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.
Green’s Function Solution of Non-Homogenous Regular Sturm-Liouville Problem
