ЗГИННІ ТА ВЛАСНІ КОЛИВАННЯ ТРИШАРОВИХ ПЛАСТИНИ З УРАХУВАННЯМ ПРУЖНЬОЇ ОСНОВИ

We investigate natural vibrations and bending sandwich plates on elastic foundation. To describe the kinematics of the supporting layers Kirchhoff hypothesis are adopted. Aggregate is calculated from the strain of bending. The reaction is described by the Winkler foundation. We proposed a numerical method for calculating a three-layer structures.In the construction of variational-difference schemes for the three-layer sandwich structures we taking triangular element, which uses the approximation of displacements on different layers. To approximate the deflection of thin bearing the words within each triangle is used incomplete cubic polynomial. Mid-plane displacement of the points along the axes of the supporting layers are defined as linear polynomials within each triangle. Thus finite element are provided continuity of the approximation of displacements in the entire region and satisfy all the requirements of convergence.To minimize the functional is proposed to use the method of descent. Choice of this method is due to the fact that when it is used there is no need in the formation and storage of mass and stiffness matrices of large dimensions, the numbering of nodes in a sampling area is arbitrary, it greatly reduces the need for the PC's memory. The method of descent is an iterative method and stable rounding errors have little effect on the accuracy of the final result. When we solve a series of practical problems of bending and vibration the maximum number of iterations was not more than 140. The error in determining of the deflection at the center of the plate is 0.2%. Results of determination the maximum deflection and fundamental natural frequencies are compared with analytical results.Рассмотрен изгиб и собственные колебания трехслойной пластини на упругом основании. Для описания кинематики несущих слоев приняты гипотезы Кирхгофа. Заполнитель рассчитывается с учетом деформаций изгиба. Реакция основания описывается моделью Винклера. Предложена численная методика расчета трехслойных конструкций.Розглянуто згинні і власні коливання тришарової пластини на пружній основі. Для опису кінематики несучих шарів прийняті гіпотези Кірхгофа. Заповнювач розраховується з урахуванням деформацій згину. Реакція основи описується моделлю Вінклера. Запропонована чисельна методика розрахунку тришарових конструкцій