An analytical vibration model of a one-dimensional two-stage periodic isolation system for the broadband vibration suppression of an underwater glider

Abstract

Periodic isolation system is effectively applied in broadband vibration control. To further enhance the broadband vibration attenuation effect, the paper proposes a two-stage periodic isolation system for an underwater glider. The analytical model of the one-dimensional two-stage periodic isolation system is developed through the multi-degree of freedom spring mass model method. For illustrating the superiority of the proposed two-stage periodic isolator, the force transmission ratio and the wave propagation constant of the SDOF isolator, the single-stage periodic isolator, and the two-stage periodic isolator are calculated and compared. In order to obtain the dynamic parameter influences on the vibration isolation performances as the design guidelines of the two-stage periodic isolator, the parametrical study is carried out based on the analytical model. Furthermore, a two-stage periodic isolator is designed for an underwater glider. The application effect of the two-stage periodic isolator is investigated through analytical modeling and finite element method, comparing to the single-stage periodic isolator. The research results from the analytical models show the proposed two-stage periodic isolator could strength the broadband vibration suppression. The parametrical study results demonstrate the vibration attenuation bandgap and attenuation amount are greatly influenced by the designed dynamic parameters, such as the mass unit and the spring unit of the periodic isolator, the intermediate mass of the two-stage isolator, and the number of the periodic cells. In application study of an underwater glider, the finite element results verify that the two-stage periodic isolator has more vibration attenuation effect than the single-stage periodic isolator. The vibration isolation assessment according to the proposed analytical model gives good predictive performance before the finite element model verification.

Keywords

two-stage vibration isolation periodic structure broadband vibration control wave propagation constant finite element method

Get full access to this article

View all access options for this article.

References

Song

Shi

Wang

, et al. Evaluation of energy consumption and motion accuracy for underwater gliders based on quadrant analysis. Ocean Eng 2023; 285: 115399.

Liu

Zhou

, et al. A simulation analysis of ball bearing lubrication characteristics considering the cage clearance. J Tribol 2023; 145(4): 044301.

Liu

Xia

. A dynamic model for the planetary bearings in a double planetary gear set. Mech Syst Signal Process 2023; 194: 110257.

Yang

Chang

Wang

, et al. A phononic crystal suspension for vibration isolation of acoustic loads in underwater gliders. Appl Acoust 2024, 216: 109731.

Liu

Pan

, et al. Dynamic analysis of an autonomous underwater glider with single-and two-stage vibration isolators. J Mar Sci Eng 2022; 10(2): 162.

Kim

Hong

Song

, et al. Analysis of noise attenuation for offshore platform silencer in duct with flow. Proc IMechE, Part M: J Engineering for the Maritime Environment 2023; 237(2): 344-356.

Pathak

Dangi

Farzbod

. Periodic structure with electrostatic forces: interactions beyond the nearest neighbor. J Vib Control. Epub ahead of print 25 June 2023. DOI: 10.1177/10775463231184009.

Prasad

Baxy

Banerjee

. Broadband sound transmission loss in a corrugated sound panel using periodic structure theory. J Vib Acoust 2022; 144(6): 061006.

Maldovan

. Phonon wave interference and thermal bandgap materials. Nat Mater 2015; 14(7): 667–674.

10.

Dauchez

Nennig

. A metaporoelastic structure that overcomes the sound insulation weaknesses of single and double panel partitions. Appl Acoust 2023; 210: 109409.

11.

J-Y

Zhu

Liu

W-L

, et al. Vibration characteristics of panel structures including periodic acoustic black hole beams. Noise Vib Control 2023; 43(3): 21.

12.

Jiang

, et al. Experimental and numerical investigation on the vibro-acoustic characteristics of periodic rib stiffened plate based on band gap theory. J Vib Control. Epub ahead of print 18 July 2023. DOI: 10.1177/10775463231188848.

13.

Zheng

Liu

. Bandgap mechanism analysis of elastically restrained periodic cylindrical shells with arbitrary periodic thickness. Int J Mech Sci 2023; 237: 107803.

14.

Gao

Zhu

, et al. Inertia modulated meta-structure with time-varying inertia amplification. J Appl Mech 2023; 91: 021006.

15.

Prasad

Sarkar

. Broadband vibration isolation for rods and beams using periodic structure theory. J Appl Mech 2019; 86(2): 021004.

16.

Szefi

Smith

Lesieutre

. Analysis and design of high frequency periodically layered isolators in compression. In: Proceedings of the 41st AIAA Structures, Structural Dynamics and Materials Conference, Atlanta, GA, 3-6 April, 2000. Sunrise Valley Drive: American Institute of Aeronautics and Astronautics.

17.

Szefi

Smith

Lesieutre

. Design and analysis of high-frequency periodically layered isolators for helicopter gearbox isolation. In: Proceedings of the 44th AIAA Structures, Structural Dynamics and Materials Conference, Norfolk, Virginia, 7-10 April, 2003. Sunrise Valley Drive: American Institute of Aeronautics and Astronautics.

18.

Song

Wen

, et al. Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators. J Sound Vib 2014; 333: 3031–3043.

19.

Jain

Pujari

Laskar

. Investigation of one-dimensional multi-layer periodic unit cell for structural base isolation. Structures 2021; 34: 2151–2163.

20.

Huang

Ren

, et al. Development of curved beam periodic structure in broadband resonance suppression for cylindrical shell structure. J Vib Control 2017; 23(8): 1267–1284.

21.

Zhu

Huang

Hua

, et al. Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators. Proc IMechE, Part C: J Mechanical Engineering Science 2016; 230(16): 2840–2850.

22.

Moore

. Analytical modelling of single and two-stage vibration isolation systems. Proc Acoust 2011; 1: 116.

23.

Jin

Liu

. Active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system. Int J Mech Sci 2014; 79: 182–194.

24.

Huang

Zhang

, et al. Vibro-acoustic optimization of an immersed cylindrical structure with a floating-raft system inside by using frequency-response-function-based substructuring sensitivity analysis. Proc IMechE, Part M: J Engineering for the Maritime Environment 2011; 225(2): 111–132.

25.

Rivin

. Passive vibration isolation. New York: ASME Press, 2003.

26.

Wang

Zhou

, et al. Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn 2016; 87(1): 633–646.

27.

Brennan

Yang

, et al. An investigation of a two-stage nonlinear vibration isolation system. J Sound Vib 2013; 332(6): 1456–1464.

28.

Song

Wen

, et al. Suppression of vibration and noise radiation in a flexible floating raft system using periodic structures. J Vib Control 2015; 21(2): 217–228.

29.

Yang

Brennan

, et al. Experimental investigation of a two-stage nonlinear vibration isolation system with high-static-low-dynamic stiffness. J Appl Mech Trans ASME 2017; 84(2): 021001.

30.

Liu

Pan

, et al. Modeling and analysis of a metal rubber vibration isolation system considering the nonlinear stiffness characteristics. Rev Sci Instrum 2023; 94(1): 015105.