Free vibration analysis of cylindrical sandwich shells with FML face and functionally graded core using a new shell theory

In this research, by improving the accuracy of existing high-order theories, a new corrected high-order composite cylindrical shell theory with twelve displacement components has been developed. In this theory, the effect of terms related to the trapezoidal shape of the shell cross-section (1+z/R) in the results of the shell stress has been accurately calculated. After adding the strain energy such as the initial stresses and the strain energy such as the prevention of the rotation of the rigid body to the shell energy functional, based on Hamilton's principle, the equilibrium equations of the cylindrical shell with two ends have been derived. By using these equations, eigenvalue analysis (free vibrations) have been performed. Validation of the results of the present research was done by comparing with the theoretical and experimental results of other researchers and the results of the ABAQUS software, and a good match has been achieved.