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Vibration analysis of variable thickness functionally graded toroidal shell segments

Vuong Pham Minh, Duc Nguyen Dinh

Archives of Civil and Mechanical Engineering

2023

Vol. 23, no. 3

art. no. e207, 2023

In this paper, for the first time, the nonlinear vibration response of toroidal shell segments with varying thickness subjected to external pressure is investigated analytically using Reddy’s third-order shear deformation shell theory. The variable thickness shells are made of functionally graded material (FGM) that is created from ceramic and metal constituents. The material properties of FGM shells are assumed to be gradually graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. Equations of motion of variable thickness FGM toroidal shell segments are established based on Reddy’s third-order shear deformation shell theory with von Kármán nonlinearity. The Galerkin method and the Runge–Kutta method are used to solve the governing system of partial differential equations of motion, and then the nonlinear vibration response of variable thickness FGM toroidal shell segment is analyzed. A numerical analysis is also performed to show the effects of material and geometrical parameters on the nonlinear vibration response of variable thickness FGM toroidal shell segments.

Nonlinear piezo-thermoelastic shell theory applied to control of variable-geometry shells

Tzou H. S., Yang R. J.

Journal of Theoretical and Applied Mechanics

2000

Vol. 38 nr 3

623-644

Complexity of multi-field opto-electromechanical coupling always poses many challenging research issues. Recently due to a rapid development in smart structures and structronic systems, multi-field coupling and control of distributed structronic systems also raises variety of new research, development, and system integration issues. This paper presents a generic nonlinear piezo(electric) -thermoelectromechanical shell theory for a piezoelectric double-curvature shell continuum with admissible boundary cinditions. Applications of the generic theory to other shell and non-shell continua based on four system parameters are also demonstrated. Detailed sensing and control electromechanical characteristics are further investigated in a series of shell of various curvatures. The results show that the membrane sensing/control component dominates the lower natutal modes of deep shells and the bending sensing/control component dominates the natural modes of shallow shell. Electromechanical characteristics and effectiveness of distributed sensors and actuators are evaluated.

Zastosowanie nieliniowej piezo-termosprężystej teorii powłok do sterowania powłok o zmiennej geometrii. W pracy przedstawiono zastosowanie ogólnej nieliniowej piezo-termoelektromechanicznej teorii do piezoelektrycznych powłok o podwójnej krzywiźnie oraz czteroparametrowego kontinuum niepowłokowego. Szczegółowo zbadano elektromechaniczne charakterystyki rozłożonego układu pomiarowego i wykonawczego w ciągu powłok o różnej geometrii. Wyniki wskazują, że membranowe elementy pomiarowe i wykonawcze panują nad dynamiką niskich częstości głębokich powłok, a giętne elementy pomiarowe i wykonawcze nadają się do sterowania powłok małowyniosłych. Zbadano elekromechaniczne charakterystyki i efektywność rozłożonych elementów pomiarowych i wykonawczych.