Core investigation of cylindrical shell with variable material: Energy variational technique

The strains and kinetic energies of a vibrating cylindrical shell are obtained in an integral form to describe the current shell problem. Three unknown displacement functions are used to generate three differential equations. The shell frequency equation is obtained using the Galerkin method. The MATLAB program are used to solve the frequency equation for the vibration of cylindrical shell. In this case, it is assumed that the cylindrical shell is made of material that works well. These tools include parts made of ceramics and metals. For this purpose, functionally graded items are selected. To exchange elements in the shell, the composition of material is controlled by a power law. The frequency coupling (Hz) vary as a function of volume fraction index, length-to-radius ratio, and height-to-radius ratio. The metal-ceramic material captures the frequency of the wave numbers using a limited range of parameters. It can be seen that the frequencies of clamped-free is less than the clamped clamped. As the power law exponent increases, the frequency increases. The present finding is supported by previous research.