Vibration of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses

Fuchun Yang,Wenlei Qiu

doi:10.1051/matecconf/201823701011

Abstract

Vibration properties of thin cylindrical shells on an elastic foundation coupled with multiple discrete stiffnesses were investigated. The discrete stiffnesses were modelled as external forces. Hamilton’s principle was applied to deduce the governing equations. To study the natural vibration properties, the wave-like solutions were applied. Then the governing equations were discretized in matrix form to obtain the eigenvalues. The properties of natural frequencies and vibration modes of thin cylindrical shells were studied. The results illustrate that each natural frequency of cylindrical shells is mainly dominated by one vibration mode, that is, flexural, longitudinal and shear modes. The natural frequency will get closer with the increase of circumferential wave numbers. The influences of several parameters to vibration properties of cylindrical shells were also investigated.

Highlights

Vibrations of cylindrical shells have received great attention for over a century in various engineering structures, such as rotor systems of gas turbine engines, high-speed centrifugal separators, rotating satellite structures, and planetary gear sets
Since this study is motivated by multiple stage planetary gear systems, the parameters of a thin cylindrical shell which denotes a ring gear in the planetary gear system are given as U=7800kg/m3, E=206GPa, P=0.3, kr=kT=1u108N/m, kip=5u108N/m, R=160mm, h=10mm, L=300mm, E=1.22, zmi=L/6, L/2, 5L/6, Tip=0, 2S/3, 4S/3, i=1, 2, 3, p=1, 2, 3, Mn=Ns=3, the discrete stiffnesses are axially and circumferentially equispaced and the phases between adjacent axial group of the discrete stiffnesses are set to S/4
Vibration properties of thin cylindrical shells with multiple-stage discrete stiffnesses and foundation stiffnesses were investigated in this paper

Summary

Introduction

Vibrations of cylindrical shells have received great attention for over a century in various engineering structures, such as rotor systems of gas turbine engines, high-speed centrifugal separators, rotating satellite structures, and planetary gear sets. This work is motivated by multiple stage planetary gear systems. Omer [9] dealt with the free vibration analysis of rotating laminated cylindrical shells. Padovan [10] obtained the complete set of natural frequencies and corresponding mode shapes for circular cylindrical shells. Huang and Soedel [11] studied the forced response of a special cylindrical shell. This work will establish the governing equations of thin cylindrical shells on an elastic foundation with multiple discrete stiffnesses and study their vibration properties

Analytical model

P w2u 2 wT 2

Numerical results

Conclusions