CONSTRUCTION OF THE MATRIX OF FUNDAMENTAL SOLUTIONS OF THE SYSTEM OF EQUATIONS DESCRIBING THE GENERALIZED PLANE ELECTRICAL ELASTIC STATE OF THE PIEZOELECTRIC PLATE - Levada, V. S.; Levitskaya, T. I.; Pozhueva, I. S.; Khizhnyak, V. K. (Computer Science and Applied Mathematics, 2017)
In constructing the matrix of fundamental solutions, the Fourier transform of the generalized slow growth functions is applied for both variables. Solving the obtained system of linear algebraic equations, we arrive at the need to solve an algebraic equation of sixth degree with real coefficients. This equation can have three variants of roots. Assuming that this solution is found, we obtain a solution of the original problem in Fourier images. When finding the inverse transformation with respect to one of the variables, the usual inverse Fourier transform is used. In order to obtain an inverse transformation with respect to another variable, it was necessary to regularize the resulting generalized functions. An exact solution of the problem is obtained. This solution is expressed in a closed form through elementary functions, which makes it possible to use it effectively.