Dynamic Stability of a Composite Cylindrical Shell with Linear-Variable Thickness under Pulsed External Pressure

Abstract

Equations have first been obtained for dynamic stability of a composite cylindrical shell with linear-variable thickness under the action of axial forces and external pulsed pressure. The solution of these equations along the axial coordinate was found in the form of trigonometric series. Using the Bubnov–Galerkin method the problem was reduced to an infinite system of ordinary differential equations that is reduced to an infinite system of homogeneous algebraic equations in the form of temporal trigonometric series. By reducing the obtained system and equating the reduced matrix determinant to zero, a characteristic equation was obtained to determine the critical frequencies of external pressure pulsations. A numerical example has been used to investigate the effect of the axial force and the length of a composite shell of linear-variable thickness on the boundaries of its instability. It has been shown that, in using medium-integral thickness of the shell in calculations, the error in identifying the area of this region may reach high values, which is indicative of the current importance of solving the problem of dynamic stability of a composite cylindrical shell with a linear-variable thickness in terms of weightwise improvement of aircraft. The developed mathematical model expands significantly the range of solvable problems and makes it possible to calculate the dynamic stability of orthotropic cylindrical shells with linear-variable thickness.