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9. Torsional vibration of a flexoelectric nanotube with micro-inertia effect.

Author

Hrytsyna, O., Sladek, J., Sladek, V., Deng, Q., and Hrytsyna, M.

Subjects
STRAINS & stresses (Mechanics), STRAIN tensors, ENERGY density, TORSIONAL vibration, FREE vibration, LAMINATED composite beams, ROTATIONAL motion, NANOTUBES, QUADRUPOLES
Abstract

The modified strain gradient theory (MSGT) with flexoelectric and micro-inertia effects is developed to study the free vibration of tube made of elastic centrosymmetric materials. Within this theory, the internal energy density is the function of the strain tensor, deviatoric part of stretch gradient and rotation gradient tensors, dilatation gradient, polarization vector, and electric quadrupoles. The linear coupled governing equations and boundary conditions are derived from the Hamilton variation principle. The torsional vibration problem is analytically solved for non-piezoelectric nanotube with fixed edges. The effect of the nanotube geometry, flexoelectric coefficient, micro-inertia, and micro-stiffness parameters on the natural frequency is studied. [ABSTRACT FROM AUTHOR]

Published
2024
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11. Bending of Piezo-Electric FGM Plates by a Mesh-Free Method

Author

Sladek, V., Sator, L., Sladek, J., Ceccarelli, Marco, Series Editor, Hernandez, Alfonso, Editorial Board Member, Huang, Tian, Editorial Board Member, Takeda, Yukio, Editorial Board Member, Corves, Burkhard, Editorial Board Member, Agrawal, Sunil, Editorial Board Member, Okada, Hiroshi, editor, and Atluri, Satya N., editor

Published
2020
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28. Higher-grade theory of heat conduction in solids.

Author

Sladek, V., Sladek, J., and Sator, L.

Subjects
*HEAT conduction, *BOUNDARY value problems, *MATHEMATICAL continuum
Abstract

The classical theory of heat conduction is scale invariant. On the other hand, it is experimentally evident that size-dependent effects are observed in small samples of nano/micro-scale dimensions. Having included the higher-order gradients of primary field variables into the constitutive relationships it is possible to explain the size effects qualitatively within the generalized theory of continua. It is evident that high gradients of temperature field can occur in a thin layer when different temperatures are applied on its surfaces. The higher-grade theory of heat conduction in solids is developed in this paper with applying the fundamental principles of thermodynamics. Making use the variation principles, the mathematical formulation of the boundary value problems is derived within higher-grade theory of heat conduction, i.e. the governing equation and the physically admissible boundary conditions are derived. Applying the developed formulation to two layer system with different material properties, we derived exact solutions to various boundary value problems. Performing parametric studies with respect to heat conduction coefficients and the micro-length scale parameter, we discus numerical results in comparison with classical solution. [ABSTRACT FROM AUTHOR]

Published
2023
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