Journal ArticleDOI
Certain integral and differential types of variational principles in nonlinear piezoelectricity
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In this article, a variational principle for the motion of a piezoelectric region with an internal surface of discontinuity was developed and used to generate Euler-Lagrange equations of nonlinear PDEs.Abstract:
Various forms of variational principles are developed and used to generate, as Euler-Lagrange equations, the fundamental differential equations of nonlinear piezoelectricity. First, Hamilton's principle is rigorously applied to the motion of an electroelastic solid with small piezoelectric coupling, and an associated variational principle is readily derived. Then, by use of the dislocation potentials and Lagrange undetermined multipliers (Friedrich's transformation), the variational principle is augmented for the motion of a piezoelectric solid region with an internal surface of discontinuity. To incorporate the constraints into the two-field variational principle, Friedrich's transformation is again applied, and a unified variational principle is systematically established. This unified variational principle is shown to produce the fundamental equations of an electroelastic solid with small piezoelectric coupling. >read more
Citations
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Journal ArticleDOI
Nonlinear dynamics of a noncontacting atomic force microscope cantilever actuated by a piezoelectric layer
K. Wolf,Oded Gottlieb +1 more
TL;DR: In this article, the nonlinear equations of motion for a silicon cantilever beam, covered by a piezoelectric lead-zirconate-titanate layer, subjected to a Lennard-Jones type boundary condition, are derived for voltage excitation.
Journal ArticleDOI
Some variational principles for linear coupled thermoelasticity
G. Aşkar Altay,M. Cengiz Dökmeci +1 more
TL;DR: In this article, the governing equations describing the physical behavior of a thermoelastic continuum were expressed as the Euler-Lagrange equations of certain variational principles, guided by the principle of virtual work.
Journal ArticleDOI
Variational Principles for Piezoelectric, Thermopiezoelectric, and Hygrothermopiezoelectric Continua Revisited
Gülay Altay,M. Cengiz Dökmeci +1 more
TL;DR: In this paper, Cimento revisited some variational principles for the fundamental equations of a regular region of piezoelectric, thermopiez-olectric and hygrothermopiezoellectric materials in the elastic range.
Journal ArticleDOI
Some comments on the higher order theories of piezoelectric, piezothermoelastic and thermopiezoelectric rods and shells
G. Aşkar Altay,M. Cengiz Dökmeci +1 more
TL;DR: In this article, the derivations of the higher-order theories for the dynamic analysis of electroelastic (i.e., piezoelectric, piezothermoelastic) structural elements of uniform cross-section (or uniform thickness) are discussed.
Journal ArticleDOI
Coupled thermoelastic shell equations with second sound for high-frequency vibrations of temperature-dependent materials
G. Aşkar Altay,M. Cengiz Dökmeci +1 more
TL;DR: In this article, a variational principle describing the fundamental equations of thermoelasticity is presented by expressing Hamilton's principle for the thermal part of a thermo-elastic region and then combining it with its mechanical part.
References
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Journal ArticleDOI
Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Thermoelasticity and Irreversible Thermodynamics
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.