The proposed and verified the technique of finding a finite number of first natural frequencies for geometrically nonlinear vibrations of layered elongated cylindrical panels at discrete consideration of components. The influence of the radius of curvature on the natural frequencies of three- and five-layered panels is investigated. The dependence between the volume of filler three-layer panels and the lowest natural frequency has been established.
The algorithm for finding a finite number of the first values of natural frequencies and forms of geometrically nonlinear free transverse vibrations of thin-walled elongated panels with arbitrary generatrix is proposed and verified. Under normal coordinate quadratic the approximation of displacements is used. Along the tangential coordinates used one-dimensional finite elements. The discrete variation problem is built. For its solving the perturbation method is applied. The numerical results are compared with previously obtained by other authors.
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A mathematical model of the process of linear free vibrations of layer plates with components pliable to transversal shear and compression is proposed. The analytical expression for the spectrum of natural frequencies of two-layer plate-strip is obtained. The influence of parameters of pliability to transversal shear and compression on their values is investigated.
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The work is devoted to the experimental investigations of dissipative properties and damage of composite materials. The experimental technique is based on the measurement of the phase, amplitude and frequency characteristics of prismatic specimens subjected to dynamic excitation. The theoretical foundations of the method and the experimental results related with nonlinear damping effects are discussed. The presented experimental data certain conclusions about delamination damage of composite material can be drawn.
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A system of differential equations describing the non-linear transverse vibrations of composite plates – pliable to transversal shear and compression strains – is presented. The analytical expressions for amplitude-frequency characteristics of such vibrations are given. The parametric analysis of dependence of a basic frequency of transverse vibrations of a strip-plate versus the amplitude at the hinge fixed and rigid fastened of the edges is made. The skeletal curves for non-linear vibrations of composite plates are constructed.
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