Dynamic Anisotropic and Piezoelectric Plate Equations - A Power Series Approach with Recursion Relations among the Expansion Functions
Doktorsavhandling, 2010

The subject of this thesis is dynamics of plates. Both anisotropic elastic plates, piezoelectric plates, thin piezoelectric layers on elastic plates and elastic laminates are considered. Piezoelectric materials are often used in sensors and actuators and common applications for these are vibration control and ultrasonic transducers. Composite laminates are used in a variety of industrial applications, due to their high strength and light weight. Throughout this thesis a systematic power series expansion approach is used to derive plate equations and the corresponding edge boundary conditions. The displacements, and for piezoelectric materials also the electric potential, are expanded in power series in the thickness coordinate, which are inserted into the three-dimensional equations of motion. Identifying equal powers of the thickness coordinate leads to recursion relations among the expansion functions. These are used in the surface boundary conditions as well as the possible interface conditions, which gives a system of plate equations for some of the lowest-order expansion functions. The equations can be truncated to any order and it is believed that they are asymptotically correct. Numerical comparisons with exact three-dimensional theory and also some other approximate theories illustrate the accuracy.


Plate equations



Recursion relations

Power series expansions

Thin layers

Hamilton's principle


HA2, Hörsalsvägen 4, Chalmers Tekniska Högskola
Opponent: Evgeny Glushkov


Karl Mauritsson


Modelling of thin piezoelectric layers on plates

Wave Motion,; Vol. 45(2008)p. 616-628

Artikel i vetenskaplig tidskrift

Modelling of finite piezoelectric patches: comparing an approximate power series expansion theory with exact theory

International Journal of Solids and Structures,; Vol. 46(2009)p. 1053-1065

Artikel i vetenskaplig tidskrift





Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3047

HA2, Hörsalsvägen 4, Chalmers Tekniska Högskola

Opponent: Evgeny Glushkov

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