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EN
The paper deals with the plane problem of an elastic layer resting on a Winkler foundation with an emptiness. The stresses in the layer are caused by a given normal loading on its upper boundary plane. The mathematical formulation of the problem leads to a mixed boundary value problem and it is solved using Fourier transform methods and Fredholm integral equation of the second kind. The detailed analysis is derived analytically and numerically for an elliptic distribution of boundary loadings. The results for the normal displacement and the stresses on the lower boundary of the layer are presented in figures.
EN
Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.
PL
Omówiono wpływ grubości na właściwości materiałowo-konstrukcyjne materiału elastycznego oraz na właściwości akustyczne układów podłogowych. Przeanalizowano podane w PN-EN 12534-2:2002 zasady szacowania zmniejszenia poziomu uderzeniowego przez podłogę na podstawie sztywności dynamicznej. Omówiono wpływ warstwy wierzchniej oraz wpływ zastosowania izolacji przyściennej na właściwości akustyczne pływających podłóg.
EN
The influence of thickness on material and structural properties of elastic material as well as on the acoustic properties of floor systems are discussed. Principles, given in PN-EN 12534-2:2002 standard for estimation of reduction of impact sound pressure level by floor based on dynamic stiffness are discussed. Influence of surface layer and influence of application of wall insulation on acoustic properties of floating floors are presented.
4
Content available remote Friction Between a Body with an Elastic Layer and Vibrating Surface
EN
This paper presents the behavior of an object that contacts a vibrating plane through an elastic layer. The Coulomb model of friction is used. The aim of this paper is to show how the vibration and elasticity of the contact zone change the magnitude of the coefficient of friction. Consequently, an equivalent friction coefficient is defined. During the analysis and simulation for different parameters of vibration, the presence of stick-slip phenomenon for a specific range of the pushing force is noted. For some ranges of vibration of the base, dry friction can be presented as an equivalent viscous damping.
EN
The aim of this paper is the discussion on the applicability of some rectangular elements to plane strain boundary value problems. Four different elements were considered: 4-node, 5-node, Serendipity 8-node and Lagrangian 9-node. Two cases: the material layer loaded by a concentrated vertical force and the same layer loaded by a symmetrical rigid punch were discussed. An elastic material was used to avoid the influence of the constitutive model on solutions. To model interface behaviour on the contact surface a Coulomb friction condition was applied. The use of the 4- and 5-node elements resulted in the prediction of the 'island' pattern of stress and strain tensors distributions and their non-applicability was proved independently from the boundary condition. The 8-node element predicted erroneous distributions of nodal forces and should be avoided in the case of contact problems. Among the discussed group of elements only the 9-node element turned out to be applicable for boundary value problems under plane strain condition.
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