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1.
SINGULAR ANALYSIS OF BIFURCATION OF NONLINEAR NORMAL MODES FOR A CLASS OF SYSTEMS WITH DUAL INTERNAL RESONANCES 总被引:3,自引:0,他引:3
IntroductionAninterestingfeatureinthefreevibrationofanonlinearsystemisthefactthatthenumberofexistingnormalmodesmayexceedthenumberofdegreesoffreedom ,aphenomenonnotencounteredinalinearsystemandcausedbymodebifurcation .Thereforemuchworkhasbeendoneonthest… 相似文献
2.
The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor. 相似文献
3.
Zhang Jianwu Professor Doctor Humboldt Research Fellow Li Qi Shu Yongping 《应用数学和力学(英文版)》2000,21(5):529-536
A new refined first-order shear-deformation plate theory of the Kármán type is presented for engineering applications and
a new version of the generalized Kármán large deflection equations with deflection and stress functions as two unknown variables
is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner
theory. In this refined plate theory two rotations that are constrained out in the formulation are imposed upon overall displacements
of the plates in an implicit role. Linear and nonlinear investigations may be made by the engineering theory to a class of
shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates,
and laminated shear-deformable plates. Reduced forms of the generalized Kármán equations are derived consequently, which are
found identical to those existe in the literature.
Foundation item: the National Natural Science Foundation of China (59675027)
Biography: Zhang Jianwu (1954-) 相似文献
4.
IntroductionMuchworkhasbeendevotedinthelastfewdecadestothemeasurementandmodelingofthescalinglawofstructurefunctionofturbulentflows.Theso_called“velocitystructurefunctionofordern”forturbulentflowsisdefinedas〈ΔV(r) n〉 ,whereΔV(r) =V(x r) -V(x)isthevelocitycomp… 相似文献
5.
Shifang Han 《Acta Mechanica Sinica》2007,23(2):149-158
A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid
crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of
the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic
unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of
LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the
modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied
for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given
in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational
motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational
viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive
equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed.
The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English
text was polished by Yunming Chen. 相似文献
6.
7.
The present study develops the fracture theory for a two-dimensional octagonal quasicrystals. The exact analytic solution of a Mode Ⅱ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate were determined, the physical sense of the results relative to phason and the difference between mechanical behaviors of the crack problem in crystal and quasicrystal were figured out. These provide important information for studying the deformation and fracture of the new solid phase. 相似文献
8.
The rheological behaviour of Ca(OH)2 suspensions is investigated, predominantly at a solid volume fraction of 0.25. The influence of standing without being subject
to shear (“contact time”) is distinguished from that of being sheared (“shearing time”). The results are interpreted on the
basis of the “elastic floc” model of energy dissipation during flow, with a view to the problem whether, in addition to an
energy dissipation term related to the viscous drag experienced by particles moving within flocs, there should be an independent
energy dissipation term related to fluid movement in the flocs when they change volume or shape. It appears that this additional
energy dissipation term is not necessary, if the increase in viscous friction, experienced by two particles which are close
together, is taken into account.
Paper, presented at the First Conference of European Rheologists at Graz, April 14–16, 1982. A short version has been published
in [18]. 相似文献
9.
The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing
harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the
problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation
of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence
of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed.
Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998.
The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386). 相似文献
10.
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blowup phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘ small ‘ solution. 相似文献
11.
In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja's tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory. 相似文献
12.
张双寅 《应用数学和力学(英文版)》2002,23(3):271-275
IntroductionAsshownbyZHANGandXIONG ( 1 997) [1],underconstantloadingthecrackinviscoelasticmaterialshasanincubationtime ,withinitthecrackopeningdisplacement (COD)ischanginglargerwithtime,whilethecracklengthkeepsconstant.Investigationonthegradualopeningofthecrac… 相似文献
13.
To predict the characteristics of dense liquid-solid two-phase flow, K-ε-T model is established, in which the turbulent flow of fluid phase is described with fluid turbulent kinetic energy Kf and its dissipation rate εf, and the particles random motion is described with particle turbulent energy Kp and its dissipation rate εp and pseudothermal temperature Tp. The governing equations are also derived. With K-ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured. 相似文献
14.
15.
Buoyant flow is analysed for a vertical fluid saturated porous layer bounded by an isothermal plane and an isoflux plane in
the case of a fully developed flow with a parallel velocity field. The effects of viscous dissipation and pressure work are
taken into account in the framework of the Oberbeck–Boussinesq approximation scheme and of the Darcy flow model. Momentum
and energy balances are combined in a dimensionless nonlinear ordinary differential equation solved numerically by a Runge–Kutta
method. Both cases of upward pressure force (upward driven flows) and of downward pressure force (downward driven flows) are examined. The thermal behaviour for upward driven flows and downward driven flows is quite different. For upward driven
flows, the combined effects of viscous dissipation and pressure work may produce a net cooling of the fluid even in the case
of a positive heat input from the isoflux wall. For downward driven flows, viscous dissipation and pressure work yield a net
heating of the fluid. A general reflection on the roles played by the effects of viscous dissipation and pressure work with
respect to the Oberbeck–Boussinesq approximation is proposed. 相似文献
16.
The numerical modeling of the conjugate heat transfer and fluid flow through the micro-heat sink was presented in the paper,
considering the viscous dissipation effect. Three different fluids with temperature dependent fluid viscosity are considered:
water, dielectric fluid HFE-7600 and isopropanol. The square shape of the cross-section is considered with D
h
= 50 μm with a channel length L = 50 mm. As most of the reported researches dealt with fully developed fluid flow and constant fluid properties in this paper
the thermal and hydro-dynamic developing laminar fluid flow is analyzed. Two different heat transfer conditions are considered:
heating and cooling at various Br. The influence of the viscous heating on local Nu and Po is analyzed. It was shown that
for a given geometry the local Po and Nu numbers are strongly affected by the viscous heating. Moreover the Po number attains
the fully developed value as the external heating is equal with the internal viscous heating. 相似文献
17.
A new micromechanics constitutive model for pure dilatant transformation plasticity of structure ceramics is proposed in this
paper. Based on the thermodynamics, micromechanics and microscalet→m transformation mechanism analysis of the TZP and PSZ ZrO2-containing ceramics, an analytic expressions of the Helmholtz and complementary free energy of the constitutive element for
the case of pure dilatant transformation is derived for the first time in a self-consistent manner. By the analysis of energy
dissipation in the forward and reverse transformations, the micromechanics constitutive law is derived in the framework of
Hill-Rice's internal variable constitutive theory.
The project is supported by the National Natural Science Foundation of China. 相似文献
18.
The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated
porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new
model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development
of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq
approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem.
Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found
that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state. 相似文献
19.
A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.The project supported by the National Natural Science Foundation of China (10172023) 相似文献
20.
Frederico J. M. F. Custódio Patrick D. Anderson Gerrit W. M. Peters António M. Cunha Han E. H. Meijer 《Rheologica Acta》2010,49(1):23-44
Residual stresses are a major issue in the mechanical and optical behavior of injection-molded parts. In this study, we analyze
their development in the case of gas-assisted injection molding (GAIM) of amorphous polymers. Flow-induced residual stresses
are computed within a decoupled approach, in which elastic effects are neglected in the momentum balance, assuming a generalized
Newtonian material behavior. In a staggered procedure, the computed viscous flow kinematics are used to calculate normal stresses
employing a compressible version of the Rolie-Poly model. For the computation of thermally and pressure-induced residual stresses,
a linear thermo-viscoelastic model is used. A 3-D finite element model for GAIM is employed, which is able to capture the
kinematics of the flow front and whose capabilities to predict the thickness of the residual material layer have been validated
by Haagh and Van de Vosse (Int J Numer Methods Fluids 28:1355–1369, 1998). In order to establish a clear comparison, the development of residual stresses is analyzed using standard injection molding
and GAIM for a test geometry. 相似文献