Mathematical model of orthotropic meshed micropolar cylindrical shells oscillations under temperature effects

Abstract

In the work the mathematical model of micropolar meshed cylindrical shells oscillations under the action of the vibrational and temperature effects is constructed. The shell material is an elastic orthotropic homogeneous Cosserat pseudocontinuum with constrained rotation of particles. The Duhamel – Neumann’s law was adopted. The mesh structure is taken into account according to the model of G. I. Pshenichnov, geometric nonlinearity according to Theodor von Karman theory. The equations of motion, boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Tymoshenko kinematic model. The constructed a mathematical model will be useful, among other things, in the study of the behavior of carbon nanotubes under various operating conditions.

Keywords

• mesh structure cylindrical shells
• mathematical modeling
• thermodynamics
• carbon nanotube