Viscoelastic vibrations of a piezoceramic cylinder subjected to electrical excitation

International Applied Mechanics -     

Natural vibrations of rectangular plates with a through crack

Summary The paper presents a finite element model of the rectangular plate with a through crack. The crack occurring in the plate is nonpropagating and open. It was assumed that the crack changes only the stiffness of the plate, whereas the mass is unchanged. The method of the formation of the stiffness matrix of a finite element for the rectangular, cracked plate is presented. The effects of the crack location and its length on the changes of the eigenfrequencies of the simply supported and cantilever plate are studied. The results of numerical computations are compared with results of theoretical and experimental data presented in the literature.

---

Eigenschwingungen von rechteckigen Platten mit Transverslriß

Übersicht Der Beitrag präsentiert ein Finite-Element-Modell einer rechteckigen Platte mit Transverslriß. Der Riß pflanzt sich nicht fort und bleibt offen. Es wird angenommen, daß der Riß nur die Steifigkeit der Platte verändert, wogegen die Masse konstant bleibt. Eine Methode zur Aufstellung der Steifigkeitsmatrix für ein finites Element der rechteckigen Platte wird vorgestellt. Der Einfluß der Lage des Risses und der Rißlänge auf die Eigenschwingungen der einfach gestützten und freitragenden Platte wird untersucht. Abschließend erfolgt ein Vergleich der numerischen Berechnungen mit den Ergebnissen von theoretischen und experimentellen Literaturdaten.

     

Coupled piezoelectric vibrations of quartz plates

The contributions of coupling with the electric field and mass of electrode coatings are taken into account in solutions of equations governing coupled thickness-shear, flexure and face-shear vibrational modes in rotated-Y-cut quartz plates.     

Flexural vibrations of fissured poroelastic plates

Summary The governing equations of flexural vibrations of thin, fluid-saturated, poroelastic plates are derived in detail. The plate material obeys the Aifantis-Beskos theory of poroelasticity with two degrees of porosity, while the plate theory employed is the one due to Kirchhoff. The dynamic response of a rectangular, simply supported, poroelastic plate with two degrees of porosity to harmonic load is obtained analytically-numerically and the effects of porosities and permeabilities on the response are studied. A comparison between the single and double porosity material models is also made. The quasi-static problem is analysed as as special case of the dynamic one.

---

Biegeschwingungen geklüfteter poroelastischer Platten

Übersicht Es werden die Gleichungen, die die Biegeschwingungen von dünnen, mit Flüssigkeit gefüllten, poroelastischen Platten beschreiben, im einzelnen hergeleitet. Das Materialverhalten der Platte wird durch die Poroelastizitätstheorie von Aifandis und Beskos für Materialien mit doppelter Porosität beschrieben, während für die Platten die Kirchhoffsche Plattentheorie angewandt wird. Man erhält auf analytisch-numerischem Weg das dynamische Verhalten einer rechteckigen, einfach gestützten, poroelastischen Platte mit doppelter Porosität bezüglich einer harmonischen Belastung. Der Einfluß der Porosität und Permeabilität auf das dynamische Verhalten wird untersucht. Weiterhin werden die Modelle für Materialien mit einfacher und doppelter Porosität miteinander verglichen. Das quasi-statische Problem wird als Spezialfall des dynamischen Problems analysiert.

     

Natural vibrations of a cylindrical shell reinforced with rectangular plates

This paper outlines a technique of determining the natural frequencies and modes of an elastic structure consisting of a cylindrical shell and noncrossing rectangular plates inserted into it. The influence of the position, number, and thickness of the plates on the natural frequencies and modes is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 89–96, March 2006.     

Viscoelastic problem for piecewise homogeneous piezoelectric plates

The electromagnetoviscoelastic problem is solved for piecewise-homogeneous plates. The problem is reduced to solving a sequence of electromagnetoelastic problems with complex potentials. General representations of approximation functions for multiply connected domains and boundary conditions for their determination are given. An analytical solution of the problem for a plate with one inclusion and an approximate solution for a plate with a finite number of inclusions are obtained. The change in the electromagnetoelastic state is investigated numerically as a function of time, the properties of the plate and inclusion materials, and the distance between the inclusions.     

Non-linear vibrations of transversely isotropic rectangular'' plates

The large amplitude free flexural vibration of transversely isotropic rectangular plate, incorporating the effects of transverse shear and rotatory inertia, is studied using the von Karman field equations. A mode shape, consisting of three generalised-coordinates together with the Galerkin technique, results in a system of three non-linear simultaneous ordinary differential equations which govern the motion of the plate. These equations are integrated using a fourth-order Runge-Kutta method to obtain the period for each amplitude of vibration. The non-linear period vs amplitude behaviour is of the hardening type and it is also found that transverse shear and rotary inertia effects increase the period and that this increase is quite significant even for thin transversely isotropic plates. The results are compared with earlier results which were based on a one-term or one generalised coordinate solution and using the Berger approximation or the von Karman field equations.     

On the flexural vibrations of sandwich plates

A simplified approach to sandwich plate free vibrations, based on the superposition method, can provide approximations to the lowest modes for various boundary conditions, showing a characteristic influence of the bending-shear stiffness ratio.

---

Sommario Un'analisi semplificata delle vibrazioni naturali di pannelli sandwich in diverse condizioni di vincolo, con il metodo di sovrapposizione degli effetti, consente l'individuazione approssimata dei modi più bassi, mostrando un comportamento vibratorio caratteristico al variare del rapporto tra le rigidezze di flessione e taglio.

     

Studying the free vibrations of multilayer plates with a complex planform

An efficient method is developed to solve the free-vibration problems for arbitrarily shaped orthotropic multilayer plates in a refined formulation. The method is based on the R-function and Ritz methods. Sequences of coordinate functions satisfying kinematic boundary conditions are constructed in an analytic form. The method is used to solve the vibration problem for multilayer square and arbitrarily shaped plates. The results obtained for square plates are analyzed. A comparison of these results with those available in the literature demonstrates the efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 119–125, January 2006.