献
6.
This paper uses a variational approach to establish existence of solutions (σ
t
, v
t
) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ
0, σ
T
are prescribed in , the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer
of the action when the time interval [0,T] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σ
t
in . When σ
t
= δ
y(t) is a Dirac mass, the Euler–Poisson system reduces to . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure
Appl Math, to appear) as a Hamiltonian system.
WG gratefully acknowledges the support provided by NSF grants DMS-02-00267,
DMS-03-54729 and DMS-06-00791.
TN gratefully acknowledges the postdoctoral support provided by NSF grants DMS-03-
54729 and the School of Mathematics.
AT gratefully acknowledges the support provided by the School of Mathematics. 相似文献
7.
A method is presented that determines photoelastic isochromatic values at the nodal points of a grid mesh which in turn is
generated by a computer program that accepts digitized input. Values of σ1 - σ2 are computed from the digitized fringe orders. The Laplace equation is solved to separate the principal stresses at each
nodal point. The method is extended to digitize isoclinics. Subsequently, σ
x
- σ
y
and τ
xy
are calculated to be used as starting values for the solution of the pertaining partial differential equations to enhance
convergence. For further accelerating the rate of convergence, superfluous boundary conditions are added from the digitized
data; significant improvement is demonstrated. Estimated values of σ
x
- σ
y
from the digitized data are further used in conjunction with the solution of the Laplace equation to determine the state
of stress without solving the boundary value problems.
Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10. 相似文献
8.
Mohamed S. Soliman 《Nonlinear dynamics》1994,6(3):317-329
In this paper we examine the response of a typical nonlinear system that is subjected to parametric excitation. Particular attention is paid to how basins of attraction evolve such that the global transient stability of the system may be assessed. We show that at a forcing level that is considerably smaller than that at which the steady-state attractor loses its stability, there may exist a rapid erosion and stratification of the basin, signifying a global loss of engineering integrity of the system.We also show, for a system near its equilibrium state, that the boundaries in parameter space can become fractal. The significance of such an analysis is not only that it corresponds to a failure locus for a system subjected to a sudden pulse of excitation, but since the phase-space basin is often eroded throughout its central region, the determination of basin boundaries in control space can often reflect the characteristics of the phase-space basin structure, and hence on the macroscopic level they provide information regarding the global transient stability of the system. 相似文献
9.
We consider a time-dependent free boundary problem with radially symmetric initial data: σt − Δσ + σ = 0 if and σ(r,0)=σ0(r) in {r < R(0)} where R(0) is given. This is a model for tumor growth, with nutrient concentration (or tumor cells density) σ(r,t) and proliferation rate then there exists a unique stationary solution (σS(r), RS), where RS depends only on the number . We prove that there exists a number μ*, such that if μ < μ* . . . then the stationary solution is stable with respect to non-radially symmetric perturbations, whereas if μ > μ* then the stationary solution is unstable. 相似文献
10.
G. Wolansky 《Archive for Rational Mechanics and Analysis》2001,156(3):205-230
Static solutions of the SO(3)-symmetric Vlasov-Einstein system are studied via a variational approach. For the constitutive
relation of the Emden-Fowler type φ(E,F)≡E
σ+ 1
F
k
we prove the existence of such solutions of sufficiently small mass-energy, provided 0<σ < k+3/2. These solutions are local minimizers of the energy-Casimir functional, subjected to a variational barrier.
Accepted July 16, 2000?Published online January 22, 2001 相似文献
11.
Noise-Induced Chaos in Duffing Oscillator with Double Wells 总被引:2,自引:0,他引:2
Chunbiao Gan 《Nonlinear dynamics》2006,45(3-4):305-317
Stochastic Melnikov method is employed to predict noise-induced chaotic response in the Duffing oscillator with double wells. The safe basin is simulated to show the noise-induced fractal boundary. Three cases are considered: harmonic excitation, both harmonic and Gaussian white noise excitations, and Gaussian white noise excitation. The leading Lyapunov exponent estimated by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can be fractal even if the system is excited only by external Gaussian white noise. 相似文献
12.
T.C.T. Ting 《Journal of Elasticity》1998,53(1):47-64
Antman and Negron-Marrero [1] have shown the remarkable nature of a sphere of nonlinear elastic material subjected to a uniform
pressure at the surface of the sphere. When the applied pressure exceeds a critical value the stress at the center r=0 of the sphere is infinite. Instead of nonlinear elastic material, we consider in this paper a spherically uniform linear anisotropic elastic material. It means that the stress-strain law referred to a spherical coordinate system is the same for any material point.
We show that the same remarkable nature appears here. What distinguishes the present case from that considered in [1] is that
the existence of the infinite stress at r=0 is independent of the magnitude of the applied traction σ0 at the surface of the sphere. It depends only on one nondimensional
material parameter κ. For a certain range of κ a cavitation (if σ0>0) or a blackhole (if σ0<0) occurs at the center of the sphere. What is more remarkable is that, even though the deformation is radially symmetric,
the material at any point need not be transversely isotropic with the radial direction being the axis of symmetry as assumed
in [1]. We show that the material can be triclinic, i.e., it need not possess a plane of material symmetry. Triclinic materials that have as few as two independent elastic
constants are presented. Also presented are conditions for the materials that are capable of a radially symmetric deformation
to possess one or more symmetry planes.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
13.
P. Balakumar 《Theoretical and Computational Fluid Dynamics》1997,9(2):103-119
Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the
full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order
compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette
flow is stable at all Reynolds numbers when the Couette velocity component σ2 exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the
combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ2. It is found that, for small σ2, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds
number gradually increases with increasing σ2. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with
an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ2 values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ2. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases
slowly up to σ2∼ 0.2 and remains constant until σ2∼ 0.58. Beyond σ2 > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear
equilibrium solutions do not exist beyond a critical σ2 value of about 0.59.
Received: 26 November 1996 and accepted 12 May 1997 相似文献
14.
15.
A critical review of microscale mechanical testing methods used in the design of microelectromechanical systems 总被引:4,自引:0,他引:4
Microelectromechanical systems (MEMS) technologies are evolving at a rapid rate with increasing activity in the design, fabrication,
and commercialization of a wide variety of microscale systems and devices. The importance of accurate mechanical property
measurement for successful design was realized early on in the development of this field. Consequently, there exist many different
techniques to measure quantities such as the Young's modulus (E), yield strength (σ
Y
), fracture strength (σ
F
), residual stress (σ
F
), and residual stress gradient (∇σ
R
) of microscale structures and materials. We review and critically compare several of the important techniques including the
microtension test, axisymmetric plate bend test, microbeam bend test, M-test, wafer curvature measurements, dynamic (resonant)
tests, fabrication of passive strain sensors, and Raman spectroscopy. We discuss the characteristics of typical test structures,
and the common sources of structure-related errors in measurement. A rational approach for the selection of test techniques
for the design of microsystems is suggested. 相似文献
16.
This paper describes a new test facility for determining material mechanical properties of structural concrete. The novel
facility subjects 100 mm cubic concrete specimens to true multiaxial compression (σ1 ≠ σ2 ≠ σ3) up to 400 MPa at temperatures of up to 300°C. Forces are delivered through three independent loading frames equipped with
servo-controlled hydraulic actuators creating uniform displacement boundary conditions via rigid platens. Specimen deformation
is calculated from displacements measured to an accuracy of 10−6 m using a system of six laser interferometers. The combination of stiff loading frames, rigid platens, an accurate and reliable
strain measurement system and a fast control system enables investigation of the material response in the post-peak range.
The in-house developed control software allows complex multi-stage experiments involving (i) load and temperature cycling,
(ii) small stress probes and (iii) arbitrary (pre-defined) loading paths. The program also enables experiments in which the
values of the control parameters and the execution of the test sequences depend on the response of the specimen during the
test. The capabilities of the facility are illustrated in this paper by experiments determining the effects of different heat-load
regimes on the strength and stiffness of the material and tests identifying the tangent stiffness matrix of the material and
the associated changes in the acoustic tensor under multiaxial compression. 相似文献
17.
The effects of localized wall blowing through a porous strip are investigated using hot-wire anemometry in a turbulent channel flow. Three blowing magnitudes are studied: σ=0.22, 0.36 and 0.58, where σ is the momentum flux gain ratio and that of the incoming channel flow at three different positions from the spanwise porous strip. The main emphasis of this work was the departure from isotropy of the turbulent flow with localized blowing. The anisotropic invariant map (AIM) for the Reynolds stress tensor revealed that blowing decreased the anisotropy of the turbulent structure in the near-wall region, and a decrease in the longitudinal integral length scale was observed when the blowing rate increased. 相似文献
18.
Experimental results are presented that reveal the relationship between the root mean square of the surface temperature field
of an air/water interface (σ) and the heat flux (q′′) emanating from that interface, over a range of wind speeds. Experiments were conducted for wind speeds ranging from 1.0
to 4.0 m/s to determine if and how the σ versus q′′ relationship was affected by wind speed. Consistent surfactant coverage conditions were maintained for wind speeds ranging
from 1.0 to 2.6 m/s, and these are the focus of the results presented herein. For wind speeds above 2.6 m/s the surfactant
was consistently pushed downstream, resulting in an inhomogeneous surface condition for the air/water interface. For wind
speeds less than 2.6 m/s the relationship between σ and q′′ is approximately linear and is weakly dependent on wind speed. The surface temperature field was obtained by infrared (IR)
imaging. Sample IR images are presented in addition to the σ versus q′′ data. IR images are presented for surfaces covered with insoluble surfactants (liquid phase and solid phase), a soluble
surfactant, and a clean water surface.
相似文献
J. R. SaylorEmail: |
19.
This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the
principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the
variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries
heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from
erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude
can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.
The project supported by the National Natural Science Foundation of China and PSF of China. 相似文献
20.
Lawrence C. Evans 《Archive for Rational Mechanics and Analysis》2010,197(3):1053-1088
We investigate the vanishing viscosity limit for Hamilton–Jacobi PDE with nonconvex Hamiltonians, and present a new method
to augment the standard viscosity solution approach. The main idea is to introduce a solution σ
ε
of the adjoint of the formal linearization, and then to integrate by parts with respect to the density σ
ε
. This procedure leads to a natural phase space kinetic formulation and also to a new compensated compactness technique. 相似文献