Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia

^* Corresponding author: kat.krylova@bk.ru

Abstract

A new mathematical model of a non-linear mesh cylindrical shell behaviour in the temperature field under normal distributed load is constructed. The construction of the mathematical model takes into account the Kirchhoff-Love kinematic model and the Duhamel-Neumann hypothesis. The scaling effect is taken into account by the modified moment theory of elasticity. It is assumed that the displacement and rotation fields are not independent. Geometric nonlinearity is taken into account according to T. von Karman's theory. The equations of motion of the smooth shell, boundary and initial conditions are derived from the variational Ostrogradsky-Hamiltonian principle. The lattice structure of the shell was modelled by the continuum theory of G. I. Pshenichny. This allowed us to replace the regular rib system by a continuous layer. The equilibrium conditions of a rectangular element were used to write down the relations connecting stresses occurring in an equivalent smooth shell with stresses in the ribs. The Lagrange multiplier method has been used to determine the physical relationships for the mesh shell. By means of the method of establishment the study of features of the shell's plasticity has been carried out and the frequencies of natural linear vibrations depending on the mesh geometry have been obtained.