Orthotropic cylindrical shell panels under dynamic loading (the load has a linear time dependency) are examined in this paper. Relationships of a mathematical model of their deformation are presented in view of the geometric nonlinearity, transverse shears and orthotropy of the material. The Kantorovich method is applied to form a system of ordinary differential equations. The derived system is solved by the Rosenbrock method. The stability of several types of orthotropic panels of modern materials (fiberglass, carbon fiber reinforced plastic, etc.) is studied and critical load values are obtained.
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