共查询到20条相似文献,搜索用时 156 毫秒
1.
M. Abu-Hilal 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(9):637-650
Summary The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random
force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed,
and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation.
Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for
three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force
on the dynamic response of beams are studied in detail.
Received 3 December 2001; accepted for publication 30 April 2002 相似文献
2.
Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of
energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation,
damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described
by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity
for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation
of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically.
Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green–Lagrange strain–displacement
relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in
advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated. 相似文献
3.
A simple Jeffcott rotor is considered with broadband temporal random variations of internal damping which are described using
the theory of Markov processes. Transverse response of the rotor with stiffening nonlinearity either in external damping or
in restoring force is studied by stochastic averaging method. This method reduces the problems to stochastic differential
equations (SDEs) for which analytical solutions are obtained for the Fokker–Planck–Kolmogorov (FPK) equations for stationary
probability density functions (PDFs) of the squared whirl radius of the shaft. These PDFs do exist beyond the dynamic instability
threshold and they correspond to forward whirl of the rotor. At rotation speeds just slightly above the instability threshold,
the response PDF has integrable singularity at zero which corresponds to intermittency in the response. 相似文献
4.
V. V. Bulatov Yu. V. Vladimirov 《Journal of Applied Mechanics and Technical Physics》2008,49(5):762-769
The field of internal gravity waves in a layer of an arbitrary stratified fluid is studied for critical generation modes and
in the vicinity of trajectories of motion of the perturbation sources. The exact solutions describing the structure of a separate
mode of the wave field in the vicinity of the perturbation source in the critical generation modes are investigated, and expressions
for the total field representing the sum of all wave modes are obtained. In the vicinity of the trajectories of the perturbation
sources, asymptotic representations of the eigenfunctions and eigenvalues of the basic vertical spectral problem of internal
waves are constructed in the approximation of large wave numbers and asymptotic expressions for a separate mode of the wave
field are obtained that describe the spatial structure and features of the fields of internal gravity waves.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 70–79, September–October, 2008. 相似文献
5.
The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep
problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions
of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found
by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value
problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form
of operators in the mathematical problem formulation 相似文献
6.
The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite.
The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are
formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed.
The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is
studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations)
or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic
problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear
factors
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005. 相似文献
7.
I. S. Chernyshenko E. A. Storozhuk F. D. Kadyrov 《International Applied Mechanics》2007,43(5):512-518
The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal
pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities.
The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration
is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear,
and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with
allowance for nonlinear factors
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 46–54, May 2007. 相似文献
8.
V. M. Shapovalov 《Journal of Applied Mechanics and Technical Physics》2000,41(2):337-346
The two-dimensional problem of the configuration of a flexible filament of finite length in a deformable viscous fluid is
solved. The flexuural stresses in the filament and the inertial and gravitational forces are not taken into account. The equilibrium
equations are obtained. The friction force that acts on the filament surface from the side of the viscous fluid is proportional
to the flow rate. The specific features of the evolution of a bent filament under the conditions of pure and simple shear
of a fluid are studied numerically. Analytical solutions are obtained for the evolution of a rectilinear filament; in particular,
the stretching force in the filament is found. For the indicated types of flow, the stability of a rectilinear filament against
small perturbations is investigated.
Volzhskii Polytechnical Institute at the Volgograd State Technical University, Volgograd 404121. Translated from Prikladnaya
Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 144–153, March–April, 2000. 相似文献
9.
The stress-strain state of an incompressible cylindrical elastic body with antiplane strain under the action of potential
forces and surface loading constant along the body is considered in a nonlinear formulation in actual variables. The stresses
are expressed via the pressure and independent strains, the pressure is expressed via the force and elastic potentials, and
nonlinear boundary-value problems are posed for strains (and displacements). Various methods for solving these problems are
developed. For the nonlinear equations obtained, some analytical solutions containing free parameters are given, which can
be used as a basis for solving particular problems.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 93–101, November–December, 2006. 相似文献
10.
A nonlinear boundary-value problem for shells is formulated. The problem statement permits us to analyze the behavior of the
postbuckling solutions in a finite-dimensional space with the dimension independent of the discretization technique. A branching
pattern is established for the solutions of the problem in the case of a uniform external pressure. Four characteristic types
of solution are recognized in the case of an arbitrary external pressure. The associated buckling loads are determined. It
is found out that five significant parameters are sufficient for a qualitative analysis of a cylindrical shell
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 103–112, January 2006. 相似文献
11.
Physically and geometrically nonlinear deformation of conical shells with an elliptic hole 总被引:1,自引:1,他引:0
I. S. Chernyshenko E. A. Storozhuk S. B. Kharenko 《International Applied Mechanics》2008,44(2):174-181
The elastoplastic state of conical shells weakened by an elliptic hole and subjected to finite deflections is studied. The
material of the shells is assumed to be isotropic and homogeneous; the load is constant internal pressure. The problem is
formulated and a technique for numerical solution with allowance for physical and geometrical nonlinearities is proposed.
The distribution of stresses, strains, and displacements along the hole boundary and in the zones of their concentration is
studied. The solution obtained is compared with the solutions of the physically and geometrically nonlinear problems and a
numerical solution of the linear elastic problem. The stress-strain state around an elliptic hole in a conical shell is analyzed
considering both nonlinearities
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 69–77, February 2008. 相似文献
12.
In this article, we study the large time behavior of solutions of first-order Hamilton–Jacobi Equations set in a bounded domain
with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence
results for viscosity solutions of these Cauchy–Neumann problems by using two fairly different methods: the first one relies
only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the
second one is an optimal control/dynamical system approach, named the “weak KAM approach”, which requires the convexity of
Hamiltonians and gives formulas for asymptotic solutions based on Aubry–Mather sets. 相似文献
13.
A. V. Fedorov V. M. Fomin T. A. Khmel' 《Journal of Applied Mechanics and Technical Physics》2005,46(6):835-841
A physicomathematical model is developed, which describes gas flows inside rapidly rotating bodies made of cellular-porous
materials. Asymptotic and numerical solutions are obtained for some problems of forced centrifugal convection inside cylindrical
cellular-porous bodies. The effect of the governing parameters (drag coefficient and dimensionless length of the cylinder)
on characteristics and types of flows is considered.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 78–85, November–December, 2005. 相似文献
14.
This note deals with the isothermal linear theory of porous viscoelastic mixtures. Questions of uniqueness and continuous
dependence for solutions of various classes of initial boundary value problems in mixtures consisting of two constituents:
a porous elastic solid and a porous Kelvin–Voigt material are studied. The Lagrange identity and Logarithmic convexity methods
are used to establish uniqueness and continuous dependence results, with no definiteness assumptions upon the internal energy. 相似文献
15.
Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are
obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect
to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing
conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of
elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008. 相似文献
16.
Fu Mo Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(8):1117-1128
This paper investigated the interaction between an edge dislocation and a nonuniformly coated circular inclusion. Based on
the technique of conformal mapping and the method of analytical continuation in conjunction with alternating technique, the
solutions to plane elasticity problems for three dissimilar media are derived explicitly in a series form. For a limiting
case when the thickness of the interphase layer is uniform, the derived analytical solutions of this paper are reduced to
exactly the same results available in the literature. The image force acting on the dislocation is then determined by using
the Peach–Koehler formula. It is found that the combination of material constants and nonuniformity of the interphase thickness
will exert a significant influence on the dislocation force. 相似文献
17.
A. E. Mamontov M. I. Uvarovskaya 《Journal of Applied Mechanics and Technical Physics》2008,49(4):629-641
The problem of formulating minimal conditions on input data that can guarantee the existence and uniqueness of solutions of
the boundary value problems describing non-one-dimensional ideal incompressible fluid flow is considered using as an example
the initial boundary value problem in a space-time cylinder constructed on a bounded flow domain with the nonpenetration condition
on its boundary (which corresponds to fluid flow in a closed vessel). The existence problems are considered only for plane
flows, and the uniqueness issues for three-dimensional flows as well. The required conditions are obtained in the form of
conditions specifying that the vorticity belongs to definite functional Orlicz spaces. The results are compared with well-known
results. Examples are given of admissible types of singularities for which the obtained results are valid, which is a physical
interpretation of these results.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 130–145, July–August, 2008. 相似文献
18.
Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes
The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are
on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure
of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when
the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value
problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account)
and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly
elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities
accounted for
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005. 相似文献
19.
We consider the Navier–Stokes equations in a thin domain of which the top and bottom surfaces are not flat. The velocity fields
are subject to the Navier conditions on those boundaries and the periodicity condition on the other sides of the domain. This
toy model arises from studies of climate and oceanic flows. We show that the strong solutions exist for all time provided
the initial data belong to a “large” set in the Sobolev space H
1. Furthermore we show, for both the autonomous and the nonautonomous problems, the existence of a global attractor for the
class of all strong solutions. This attractor is proved to be also the global attractor for the Leray–Hopf weak solutions
of the Navier–Stokes equations. One issue that arises here is a nontrivial contribution due to the boundary terms. We show
how the boundary conditions imposed on the velocity fields affect the estimates of the Stokes operator and the (nonlinear)
inertial term in the Navier–Stokes equations. This results in a new estimate of the trilinear term, which in turn permits
a short and simple proof of the existence of strong solutions for all time. 相似文献
20.
A. M. Kovrizhnykh 《Journal of Applied Mechanics and Technical Physics》2009,50(1):147-154
A new solution for the shear angle is proposed which is a generalization of the solution Lee-Shaffer solution and allows the
determination of the cutting force and the shearing-element size. Merchant’s experimental data are processed taking into account
the resistance force at the cutting edge, and it is shown that accounting for this force leads to the need to increase the
internal friction angle in the calculated dependences in order to match theory with experiment. It is shown that the obtained
theoretical results agree well with experimental results.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 177–186, January–February, 2009. 相似文献