PARAMETRIC VIBRATIONS OF lATERALLY STRENGTHENED, ANISOTROPIC, DAMAGED, VISCOUS FLUID-FILLED CYLINDRICAL SHELL MADE OF GLASS-REINFORCED PLASTIC - Iskanderov, R. A.; Alimamedov, R. K. (Computer Science and Applied Mathematics, 2018)
The problem of cylindrical shell parametric oscillations under external periodic pressure is considered in this paper. It is supposed that shell is transversely reinforced and additionally anisotropic damaged. Shell is made from fiberglass with viscous fluid inside. The bounadary conditions considered simplysupported edge. Ostrogradsky–Gauss variation principle is used for solving the problem. It is assumed the linear theory of elastic shells, based on Kirchhoff-Love hypothesis and Kirchhoff–Klebis theory for curvilinear roads. The hereditary theory in an integral form of damage is used for describing the shell damage process. The function of healing defects depending on the amount of damage during the loading cycle taking values in the range 0, 1. The surface loads acting on the transversely supported shell from the viscous fluid side. This loads are determined from the solutions of the linearized Navier–Stokes equation. The unknown components of the displacement vector points of the middle surface of the shell are represented as a combination of trigonometric functions by both the coordinates of the shell and the time with unknown coefficients. The coefficients are found from a system of linear algebraic equations, obteined as a result of the integration of the total energy and the fluid motion equations. The contact conditions on the surface are taking into the account. For shall ratios of the shell radius to its length, the natural frequencies of the system weakly depend on the winding angle. With the increase of this ratio, the dependence of the natural frequencies of the system of the winding angle is complex.