Nonlinear thermal vibration of a nanoplate attached to a cavity

Dynamic problems of a nanocircular plate-cavity system are investigated using molecular dynamics (MD) method. A nonlinear plate model considering gas action is developed. The results of the MD simulation show that the helium atoms adsorb on the wall of the cavity at low temperature, resulting in a negative deflection of the molybdenum disulfide (MoS2) plate. As the temperature increases, the pressure in the cavity increases, leading to a gradual rise in the deflection of the plate. A nonlinear phenomenon of stiffness hardening is shown with increasing temperature. The nonlinear plate model can give a relatively good prediction compared with the results of MD simulations. The natural frequency of the plate is affected by temperature and the presence of gas in the cavity. The phenomenon of stiffness hardening and softening can be well simulated by the nonlinear plate model and MD method. The present study provides a reference for vibration experiments of two-dimensional nanostructures.

The stability of geometrically nonlinear plate systems under the action of dynamic loads

Relevance. Single-connected and multi-connected plate systems are widely used in construction, aircraft, shipbuilding, mechanical engineering, instrument making. As a result, the study of the stability of geometrically nonlinear plate systems is an urgent topic. But, despite significant achievements in this area, there are still many unsolved problems. Thus, the requests of the above-mentioned areas of application of thin-walled spatial systems require further study of the issue of static and dynamic stability. The aim of the work - development of a method of the dynamic stability analysis of geometrically nonlinear plate systems such as prismatic shells under the action of dynamic compression loads. Methods. A plate system, which is subject to dynamic compression loads in the longitudinal direction, is considered. Kirchhoff - Love hypotheses are taken into account. The material stress-deformation diagram is linear. The displacement of points in the normal direction to the median plane of the plates is determined in the form of the Vlasov expansion. To derive the basic differential equations of stability, the energy method and the variational Vlasov method are used. The extreme value of the total energy is determined using the Euler - Lagrange equation. As a result, a set of basic nonlinear differential equations for studying the buckling of the plate system under the action of dynamic compression loads is obtained. Results. The developed method is used to stability analysis of a geometrically nonlinear prismatic shell with a closed contour of the cross section, under central compression under the action of dynamic loading. The edges of the shell rest on the diaphragm. The buckling of the prismatic shell in the longitudinal direction along one and two half-waves of a sinusoid is studied. The numerical integration of nonlinear differential equations is performed by the Runge - Kutta method. Based on the calculation results, graphs of the dependence of the relative deflection on the dynamic coefficient are constructed. The influence of the rate of change of compression stress, the initial imperfection of the system, and other parameters on the criteria for the dynamic stability of the plate system is investigated.

Existence and stability of fourth-order nonlinear plate problem

In this paper, we study a fourth-order plate problem as a model for a suspension bridge in the presence of a nonlinear frictional damping and a hanger restoring force. We establish the existence of a global weak solution and prove a stability result.

ANALYSIS OF FORCED VIBRATIONS OF NONLINEAR PLATES IN A VISCOELASTIC MEDIUM UNDER THE CONDITIONS OF THE DIFFERENT COMBINATIONAL INTERNAL

In the present paper, the force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied. The motion of the plate is described by three coupled nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal combinational resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. A comparative analysis of numerical calculations for the cases of free and forced vibrations has been carried out.