A new analytical model for vibration of a cylindrical shell and cardboard liner with focus on interfacial distributed damping

Abstract

This paper proposes a new analytical model for a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Such cardboard liners are frequently used as noise and vibration control devices for cylindrical shell-like structures in automotive drive shafts. However, most prior studies on such lined structures have only investigated the associated damping mechanisms in an empirical manner. Only finite element models and experimental methods have been previously used for characterization, whereas no analytical studies have addressed sliding friction interaction at the shell-liner interface. The proposed theory, as an extension of a prior experimental study, uses the Rayleigh-Ritz method and incorporates material structural damping along with frequencydependent viscous and Coulomb interfacial damping formulations for the shell-liner interaction. Experimental validation of the proposed model, using a thin cylindrical shell with three different cardboard liner thicknesses, is provided to validate the new model, and to characterize the damping parameters. Finally, the model is used to investigate the effect of the liner and the damping parameters on the modal attenuation of the shell vibration, in particular for the higher-order coupled shell modes.

Design of an Active Low Frequency Vibration Isolation System for Atom Interferometry by Using Sliding Mode Control

“…Equation 8 shows that with the increase in feedback gain H which lower the effective resonance frequency and thus increase the range over which the system tends to isolate motions of the ground from motions of the mass [22][23].…”

Vibration control of a cylindrical shell with concurrent active piezoelectric patches and passive cardboard liner

“…Aside from these empirical or computational studies, few other publications exist for lined shell systems outside of the recent article [1] and an experimental study by Koruk et al [6]. The chief goals of this companion article are to extend the prior article [1] by proposing a semi-analytical model for a thin cylindrical shell with concurrent active (piezoelectric patches) and passive (distributed cardboard liner) damping treatments. Given a practical need for exploring lightweight vibro-acoustic treatments for vehicle applications [2][3][4][5][6], this article aims to develop a mathematical framework for the evaluation of vibration control strategies.…”

“…In a recent article [1], the authors developed a semi-analytical model to predict the vibration of a thin cylindrical shell subject to a homogenous cardboard damping liner. The motivation for the prior paper was the lack of physics-based analytical studies, despite the common usage of such damping liners for noise reduction in automotive drive shafts [2][3][4][5].…”

“…The motivation for the prior paper was the lack of physics-based analytical studies, despite the common usage of such damping liners for noise reduction in automotive drive shafts [2][3][4][5]. Aside from these empirical or computational studies, few other publications exist for lined shell systems outside of the recent article [1] and an experimental study by Koruk et al [6]. The chief goals of this companion article are to extend the prior article [1] by proposing a semi-analytical model for a thin cylindrical shell with concurrent active (piezoelectric patches) and passive (distributed cardboard liner) damping treatments.…”

Viscoelastic Substrates Effects on the Elimination or Reduction of the Sandwich Structures Oscillations Based on the Kelvin-Voigt Model

“…Zenkour (2016) applied the classical plate theory and Fourier transformmethod for transient thermal analysis of a single layered graphene sheet embedded in viscoelastic medium.The governing dynamical equation was obtained and solved for simply-supported grapheme sheet. By using the Rayleigh-Ritz method, Plattenburg et al (2016) proposed a new analytical modelfor a thin cylindrical shell that utilizes a homogeneous cardboard liner to increase modal damping. Theproposed theory, incorporated material structural damping along with frequency-dependent viscousand Coulomb interfacial damping formulations for the shell-liner interaction.…”