Abstract:

The 4th-order equation describing the propagation of axially symmetric bending-longitudinal waves in a cylindrical shell interacting with an external nonlinear elastic medium is considered. The dependence of the stress – strain environment is represented by 5th-order polynomial. It is shown that under some conditions on the coefficients the initial equation is reduced to a generalized Duffing equation, for which exact solitary-wave solution using the geometric series method is obtained. Еhe conditions under which this solution is expressed via the square root of hyperbolic secant or hyperbolic tangent is found.

Keywords: exact solitary-wave solutions, cylindrical shell, bending-longitudinal waves