Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem

Kochetkov, Ivan; Rogacheva, N.N.

doi:10.1016/j.jappmathmech.2017.07.006

Cited by 1 publication

(2 citation statements)

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“…where e a and e s = (0:5 × 10 2Àm )% are the relative percentage error and the tolerance of the relative percentage error, respectively. The satisfaction of Equation (30) can guarantee that the m significant digits of solution are accurate. As an example, the calculation times for m = 2 under different loads are listed in Table 3.…”

Section: The Precision and Validity Of This Methodsmentioning

confidence: 99%

“…Maurini et al [29] presented a model for multilayered piezoelectric beams considering the high-order shear deformation theory. Kochetkov and Rogacheva [30] simplified the 3D equations to two-dimensional (2D) equations by the asymptotic method. Based on the thin plate theory, Kumari and Shakya [31] presented the 2D solution of a rectangular piezoelectric plate by the Extended Kantorovich Method.…”

Section: Introductionmentioning

confidence: 99%

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A method for the coupled field of an orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load

Shang¹,

Hou

Tong

2020

Mathematics and Mechanics of Solids

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There are a number of plate-type piezoelectric devices in engineering, hence it is crucial to search for a method that can accurately acquire the electro-mechanical coupled field of a piezoelectric plate. A method for calculating the coupled field of an orthotropic piezoelectric plate with arbitrary thickness under an arbitrary electro-mechanical load is put forward in this article. First, the Green’s function solution of an orthotropic piezoelectric plate subjected to a line charge and a normal line force is derived based on the general solution of the orthotropic piezoelectric material. All stress and electric components of the orthotropic piezoelectric plate are derived when the general solution is substituted into suitable harmonic functions containing undetermined constants. Once the boundary conditions and electro-mechanical equilibrium conditions are satisfied, those constants can be solved. In addition, according to the obtained Green’s function solution and superposition principle, the coupled field of the orthotropic piezoelectric plate subjected to an arbitrary electro-mechanical load can be solved. Numerical results indicate that the convergence and precision of the method are quite good. A concise skill without repeated calculations is also presented for acquiring the coupled fields in the orthotropic piezoelectric plates with various thickness, which facilitates the effective design of plate thickness in plate-type piezoelectric devices. Finally, some valuable conclusions for the fine design of plate-type piezoelectric sensors, energy harvesters and actuators are presented based on the numerical results.

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Section: The Precision and Validity Of This Methodsmentioning

confidence: 99%