Nonlinear Dynamic Modeling and Model Reduction Strategy for Rotating Thin Cylindrical Shells

Shupeng Sun,Lun Liu

doi:10.1155/2019/4536012

Abstract

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in-plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in-plane vibrations. Meanwhile, for the reduced-order model, the in-plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude-frequency responses under different excitation levels.

Highlights

Rotating thin cylindrical shells have been widely used in engineering applications, such as rotors of aircraft engines, rotating satellite structures, and high-speed centrifugal separators
The nonlinear shell theory instead of linear one should be applied, and it is of practical importance to carry out nonlinear dynamic studies on thin rotating cylindrical shells
Some researchers proposed several analytical and numerical methods to study the dynamic characteristics of rotating shells, such as Fourier series expansion approach [4], wave propagation method [5], discrete singular convolution method [6, 7], harmonic reproducing kernel particle approach [8], Rayleigh–Ritz technique [9], and finite element method [10]

Summary

Introduction

Rotating thin cylindrical shells have been widely used in engineering applications, such as rotors of aircraft engines, rotating satellite structures, and high-speed centrifugal separators. In order to facilitate the investigations of rotating cylindrical shells’ nonlinearities, most scholars neglected all inertia terms along in-plane directions to derive simplified governing equations, which means the contributions of in-plane vibrations to the dynamic response are discarded directly. It is a question whether the system described by this simplified governing equations can retain the characteristics of nonlinear vibration, especially the low-frequency characteristics. Considering the quadratic nonlinear terms neglected in authors’ previous study [46], the nonlinear dynamic model for the shell with supported conditions is first derived in terms of ordinary differential equations This model can reflect the coupling of three deformation directions and describe both the flexural and the in-plane vibrations. Comparisons and simulations are conducted to validate the original nonlinear dynamic model and model reduction strategy, and nonlinear dynamic behaviors are investigated preliminarily

Nonlinear Dynamic Modeling

Model Reduction

Numerical Results and Discussions

Conclusions