Asymptotic analysis of 3D thin anisotropic plates with a piezoelectric patch

作者：Leugering Guenter R^*; Nazarov Serguei A; Slutskij Andrey S

来源：Mathematical Methods in the Applied Sciences, 2012, 35(6): 633-658.

DOI：10.1002/mma.1566

• Asymptotic analysis
• piezoelectric material
• anisotropic material
• plate equation
• effective material

We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two-dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth-order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second-order in-plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures.

• 出版日期2012-4