Mazur O. Parametric vibrations of orthotropic plates with complex form

Object of research is elastic mechanical systems, which elements can be simulated by orthotropic plates. The aim is the creation of method to research of parametric vibrations and dynamic stability of thin-walled constructions elements that can be modeled by orthotropic plates with an arbitrary planform and different boundary conditions. Research methods are combined using variational methods and the R-function theory (RFM). The theoretical meaning of the work is the creation of the new numerical-analytic method of parametric vibrations for orthotropic plates with complex form. The algorithms and corresponded software, which allows constructing dynamic instability domains and analyzing the dynamic behavior in resonance zone, are the practical meanings. The novelty of the work is developing of the numerically analytical method of parametric vibrations research for orthotropic plates with complex form. The offered approach is based on application of the R-functions theory and variational methods. Using proposed algorithm of discretization initial nonlinear movement system is reduced to system of nonlinear ordinary differential equations (ODEs) in result of solving a series of linear boundary value problems. Coefficients of obtained ODEs are received in the analytical form. The problem was solved in displacements and in mixed form. Ancillary linear tasks (the linear vibration problem of unloaded plate, sequences of the plane elasticity problem) are solved by variational methods and the R-functions theory. The approach of constructing instability domain and response curve in resonance zone for plate with complex form is offered. New problems of parametric vibrations of orthotropic and isotropic plates with complex form are solved with use of one and three modes approximation. The effects of geometrical parameters, parameters of load, boundary conditions, material properties and damping on stability regions and nonlinear vibrations are investigated. The field of application is mechanical engineering, aeronautics, building industry.