Chistilina A. The investigation of free vibrations of multi-layer shallow shells and plates complex form in plane

Object of research - free vibrations of multilayer shallow shells and plates complex form in the plane. The purpose of work - creation of an effective method of research of free vibrations of multilayer shallow shells and plates, and also development of software for solving of indicated class of problems. General means of researches are the variational methods, theory of R-functions and computing methods. The theoretical value of work consists in creation of an effective method of research of free vibrations of multilayer shallow shells and plates complex form which based on variational methods and theory of R-functions within the framework of classical and refined theories. A practical outcome of work is development of algorithms and software which allows to automate process of calculation of free vibrations of multilayer shallow shells and plates. The scientific novelty of work consists in the following: for the first time on the basis of the theory of R-functions and variational methods the effective method of research of free vibrations of multilayer shallow shells and plates with complex form in the plane is developed within the framework of the classical theory; the offered method is generalized on problems about free vibrations of multilayer shallow shells and plates which are considered within the framework of the refinad theory; the design facilities of the theory of R-functions for the considered class of problems as constructed structures of the solutions for different boundary conditions are advanced; the knowledge base for problems about free vibrations of multilayer shallow shells and plates with complex form in the plane including variational statement of the indicated class of problems, analytical expressions for calculation of elements of a Ritz's matrix , structures of the solutions satisfying to given boundary conditions is created; the new problems about vibrations of multilayer shallow shells and plates with complex form in the plan are solved with the purpose of detection of regularities of their behaviour depending on the geometric information, boundary condition, quantity of layers and angle of their turn, properties of a material. The introduction of outcomes of researches in an industrial complex is planned, the outcomes of a thesis are used in scientific researches NTU "KhPI", and also at an exposition of a course " Equations of mathematical physics " for a speciality " Dynamics and strength ".The outcomes of research can be used at designing of multilayer elements of designs in aerospace branch, industrial construction, motor-car industry.