Ganilova O. Solution of the vibration problems for piezoelectric laminated beams and plates under dynamic loading applying an asymptotic approach

Dissertation is devoted to the modelling and solution of a range of practical problems in deformable solid mechanics applying a hybrid WKB-Galerkin method to the group of fundamental linear differential equations with variable coefficients and a parameter multiplying the highest order derivative. Suggested asymptotico-numerical approach was used for solution of vibration problems for a piezoelectric multilayered beam, an orthotropic sandwich plate and a piezoelectric sandwich plate, described in a more general way, and a problem of the plate vibration in terms of nonlinear case, taking into account variable in time damping coefficient. Approximate analytical solutions obtained in this work give an opportunity to investigate the character of the influence of the damping coefficient in case of dynamic loading even for the systems with a variable damping coefficient and let us obtain effective analytic solutions.