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1.
James A. Ellison Martin Kummer A. W. Sáenz 《Journal of Dynamics and Differential Equations》1993,5(2):241-277
The rapidly forced pendulum equation with forcing sin((t/), where =<0p,p = 5, for
0, sufficiently small, is considered. We prove that stable and unstable manifolds split and that the splitting distanced(t) in the (
,t) plane satisfiesd(t) = sin(t/) sech(/2) +O(
0
exp(–/2)) (2.3a) and the angle of transversal intersection,, in thet = 0 section satisfies 2 tan/2 = 2S
s
= (/2) sech(/2) +O((
0
/) exp(–/2)) (2.3b) It follows that the Melnikov term correctly predicts the exponentially small splitting and angle of transversality. Our method improves a previous result of Holmes, Marsden, and Scheuerle. Our proof is elementary and self-contained, includes a stable manifold theorem, and emphasizes the phase space geometry. 相似文献
2.
The paper reports the outcome of a numerical study of fully developed flow through a plane channel composed of ribleted surfaces adopting a two-equation turbulence model to describe turbulent mixing. Three families of riblets have been examined: idealized blade-type, V-groove and a novel U-form that, according to computations, achieves a superior performance to that of the commercial V-groove configuration. The maximum drag reduction attained for any particular geometry is broadly in accord with experiment though this optimum occurs for considerably larger riblet heights than measurements indicate. Further explorations bring out a substantial sensitivity in the level of drag reduction to the channel Reynolds number below values of 15 000 as well as to the thickness of the blade riblet. The latter is in accord with the trends of very recent, independent experimental studies.Possible shortcomings in the model of turbulence are discussed particularly with reference to the absence of any turbulence-driven secondary motions when an isotropic turbulent viscosity is adopted. For illustration, results are obtained for the case where a stress transport turbulence model is adopted above the riblet crests, an elaboration that leads to the formation of a plausible secondary motion sweeping high momentum fluid towards the wall close to the riblet and thereby raising momentum transport.Nomenclature
c
f
Skin friction coefficient
-
c
f
Skin friction coefficient in smooth channel at the same Reynolds number
-
k
Turbulent kinetic energy
-
K
+
k/
w
-
h
Riblet height
-
S
Riblet width
-
H
Half height of channel
-
Re
Reynolds number = volume flow/unit width/
-
Modified turbulent Reynolds number
-
R
t
turbulent Reynolds numberk
2/
-
P
k
Shear production rate ofk,
t
(U
i
/x
j
+ U
j
/x
i
) U
i
/x
j
- dP/dz
Streamwise static pressure gradient
-
U
i
Mean velocity vector (tensor notation)
-
U
Friction velocity, w/ where w=–H dP/dz
-
W
Mean velocity
-
W
b
Bulk mean velocity through channel
-
y
+
yU
/v. Unless otherwise stated, origin is at wall on trough plane of symmetry
-
Kinematic viscosity
-
t
Turbulent kinematic viscosity
-
Turbulence energy dissipation rate
-
Modified dissipation rate – 2(k
1/2/x
j
)2
-
Density
-
k
,
Effective turbulent Prandtl numbers for diffusion ofk and 相似文献
3.
SEBASTIAN Şlicaru 《Journal of Elasticity》1997,46(1):33-42
We consider a surface S = (), where 2 is a bounded, connected, open set with a smooth boundary and : 3 is a smooth map; let () denote the components of the two-dimensional linearized strain tensor of S and let 0 with length 0 > 0. We assume the the norm ,|| ()||0, in the space V0() = { H1() × H1() × L2(); = 0 on 0 } is equivalent to the usual product norm on this space. We then establish that this assumption implies that the surface S is uniformly elliptic and that we necessarily have 0 = . 相似文献
4.
R. G. Deissler 《Applied Scientific Research》1978,34(4):379-392
By utilizing available experimental data for net energy transfer spectra for homogeneous turbulence, contributions P(, ) to the energy transfer at a wavenumber from various other wavenumbers are calculated. This is done by fitting a truncated power-exponential series in and to the experimental data for the net energy transfer T(), and using known properties of P(, ). Although the contributions P(, ) obtained by using this procedure are not unique, the results obtained by using various assumptions do not differ significantly. It seems clear from the results that for a region where the energy entering a wavenumber band dominates that leaving, much of the energy entering the band comes from wavenumbers which are about an order of magnitude smaller. That is, the energy transfer is rather nonlocal. This result is not significantly dependent on Reynolds number (for turbulence Reynolds numbers based on microscale from 3 to 800). For lower wavenumbers, where more energy leaves than enters a wavenumber band, the energy transfer into the band is more local, but much of the energy then leaves at distant wavenumbers. 相似文献
5.
LDA measurements of the mean velocity in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U
from the value of /y at the wall. The trend of the Reynolds number dependence of /
is similar to the direct numerical simulations of Spalart (1988). 相似文献
6.
J. Meiβner 《Rheologica Acta》1971,10(2):230-242
Zusammenfassung In einem Dehnungsrheometer werden Spannungs-Dehnungs-Diagramme von Polyäthylen-Schmelzen bei 150 °C und bei konstanter Dehnungsgeschwindigkeit
gemessen (
zwischen 0,001 und 1 sec–1). Weiterhin wird der reversible (elastische) Dehnungsanteil bestimmt. Messungen mit einem Dehnungstester für Kunststoff-Schmelzen ergänzen die Ausführungen.Die Ergebnisse zeigen deutlich, daß bei Dehnung mit zunehmender Verformungsgeschwindigkeit die Dehnungsviskosität nicht abnimmt, im Gegensatz zu dem bekannten strukturviskosen Verhalten bei Scherung.Bei Dehnungen bis zu=1 kann das Verhalten unabhängig von
beschrieben werden, wenn als viskoelastische Materialfunktion die Dehnungs-Spannviskosität
betrachtet wird. In diesem Bereich von gilt dabei die BeziehungT(t)=3
s
(t) mit
s
(t) als zeitabhängige Scherviskosität im linear-viskoelastischen Bereich.Bei größeren Dehnungen und nicht zu kleinen Dehnungsgeschwindigkeiten zeigt verzweigtes Polyäthylen eine zusätzliche starke Spannungszunahme. In dem Bereich dieser zusätzlichen Verfestigung ist das Verhalten im wesentlichen eine Funktion der Dehnung und fast unabhängig von
. Die zusätzliche Verfestigung scheint eine Folge der Verzweigungsstruktur des verzweigten Polyäthylens zu sein, da bei Linear-PE ein derartiger Verlauf des Spannungs-Dehnungs-Diagramms nicht beobachtet wird.Die Betrachtung des reversiblen Dehnungsanteils
R
zeigt bei der ausführlich untersuchten Schmelze I (verzweigtes PE) drei verschiedene Bereiche: Unterhalb einer Grenzdehnungsgeschwindigkeit
ist
R
=0, unterhalb einer Versuchszeitt
** ist
R
=. Im dazwischenliegenden Bereich treten elastische und viskose Dehnungsanteile auf,=
R
+
V
, wobei für niedrige
gilt, daß
R
lg
. Die Grenze
wird der Frequenz der thermisch aktivierten Platzwechsel zugeordnet,t
** erscheint als Zeit, innerhalb der die Verhakungen wie fixierte Vernetzungen wirken.In dem Anhang wird der Einfluß der Grenzflächenspannung zwischen PE-Schmelze und Silikonöl auf die Ergebnisse der Dehnungsversuche diskutiert.
Vorgetragen auf der Deutschen Rheologen-Tagung, Berlin, 11.-13. Mai 1970.
An der Weiterentwicklung des Dehnungsrheometers, an der Durchführung und Auswertung der Messungen waren die HerrenB. Kienle, F. Landmesser, M, Reuther undF. Scherr beteiligt. Herr Dr.F.Ramsteiner und HerrH. Schroeck haben sich um die Herstellung der Stränge aus Linear-PE bemüht. Herr Dr.W. Ball besorgte die GPC-Messungen und Herr Dr.P. Simak die Ultrarot-Untersuchung. Den vorgenannten Herren sei für ihre Hilfe beim Zustandekommen dieser Arbeit gedankt. Herrn Dr.H. Baur danke ich für wertvolle Diskussionen. 相似文献
Summary Stress-strain relations for different PE melts are measured at 150 °C in an extensional rheometer under the condition of a constant extensional strain rate ( between 0,001 and 1 sec–1). Further, the recoverable (elastic) portion R of the total strain ( in Hencky's measure) is determined and additional measurements with a tensile tester for polymer melts are described.The results show clearly that in extension there is no decrease of the tensile viscosity with increasing deformation rate, in contrast to the well-known pseudoplastic behaviour in shear. Within total strains<1 the tensile behaviour can be described independently from by means of a viscoelastic material function called stressing viscosity . In this range of the relation T (t)=3 s (t) holds, where s (t) is the stressing viscosity in shear in the linear viscoelastic range. For larger tensile strains and not too small branched PB shows a remarkable increase in stress. This work-hardening behaviour is mainly a function of and almost independent from . This additional hardening seems to be due to the branches in branched PE, because linear PE does not show this effect.The discussion of the recoverable tensile strain R gives three regions of tensile rate: Below a critical there is R =0. At times shorter thant ** the equation R = is valid. Within these limits both elastic and viscous portions of the total strain= R + V exist. may correlate with the frequency of the thermally activated position changes of the molecular segments.t ** is assumed to be the time for the entanglements to act as fixed cross-links.In the appendix the influence of the interface tension between PE melt and silicone oil on the results of the tensile experiments is discussed.
Vorgetragen auf der Deutschen Rheologen-Tagung, Berlin, 11.-13. Mai 1970.
An der Weiterentwicklung des Dehnungsrheometers, an der Durchführung und Auswertung der Messungen waren die HerrenB. Kienle, F. Landmesser, M, Reuther undF. Scherr beteiligt. Herr Dr.F.Ramsteiner und HerrH. Schroeck haben sich um die Herstellung der Stränge aus Linear-PE bemüht. Herr Dr.W. Ball besorgte die GPC-Messungen und Herr Dr.P. Simak die Ultrarot-Untersuchung. Den vorgenannten Herren sei für ihre Hilfe beim Zustandekommen dieser Arbeit gedankt. Herrn Dr.H. Baur danke ich für wertvolle Diskussionen. 相似文献
7.
Equations are derived for the gasdynamics of a dense plasma confined by a multiple-mirror magnetic field. The limiting cases of large and small mean free paths have been analyzed earlier: 0 and k, where is the length of an individual mirror machine, 0 is the size of the mirror, and k is the mirror ratio. The present work is devoted to a study of the intermediate range of mean free paths 0 k. It is shown that in this region of the parameters the process of expansion of the plasma has a diffusional nature, and the coefficients of transfer of the plasma along the magnetic field are calculated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 14–19, November–December, 1974.The authors thank D. D. Ryutov for the statement of the problem and interest in the work. 相似文献
8.
The two-dimensional stationary turbulent buoyant flow and heat transfer in a cavity at high Rayleigh numbers was computed numerically. The k– turbulence model was used. The time-averaged equations for momentum, energy and continuity, which are coupled to the turbulence equations, were solved using a finite difference formulation. In order to validate the computer code, a comparison exercise was carried out. The test results are in good agreement with the internationally accepted benchmark solution. Grid-refinement shows the necessity of a very fine grid at high Rayleigh numbers with especially small grid-distances in the near-wall region. The computed boundary layer velocity profiles are in excellent agreement with available experimental data. The local heat transfer in the turbulent part of the boundary layers is predicted 20% too high. Computations were carried out for the natural convective flow in a room induced by a hot radiator and a cold window. Various radiator configurations and types of thermal boundary conditions were applied including thermal radiation interaction between surfaces.Nomenclature
a
thermal diffusivity (m2/s)
-
C
constant in
t expression
-
D
cavity dimensions (m)
-
g
acceleration of gravity (m/s2)
-
G
k
production/destruction of k by buoyancy (kg/ms3)
-
h
enthalpy (J/kg)
- IX
index of grid point
-
k
turbulent kinetic energy (m2/s2)
-
m
dimensionless stratification parameter
- Nu
overall Nusselt number
- Nu
y
local Nusselt number
- NX
total number of grid points
-
p
pressure (N/m2)
-
P
k
production of k by shear stress (kg/ms3)
-
Q
heat flux through wall (W/m)
- Ra
overall Rayleigh number
- Ra
y
local Rayleigh number
- Re
t
turbulent Reynolds number
-
S
source term in -equation (kg/ms4)
-
S
source term for
-
T
c, T
h
temperatures of cold and hot walls (K)
-
T
s
(y)
stratification temperature on vertical mid-line (K)
-
T
0
mean cavity temperature (K)
-
u, v
horizontal and vertical velocity components (m/s)
-
u
0
Brunt-Vaisälä velocity scale (m/s)
-
x, y
horizontal and vertical coordinates (m)
-
non-linearity parameter for grid
-
coefficient of thermal expansion (l/K)
-
jet angle (°)
-
diffusivity for
-
S
dissipation rate for turbulent kinetic energy (m2/s3)
-
variable to be solved
-
thermal conductivity (W/mK)
-
,
t
kinematic and eddy viscosities (m2/s)
-
stream function (kg/ms)
-
density (kg/m3)
-
k,
,
t
constants in k– model 相似文献
9.
P. H. Ong 《Rheologica Acta》1970,9(2):299-305
Summary The dielectric properties of the composite system polyurethane-sodium chloride have been measured at frequencies between 10–4 Hz and 3 · 105 Hz in the temperature range from –150 °C up to +90 dgC. Three dielectric loss mechanisms have been found; they are indicated by
1,
2 and. The activation energy of the
1-transition is 35 kcal/mole, that of the-transition 6.7 kcal/mole. The
2-loss peak was only observed at frequencies of 103 Hz and higher, forming one broad peak with the
1-loss peak at lower frequencies. In the composite materials, the- and
2-loss peaks measured at fixed frequencies were found at the same temperature. The
2-loss peak, however, was shifted to a lower temperature, due to the sodium chloride filler. Comparison of experimental data of and tan with theoretical predictions concerning the dielectric properties of composite systems showed only partial agreement. The difference mainly consisted in. the temperature shift in the tan-peak of the
1-transition.
Zusammenfassung Die dielektrischen Eigenschaften des Verbundssystems Kochsalz-Polyurethankautschuk wurden im Frequenzgebiet zwischen 10–4 Hz und 3.105 Hz und im Temperaturbereich von –150 °C bis +90 °C gemessen. Es wurden drei dielektrische Verlustmaxima gefunden, die mit 1, 2 und angedeutet werden. Die Aktivierungsenergie des 1-Überganges beträgt 35 kcal/Mol, die des-Überganges 6.7 kcal/Mol. Das 2-Maximum konnte nur bei Frequenzen höher als 103Hz vom 1-Maximum gesondert erfaßt werden. Die Lage der 2- und-Maxima war vom Füllgrad unabhängig. Das 1-Maximum verschiebt sich mit steigendem Füllgrad zu niedrigeren Temperaturen. Die gemessenen Werte von und tan stimmen nur teilweise mit den Aussagen einer Theorie der dielektrischen Eigenschaften von Mischkörpern überein.相似文献
10.
In this paper, we investigate the interaction of subharmonicresonances in the nonlinear quasiperiodic Mathieu equation,x + [ + (cos 1 t + cos 2 t)] x + x3 = 0.We assume that 1 and that the coefficient of the nonlinearterm, , is positive but not necessarily small.We utilize Lie transform perturbation theory with elliptic functions –rather than the usual trigonometric functions – to study subharmonic resonances associated with orbits in 2m:1 resonance with a respective driver. In particular, we derive analytic expressions that place conditions on (, , 1, 2) at which subharmonic resonance bands in a Poincaré section of action space begin to overlap. These results are used in combination with Chirikov's overlap criterion to obtain an overview of the O() global behavior of equation (1) as a function of and 2 with 1, , and fixed. 相似文献
11.
H. Tennekes 《Applied Scientific Research》1968,18(1):273-279
Summary Similarity laws for the mean flow and scaling laws for the turbulent motion are used in an attempt to obtain a general expression for the eddy viscosity of equilibrium layers. It is found that =0.09 w
2
/w*, in which w
2
is a Reynolds stress representative for the region of overlap between the law of the wall and the velocity-defect law, while w* is the logarithmic slope of the mean velocity profile in that region. The distinction between w
and w* is related to the strong inhomogeneity of the mean rate of strain in the inner layer. The results of the theory agree with experimental evidence obtained from transpired equilibrium layers. 相似文献
12.
The thermal decomposition of nitric oxide (diluted in Argon) has been measured behind incident shock waves by means of IR diode laser absorption spectroscopy. In two independent runs the diode laser was tuned to the=0 =12
3/2
R(18.5)-rotational vibrational transition and the=1 =22
3/2
R(20.5)-rotational vibrational transition of nitric oxide, respectively. These two transitions originating from the vibrational ground state (=0) and the first excited vibrational state (=1) were selected in order to probe the homogeneity along the absorption path. The measured NO decomposition could satisfactorily be described by a chemical reaction mechanism after taking into account boundary layer corrections according to the theory of Mirels. The study forms a further proof of Mirels' theory including his prediction of the laminar-turbulent transition. It also shows, that the inhomogeneities from the boundary layer do not affect the IR linear absorption markedly.This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society. 相似文献
13.
A. V. Zhukov 《Journal of Applied Mechanics and Technical Physics》1986,27(3):424-426
The numerical model of phase transition in iron in stress waves described in [1] contains equations of state with a limited range of applicability. They do not consider thermal excitation of conduction electrons and the presence of and — -triple point on the phase equilibrium curve, the effect of which should appear in shock loading of porous or preheated specimens. The present study will offer thermodynamically complete equations of state for the -, -, -phases of iron, free of these shortcomings.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 112–114, May–June, 1986. 相似文献
14.
A. L. Urintsev 《Fluid Dynamics》1976,11(3):455-457
The character of stability loss of the circular Couette flow, when the Reynolds number R passes through the critical value R0, is investigated within a broad range of variation of the wave numbers. The Lyapunov-Schmidt method is used [1, 2]; the boundary-value problems for ordinary differential equations arising in the case of its realization are solved numerically on a computer. It is shown that the branching character substantially depends on the wave number . For all a, excluding a certain interval (1, 2), the usual postcritical branching takes place: at a small supercriticality the circular flow loses stability and is softly excited into a secondary stationary flow — stable Taylor vortices. For wave numbers from the interval (1,2) a hard excitation of Taylor vortices takes place: at a small subcriticality R=R0–2 the secondary mode is unstable and merges with the Couette flow for 0; however, for a small supercriticality in the neighborhood of a circular flow there exist no stationary modes which are different.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–135, May–June, 1976. 相似文献
15.
The seepage velocity arising from pressure and buoyancy driving forces in a slender vertical layer of fluid-saturated porous media is considered. Quadratic drag (Forcheimer effects) and Brinkman viscous forces are included in the analysis. Parameters are identified which characterize the influence of matrix permeability, quadratic drag and buoyancy. An explicit solution is obtained for pressure-driven flow which illustrates the influence of quadratic drag and the strong boundary layer behavior expected for low permeability media. The experimental data of Givler and Altobelli [2] for water seepage through a high porosity foam is found to yield good agreement with the present analysis. For the case of buoyancy-driven flow, a uniformly valid approximate solution is found for low permeability media. Comparison with the pressure-driven case shows strong similarities in the near-wall region.Nomenclature
B
function of
-
d
layer thickness
-
D
discriminant defined by Equation (9)
-
modified Darcy number
- F
Forcheimer constant
-
g
gravitational acceleration
-
k
porous matrix permeability
-
m
parameter defined by Equation (11)
-
p
pressure
-
p
modified pressure
-
pressure gradient
-
R
buoyancy parameter
-
T
0
nominal layer temperature
-
u
seepage velocity
-
dimensionless seepage velocity
-
c
composite approximation
-
i
boundary layer velocity
-
o
outer or core flow approximation
-
m
midplane velocity
-
U
matching velocity
-
V
cross-sectional average velocity
-
w
variable defined by Equation (12)
-
x, z
Cartesian coordinates
-
,
dimensionless Cartesian coordinates
-
inertia parameter
- T
layer temperature difference
-
larger root of cubic given by Equation (8)
-
fluid dynamic viscosity
-
e
effective viscosity of fluid saturated medium
-
variable defined by Equation (18)
-
0
fluid density
-
smaller root of cubic given by Equation (8)
-
variable defined by Equation (18)
-
stretched inner coordinate
-
porosity
-
function of 相似文献
16.
When blunt bodies are in hypersonic flight, a high-entropy layer of gas with nonzero vorticity is formed near their surface. The transverse gradients of the entropy, density, and gas velocity in the layer are high, which makes it necessary to take into account its absorption by the boundary layer of finite thickness . This vortex interaction is usually accompanied by an increase in the heat flux q and the frictional stress on the wall compared with their values as calculated in accordance with the classical scheme of a thin boundary layer, when the parameters on the outer edge of the boundary layer are set equal to the inviscid parameters on the body. This effect has been investigated on the side surface of slender (with angle 1 to the undisturbed flow) blunt bodies in a hypersonic stream [1–3]. It is shown in the present paper that the effect can have a stronger and even qualitative influence on the flow over blunt bodies with 1 if the radius of curvature Rs of the detached shock wave on the axis is small compared with the midsection radius R of the body. It is shown that the distributions of the heat fluxes with allowance for the vorticity of the inviscid shock layer are similar in the case of slightly blunt (r0/R 0) cones with half-angles less than a critical *.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 50–57, March–April, 1981. 相似文献
17.
In dynamic rheological experiments melt behavior is usually expressed in terms of complex viscosity
*
() or complex modulusG
*
(). In contrast, we attempted to use the complex fluidity
*
() = 1/µ
*
() to represent this behavior. The main interest is to simplify the complex-plane diagram and to simplify the determination of fundamental parameters such as the Newtonian viscosity or the parameter of relaxation-time distribution when a Cole-Cole type distribution can be applied.
*
()
complex shear viscosity
-
()
real part of the complex viscosity
-
()
imaginary part of the complex viscosity
-
G
*
()
complex shear modulus
-
G()
storage modulus in shear
-
G()
loss modulus in shear
-
J
*
()
complex shear compliance
-
J()
storage compliance in shear
-
J()
loss compliance in shear
-
shear strain
-
rate of strain
-
angular frequency (rad/s)
-
shear stress
-
loss angle
-
*
()
complex shear fluidity
-
()
real part of the complex fluidity
-
()
imaginary part of the complex fluidity
-
0
zero-viscosity
-
0
average relaxation time
-
h
parameter of relaxation-time distribution 相似文献
18.
B. Donaev N. Mamadaliev A. I. Yusupov 《Journal of Applied Mechanics and Technical Physics》1986,27(4):565-570
The problem of spherical wave propagation in soil under the action of an intense uniformly decreasing load 0(t) applied to the boundary of a cavity with radius r0 is considered. Soil with a high stress level is modeled either by ideally nonlinearly compressible or elastoplastic material, taking account of linear irreversible unloading for the material. In contrast to [1–7], in order to describe material movement use is made of strain theory [8] with determining functions = (), i=i(i), where , i, , i are the first and second invariants of strain and stress tensors. During material loading these functions are presented in the form of polynomials ()=(i+2¦¦), ii)=(i-2i)i, in which constant coefficients i, i=1, 2) are determined by experiment, taking account of the triaxial stressed state of soil. Solution of the problem is constructed by an analytically reversible method, with prescribed shape for the shock-wave (SW) surface in the form of a second-degree polynomial relating to time t and a numerical method of characteristics for a prescribed arbitrarily decreasing load i(t). On the basis of the analytical equations obtained, calculations are carried out for material parameters (including loading profile) in a computer and stresses and mass velocity of plastic and elastoplastic materials are compared.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 95–100, July–August, 1986.The authors express their sincere thanks to Kh. A. Rakhmatulin for discussing the results of this work. 相似文献
19.
ON THE UNIFICATION OF THE HAMILTON PRINCIPLES IN NONHOLONOMIC SYSTEM AND IN HOLONOMIC SYSTEM 总被引:1,自引:0,他引:1
ONTHEUNIFICATIONOFTHEHAMILTONPRINCIPLESINNONHOLONOMICSYSTEMANDINHOLONOMICSYSTEM(梁立孚)(韦扬)ONTHEUNIFICATIONOFTHEHAMILTONPRINCIPL... 相似文献
20.
For many solid materials the stress relaxation process obeys the universal relationF = – (d/d lnt)max = (0.1 ± 0.01) (
0 —
i
), regardless of the structure of the material. Here denotes the stress,t the time,
0 the initial stress of the experiment and
i
the internal stress. A cooperative model accounting for the similarity in relaxation behaviour between different materials was developed earlier. Since this model has a spectral character, the concepts of linear viscoelasticity are used here to evaluate the corresponding prediction of the dynamic mechanical properties, i.e. the frequency dependence of the storageE () and lossE () moduli. Useful numerical approximations ofE () andE () are also evaluated. It is noted that the universal relation in stress relaxation had a counterpart in the frequency dependence ofE (). The theoretical prediction of the loss factor for high-density polyethylene is compared with experimental results. The agreement is good. 相似文献