Izotropowa Plaska Powłoka Walcowa o Dowolnych Warunkach Brzegowych

The object of the present considerations is a circular shell. The equilibrium of the shell is described by approximate differential equations (1.1) established by V. VLASOV, [1]. To obtain the solution of the system of equations (1.1), with any continuous boundary conditions, the method of eigen-transforms is used, [7]. In the case considered there appear transformations of three types (2.2). The form of the kernels follows from the basic scheme assumed, which consists in a shell on a hinged sliding support along the contour (cf. [3]). After transformation the system (1.1) takes the form of the algebraic equations (2.9). Unknown boundary functions are assumed in the form of simple FOURIER series (3.1). After inverse transformation the solutions (3.3), (3.4) and (3.5) are obtained, from which, the remaining boundary quantities, (3.12)-(3.33), are found by differentiation. The equations derived enable static and dynamic solution (steady-state vibration) of a shell with arbitrary boundary conditions. The series are summed up in a manner similar to that of the Ref. [11].