The work presents an analysis of dynamic buckling of a sandwich bar compressed by a periodically variable force. In order to determine the stability of the bar transverse motion, equations of its transverse vibration were formulated. From the equations of motion, differential equations interrelating of the bar dynamic deflection with space and time were derived. The partial differential equations were solved using the method of separation of variables (Fourier’s method). Then an ordinary differential equation (Hill’s equation) describing the bar vibration was solved. An analysis of the solution became the basis for determining the regions of sandwich bar motion instability. Finally, the critical damping coefficient values at which parametric resonance occurs have been calculated.
In the work, creep processes are analyzed in case of layered beam. Slips of the layers are described by means of the gradient mechanics. They are considered as causing micro-discontinuity in the stress field. Consequently, the gradient theory gives a description and explanation of the rheological processes in this case. Such a description of the problem is impossible in the classical structural mechanics. The proposed model of process may be also used in a description of deformations in the biological materials.
W artykule przedstawiono analizę problemu stateczności pręta warstwowego z warstwami sprężystymi i lepkosprężystymi, z uwzględnieniem wpływu ścinania. Wyprowadzono równania linii ugięcia takiego pręta w przypadku ogólnym oraz pręta z warstwami lepkosprężystymi opisanymi modelem standardowym. Rozwiązanie zastosowano w przykładzie dla pręta o przekroju złożonym z elementu stalowego i warstwy betonu.
EN
The article shows the analysis of stability of layered bar with elastic and viscoelastic layers taking shear stress into consideration. Formulas of bending line of the bar for general case and also for viscoelastic layers based on standard model were derived in the article. The solution was used in the example for the bar consisting of steel element and layer of concrete.
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