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This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability.

The parametric instability of simply-supported sandwich cylindrical shell with a functionally graded (FG) core under static and time dependent periodic axial compressive loads is investigated in this study. The governing equations of sandwich cylindrical shell with an FG core are derived based on Donnell׳s shell theory using first order shear deformation theory (FSDT). Considering the time-dependent periodic axial compressive load, the governing equations are reduced the second order differential equation with the time-dependent periodic coefficient or Mathieu-type equation by using the Galerkin׳s method. This equation is solved by Bolotin׳s method and the closed form solutions for dimensionless excitation frequencies of parametric vibration of sandwich cylindrical shells with an FG core based on the FSDT are obtained. Numerical simulations are conducted to verify the analytical results. Finally, the effects of variations of volume fraction index of the FG core, static and dynamic load factors and shell characteristics on the dimensionless excitation frequencies of parametric vibration are studied numerically. [ABSTRACT FROM AUTHOR]