Forced vibrations of multilayered cylindrical shells taking into account the discresibility of the ribs with non-steady loads

This work considers the problem of nonstationary behavior of multilayered discretely reinforced cylindrical shells.By the way the problem is very important. Multiplayed shells with allowance for discrete ribs are widely used in engineering, industrial and public building, aviation and space technology, shipbuilding. In the framework of the Timoshenko type non – linear theory of shells and ribs nonstationary vibrations multilayered shells of revolution with allowance for discrete ribs are investigated. Reissner’s variational principle for dynamical processes is used for deduction of the motion equations. An efficient numerical method with using Richardson type finite difference approximation for solution of problems on nonstationary behaviour of multiplayer shells of revolution with allowance for discrete ribs which permit to realize solution of the investigated wave problems with the use of personal computers, as well as bringing their solutions to receiving concrete numerical results in wide diapason of geometrical, physico–mechanical parameters of structures are elaborated. In particular three-layer discretely reinforced cylindrical shells were investigated.

Hysteresis Modelling of Mechanical Systems at Nonstationary Vibrations

This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.