Free vibration and damping analysis of the cylindrical shell partially covered with equidistant multi-ring hard coating based on a unified Jacobi-Ritz method

Abstract

In this study, the aim was to evaluate the vibration suppression performance of the partially covered equidistant multi-ring hard coating damping treatment for the cylindrical shell structure in aviation power equipment. A continuous rectangular pulse function was presented to describe the local thickness variation of arbitrary coating proportion and arbitrary number of coating rings. A semi-analytical unified solution procedure was established by combining the rectangular pulse function, the generalized Jacobi polynomials, and the Rayleigh-Ritz method. The stiffness coefficient k = 1013 N/m2 and the truncation number N = 8 were found to be large enough to achieve an accurate and efficient solution of the vibration analysis of the shell. The modal loss factor generally increased with the increase of the coating proportion ranging from 0.0 to 1.0 for all the circumferential wave numbers. The modal loss factor increased roughly linear with the coating proportion for all the circumferential wave numbers. And the modal loss factor was increased with the circumferential wave number, and the greater the number of circumferential waves, the greater the rate of change. The increase of the ring number was not always beneficial for vibration reduction of the shell, while the modal loss factor increased roughly linear with the coating proportion. The increased ring number and coating proportion tend more to exhibit an obvious incremental damping effect under larger circumferential wave number.

Performance evaluation for the domain decomposition method in nonlinear vibration of the composite hard-coating cylindrical shell

“…Correspondingly, the subscripts c and s denote the layers of hard coating and shell substrate. According to the first-order shear deformation theory, 39 the strains at an arbitrary point of the shell are given by Substituting equation (3) into equation (7) one can obtain where Aij, Bij, and Dij are the extensional, coupling, and bending stiffness defined, respectively, by In accordance with the well-known Rayleigh-Ritz method, 38 the so-called Lagrangian energy function can be constructed by using the maximum of the above kinetic energy, potential energy, and strain energy. Then, the equations of motion of the composite hard-coating cylindrical shell can be achieved in the following matrix form, expressed as where Kfalse^ is the complex stiffness matrix, written by Here K and D represent the stiffness matrix and material damping matrix, respectively.…”

“…Correspondingly, the subscripts c and s denote the layers of hard coating and shell substrate. According to the first-order shear deformation theory, 39 the strains at an arbitrary point of the shell are given by…”