Isogeometric free vibration of sector cylindrical shells with carbon nanotubes reinforced and functionally graded materials

Abstract

An isogeometric numerical procedure based on non-uniform rational B-splines is applied to solve the free vibration of carbon nanotubes reinforced and functionally graded material sector cylindrical shells. A typical isogeometric analysis cylindrical shell element is introduced to transform curvilinear domain to parametric domain. The effects of the shear deformation, rotary inertia and axis extensibility are taken into consideration. The material properties are estimated by a mixture rule and effective carbon nanotube parameters. The weak form is derived in detail by applying virtual principle. The novelty of this paper is to use the isogeometric finite element method to analyze the dynamic behaviors of sector cylindrical shells with functionally graded material and four types of carbon nanotubes distributed material. By numerical examples, the convergence and accuracy of the current method are validated. Then, a series of natural frequencies and mode shapes are presented to serve as benchmark solutions in future researches. Moreover, the effects of boundary conditions, geometric proprieties as well as material parameters on the frequencies of the carbon nanotubes reinforced and functionally graded material sector cylindrical shells are examined.

Keywords

• Free vibration
• Carbon nanotubes
• Functionally graded material
• Sector cylindrical shells
• Isogeometric analysis