Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory

In this paper, three-dimensional vibrations of carbon nanotubes (CNTs) reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher-order shear deformation theory (HSDT) is investigated. The considering higher-order shear deformation theory is a combination of sinus and exponential power with cosine function which is one of the most accurate shear deformation theory. One can conclude that combination of important theories such as Reddy's doubly-curved shells theory, nonlocal elasticity theory and higher-order shear deformation theory to a more complicated structure such as doubly-curved shells leads to important and novel work in context of mechanical engineering. The equations of motion and boundary conditions are derived using Hamilton's principle. The equations of motion are solved via Navier-type, closed-form solutions. From the best knowledge of authors, it is the first time that present formulation is used to investigate the vibration of carbon nanotubes reinforced doubly-curved nanoshells based on a new higher-order shear deformation theory. Also, it is the first time that small scale effects are considered in carbon nanotubes reinforced doubly-curved nanoshells made of isotropic materials. The effects of mechanical properties, geometrical properties and the different types of CNTs on the vibration frequencies of doubly-curved nanoshell are investigated. The comparison study is carried out to verify the accuracy of the proposed method. Numerical results indicate that the volume fraction and types of distribution of CNTs have considerable effects on the vibration characteristics of CNTs doubly-curved nanoshells. Presented results for vibrations can minister as benchmarks for future analysis of CNTs doubly-curved nanoshells.