Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Active vibration control of a cylindrical shell coupled with complex interior structures
Wenchao Jia, Meixia Chen, Zhiwei Zhou
1School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology.

Wuhan, Hubei, China
Kun XieCollege of Engineering, Huazhong Agricultural University.
Wuhan, Hubei, China

isolators. The vibration from the devices is significantly counteracted
by applying a control force on the intermediate body. Further, Xu et al.
(2019) introduced a flexible deck acting as a base under this massequipment system, and considered the role of the elastic partition
during the vibration control research. Using the energy method, thetheoretical model of shell-plate-mass sound vibration is established.
This model is closer to the real hull structure. However, the internalstructure considered is only a rectangular plate, which can beanalytically modeled. In the real submarine, many equipment isinstalled on bases irregular shapes. It is difficult establish the dynamic
model of the shell-base coupled system by above unified analyticalmethods.

ABSTRACTThe active vibration control of a cylindrical shell coupled with complex
inner foundations is theoretically investigated using a hybrid analyticalnumerical approach. The motion and solution of the shell are describedby Flugge theory and wave based method, respectively. Inner
foundations are analyzed by using finite element method due to theirirregular shapes. These two substructures are connected through virtual
springs with six degrees of freedom (DOFs), which is convenient for
simulating the rigid and elastic coupling between the shell and interiorstructures. By employing the continuity conditions at the junction nodes,
the final governing equation of the whole structure is assembled. Twotypes of frequency response functions are chosen as the cost functions
and the optimal control force corresponding to every control strategy isderived. Numerical analysis is conducted to evaluate the performanceof these control strategies in terms of mean quadratic velocity andamplitude of control forces.

For the past few years, some hybrid methods are developed byresearchers to study the vibration of the coupled structure. Wu et al.
(2018) utilized a combination of the finite element method (FEM) andstatistical energy analysis (SEA) to investigate the vibration response ofa stiffened plate. Ma et al. (2016) discussed the energy flow of a beamcoupled with several beams by combining the analytical wave methodand FEM. Liu et al. (2020) simplified the railway bridge into a plate
reinforced by T-shaped beams and established the vibration equation
through a hybrid FEM-SEA method. Meyer et al. (2016) developed asemi-analytical method to predict the vibration response of a shell
reinforced by non-axisymmetric stiffeners.

KEY WORDS:

cylindrical shell; internal structures; hybrid
analytical-numerical approach; active control; control strategies.

INTRODUCTION
Vibration characteristics of cylindrical shells and associated coupledstructures have received extensive attention. At present, the research
papers involving vibration responses of cylindrical shells directlyexcited by point forces are really sufficient. In fact, a considerable partof the noise radiated by the shells is caused by the vibration of theequipment inside the hull transmitted to the shell via the bases.
Therefore, it is very critical to study the active control characteristics ofthe vibration transmitted from the internal equipment. Pan et al. (2008)
and Caresta (2011) studied the active control of the submarine hullshafting coupled system subjected to a harmonic force on the propeller.
By placing an inertial vibration isolator on the shell, the vibration
caused by the wake-excited blades decreased. Jin et al. (2011)
presented some active control strategies to reduce the vibration of acylindrical shell and then carried out an experiment to verify theeffectiveness of the methods. Ma and Liu (2014) presented a two-stage
vibration isolation system, which consisted of the rigid machine and arigid vibration isolation stage connected with each other by someIn this work, a semi-analytical method is firstly presented to establish
the vibrational model of the cylindrical shell coupled with internalstructures. Then the investigation of active structural vibration control
for this system is carried out. The vibration equations of these twosubstructures are established by analytical and numerical approaches,respectively. Via the continuity conditions between the internalstructure and cylindrical shell, the governing equations of the wholesystem are assembled. To study the active control of this coupledstructure, some control strategies are proposed through setting thefrequency response functions as the cost functions and the optimal
control forces corresponding to these strategies are figured out. The
control effects of the above control strategies are compared and studied.
Some useful conclusions are drawn. This method provides a powerfultool to control the vibration of the shell coupled with complex internal
structures.

3083