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Use of the higher-order plate theory of I. N. Vekua type in problems of dynamics of heterogeneous plane waveguides

Egorova O. V., Rabinskiy L. N., Zhavoronok S. I.

Archives of Mechanics

2020

Vol. 72, nr 1

3--25

The dynamics of elastic plane waveguides is studied on the basis of the extended formulation of the plate theory of Nth order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.

Dynamic systems with a finite degrees of freedom number

Ładziński R.

Archives of Control Sciences

2014

Vol. 24, no. 2

207--234

Taking as a starting point the law of conservation of the total energy of the system, and introducing two basic state functions - the Lagrangian and the Rayleigh function, the general form of the equation of motion for any dynamic system with a finite number of degrees of freedom is derived. The theory is illustrated by considering the rotating - type electromechanical energy converter with six degrees of freedom being the model of all essentially important types of DC and AC machines, including rotating power amplifiers, induction - and synchronous type motors - all of them discussed from both, the steady-state and the transient point of view. In the next part of the paper there is described a simple electric circuit with its model characterized by the holonomic constraints of the velocity-type. Finally, there is presented the kinematics and dynamics of the interesting mechanical system - the gyroscope placed on the rotating Earth.

Dynamika sztywnych kul w ruchu złożonym

Szczęśniak W., Ataman M.

Logistyka

2011

nr 6

W referacie przedstawiono rozwiązania wybranych trudniejszych zadań dotyczących dynamiki dwóch sztywnych kul w ruchu złożonym. Te nietypowe zadania są sformułowane, bez podania rozwiązań, w starych, trudnodostępnych pozycjach literatury [1-4] i były przedmiotem egzaminów na uniwersytetach angielskich w końcu XIX wieku.

In the paper solutions of selected problems of dynamics of rigid spheres in compound motion are presented. Formulation of these examination problems, date the end of the nineteenth century, one can find in the old books [1-4].