Natural vibrations of a strip made of a composite material with a locally curved structure

The possibility of using the finite-element method for investigating two-dimensional problems on natural vibrations in the mechanics of composite materials with curved structures is considered. With the example of a hinge-supported strip made of a composite material with a locally curved structure, the influence of geometrical and mechanical parameters of the strip on its eigenfrequencies is examined. It is established that the presence of local curving in the structure of strip material decreases the magnitude of eigenfrequencies.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 71–78, January–February, 2005.     

A dynamical (time-harmonic) axisymmetric stress field in a finitely prestretched multilayered slab on a rigid foundation

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the dynamical (time-harmonic) axisymmetric stress field in a finitely prestretched multilayered slab resting on a rigid foundation is studied. It is assumed that the slab consists of two-layer packets. The elasticity of layer materials is described by the Treloar potential. It is assumed that the material of the lower layer in the packets is more rigid than that of the upper one. Numerical results are presented for the cases where the number of layers (packets) in the slab is 2 (1), 4 (2), or 6 (3). These results concern the normal stresses acting on the interface between the layers of the first, upper packet and on the interface between the first and second packets. The influence of the number, prestretch level, and thickness of the layers on relation ships between the stresses and the frequency of the external force is analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 667–680, September–October, 2006.     

Wave propagation in a pre-strained compressible elastic sandwich plate

The extensional and flexural Lamb waves in a sandwich plate with finite initial strains made from compressible highly elastic materials is investigated. It is assumed that the initial strains are caused by the uniformly distributed normal compression forces acting on the face planes of the plate. The cases where the compression forces are “dead” (Case 1) and “follower” (Case 2) are considered. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the 3D linearized theory of elastic waves in initially stressed bodies. Numerical results for the dispersion of the extensional and flexural Lamb waves on the influence of the initial strains and on the influence of the character of the external compression forces are presented and discussed.     

Natural vibrations of composite materials having structures with small-scale curvatures

Conclusions We have used the continuum theory in [1] to develop an approach to determination of the natural frequency and mode of composite structural elements with locally and regularly curved structures. We used the approach to examine the solution of a specific problem concerning natural vibration. It was shown that the fundamental frequency of the structural elements may be reduced considerably by the presence of curvature in the structure of the composite.Institute of Mathematics and Mechanics, Azerbaidzhan Academy of Sciences, Baku. Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 24–30, December, 1992.     

Dispersion of lamb waves in a three-layer plate made from compressible materials with finite initial deformations

A three-layer plate made from compressible elastic materials with finite initial deformations caused by compressive forces applied to their faces is considered. By using the three-dimensional linearized theory of propagation of elastic waves in bodies with initial stresses, the propagation of Lamb waves in this plate is investigated.     

Forced Vibration of a Prestretched Two-Layer Slab on a Rigid Foundation

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the forced vibration of a prestretched two-layer slab resting on a rigid foundation is studied. To the upper plane of the slab, a harmonic point force is applied. It is assumed that the layer materials are incompressible, and their elastic properties are characterized by Treloar’s potential. Numerical results are presented for the case where the material stiffness of the lower layer is greater than that of the upper one. The influence of prestretching the layers on the frequency dependences of the normal stresses operating on the interface between the layers and between the slab and the rigid foundation are analyzed.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 335–350, May–June, 2005.     

Delamination of a two-layer corroded ring under radial vibrations

A two-layer ring, with account of its initial state caused by internal pressure and corrosion, leading to wear, is considered. The ring is subjected to an additional pressure causing its radial vibrations. It is shown that, under certain conditions, there is a vibration frequency at which the delamination of the ring is possible. Expressions are found which determine this frequency as a function of problem parameters, in particular, of the time of corrosive wear.     

Natural vibration of a rectangular plate of composite material with periodically bent structures

The natural vibration of a thin rectangular plate made of a composite material with periodically bent structures is studied. The problem is examined by the finite-element method using the variation principle. The effect of the bending parameters on the natural frequency of the plate is analyzed using the numerical results obtained. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 68–73, October, 1999.