Abstract
A simple passive technique of vibration isolation for flexible structures by nonlinear boundaries is investigated, which to our best knowledge is the first study of its kind reported in the literature. The equations of the structure are derived with Hamilton’s principle. An iterative analytic method is investigated to improve the accuracy of the response prediction. The effect of nonlinear boundaries of the structure is studied compared with the linear structure. It is found that stronger nonlinearities in the boundary make the system more stable. Analytical and simulation results show that nonlinear boundaries can significantly reduce the vibration and stress of flexible structures. It is important to point out that with the help of nonlinear boundaries, structural vibration and stress control can be achieved without altering the original structure.
Issue Section:
Research Papers
References
1.
Bel-Hadj-Ali
, N.
, and Smith
, I. F. C.
, 2010
, “Dynamic Behavior and Vibration Control of a Tensegrity Structure
,” Int. J. Solids Struct.
, 47
(9
), pp. 1285
–1296
. 2.
Tu
, Y. Q.
, and Zheng
, G. T.
, 2007
, “On the Vibration Isolation of Flexible Structures
,” J. Appl. Mech.
, 74
(3
), pp. 415
–420
. 3.
Yang
, B. B.
, Hu
, Y. F.
, Vicario
, F.
, Zhang
, J. G.
, and Song
, C. S.
, 2017
, “Improvements of Magnetic Suspension Active Vibration Isolation for Floating Raft System
,” Int. J. Appl. Electromagn. Mech.
, 53
(2
), pp. 193
–209
. 4.
Alhan
, C.
, and Gavin
, H.
, 2004
, “A Parametric Study of Linear and Non-Linear Passively Damped Seismic Isolation Systems for Buildings
,” Eng. Struct.
, 26
(4
), pp. 485
–497
. 5.
Zhu
, H. P.
, Chen
, C. L.
, Zhu
, A. Z.
, and Yuan
, Y.
, 2013
, “Isolation Performance Study of the Hong Kong-Zhuhai-Macao Bridge Engineering
,” J. Earthq. Tsunami
, 7
(3
), 1350018
. 6.
Crede
, C. E.
, 1951
, Vibration and Shock Isolation
, Wiley
, New York
.7.
Rivin
, E. I.
, 2001
, Passive Vibration Isolation
, ASME Press
, New York
.8.
Ibrahim
, R. A.
, 2008
, “Recent Advances in Nonlinear Passive Vibration Isolators
,” J. Sound Vib.
, 314
(3–5
), pp. 371
–452
. 9.
Daley
, S.
, Hatonen
, J.
, and Owens
, D. H.
, 2006
, “Active Vibration Isolation in a “Smart Spring” Mount1 Using a Repetitive Control Approach
,” Control Eng. Pract.
, 14
(9
), pp. 991
–997
. 10.
Yan
, B.
, Brennan
, M. J.
, Elliott
, S. J.
, and Ferguson
, N. S.
, 2010
, “Active Vibration Isolation of a System With a Distributed Parameter Isolator Using Absolute Velocity Feedback Control
,” J. Sound Vib.
, 329
(10
), pp. 1601
–1614
. 11.
Sahasrabudhe
, S. S.
, and Nagarajaiah
, S.
, 2005
, “Semi-Active Control of Sliding Isolated Bridges Using MR Dampers: An Experimental and Numerical Study
,” Earthq. Eng. Struct. Dyn.
, 34
(8
), pp. 965
–983
. 12.
Zhang
, X.-X.
, and Xu
, J.
, 2016
, “Time Delay Identifiability and Estimation for the Delayed Linear System With Incomplete Measurement
,” J. Sound Vib.
, 361
, pp. 330
–340
. 13.
Zhang
, X.-X.
, Xu
, J.
, and Feng
, Z.-C.
, 2017
, “Nonlinear Equivalent Model and Its Identification for a Delayed Absorber With Magnetic Action Using Distorted Measurement
,” Nonlinear Dyn.
, 88
(2
), pp. 937
–954
. 14.
Blair
, D. G.
, Ju
, L.
, and Peng
, H.
, 1993
, “Vibration Isolation for Gravitational Wave Detection
,” Class. Quantum Gravity
, 10
(11
), pp. 2407
–2418
. 15.
Losurdo
, G.
, Bernardini
, M.
, Braccini
, S.
, Bradaschia
, C.
, Dattilo
, C. C. V.
, De-Salvo
, R.
, Di-Virgilio
, A.
, Frasconi
, F.
, and Gaddi
, A.
, 1999
, “An Inverted Pendulum Preisolator Stage for the Virgo Suspension System
,” Rev. Sci. Instrum.
, 70
(5
), pp. 2507
–2515
. 16.
Platus
, D. L.
, 1992
, “Negative-Stiffness-Mechanism Vibration Isolation Systems
,” Proc. Vib. Control Microelectron. Opt. Metrol.
, 1619
, pp. 44
–55
. 17.
Platus
, D. L.
, 1999
, “Negative-Stiffness-Mechanism Vibration Isolation Systems
,” Proc. Optomech. Eng. Vib. Control
, 3786
, pp. 98
–106
. 18.
Sapountzakis
, E. J.
, Syrimi
, P. G.
, Pantazis
, I. A.
, and Antoniadis
, I. A.
, 2017
, “KDamper Concept in Seismic Isolation of Bridges With Flexible Piers
,” Eng. Struct.
, 153
, pp. 525
–539
. 19.
Zhou
, J. X.
, Wang
, X. L.
, Xu
, D. L.
, and Bishop
, S.
, 2015
, “Nonlinear Dynamic Characteristics of a Quasi-Zero Stiffness Vibration Isolator With Cam-Roller-Spring Mechanisms
,” J. Sound Vib.
, 346
, pp. 53
–69
. 20.
Zhou
, J. X.
, Xiao
, Q. Y.
, Xu
, D. L.
, Ouyang
, H. J.
, and Li
, Y. L.
, 2017
, “A Novel Quasi-Zero-Stiffness Strut and Its Applications in Six-Degree-of-Freedom Vibration Isolation Platform
,” J. Sound Vib.
, 394
, pp. 59
–74
. 21.
Li
, Q.
, Zhu
, Y.
, Xu
, D. F.
, Hu
, J. C.
, Min
, W.
, and Pang
, L. C.
, 2013
, “A Negative Stiffness Vibration Isolator Using Magnetic Spring Combined With Rubber Membrane
,” J. Mech. Sci. Technol.
, 27
(3
), pp. 813
–824
. 22.
Carrella
, A.
, Brennan
, M. J.
, and Waters
, T. P.
, 2007
, “Static Analysis of a Passive Vibration Isolator With Quasi-Zero-Stiffness Characteristic
,” J. Sound Vib.
, 301
(3–5
), pp. 678
–689
. 23.
Peng
, Z. K.
, Lang
, Z. Q.
, Zhao
, L.
, Billings
, S. A.
, Tomlinson
, G. R.
, and Guo
, P.
, 2011
, “The Force Transmissibility of MDOF Structures With a Non-Linear Viscous Damping Device
,” Int. J. Nonlinear Mech.
, 46
(10
), pp. 1305
–1314
. 24.
Peng
, Z. K.
, Meng
, G.
, Lang
, Z. Q.
, Zhang
, W. M.
, and Chu
, F. L.
, 2012
, “Study of the Effects of Cubic Nonlinear Damping on Vibration Isolations Using Harmonic Balance Method
,” Int. J. Nonlinear Mech.
, 47
(10
), pp. 1073
–1080
. 25.
Guo
, P. F.
, Lang
, Z. Q.
, and Peng
, Z. K.
, 2012
, “Analysis and Design of the Force and Displacement Transmissibility of Nonlinear Viscous Damper Based Vibration Isolation Systems
,” Nonlinear Dyn.
, 67
(4
), pp. 2671
–2687
. 26.
Tang
, B.
, and Brennan
, M. J.
, 2013
, “A Comparison of Two Nonlinear Damping Mechanisms in a Vibration Isolator
,” J. Sound Vib.
, 332
(3
), pp. 510
–520
. 27.
Sun
, J. Y.
, Huang
, X. C.
, Liu
, X. T.
, Xiao
, F.
, and Hua
, H. X.
, 2013
, “Study on the Force Transmissibility of Vibration Isolators With Geometric Nonlinear Damping
,” Nonlinear Dyn.
, 74
(4
), pp. 1103
–1112
. 28.
Ho
, C.
, Lang
, Z.-Q.
, and Billings
, S. A.
, 2014
, “Design of Vibration Isolators by Exploiting the Beneficial Effects of Stiffness and Damping Nonlinearities
,” J. Sound Vib.
, 333
(12
), pp. 2489
–2504
. 29.
Huang
, D. M.
, Xu
, W.
, Xie
, W. X.
, and Liu
, Y. J.
, 2015
, “Dynamical Properties of a Forced Vibration Isolation System With Real-Power Nonlinearities in Restoring and Damping Forces
,” Nonlinear Dyn.
, 81
(1–2
), pp. 641
–658
. 30.
Cheng
, C.
, Li
, S. M.
, Wang
, Y.
, and Jiang
, X. X.
, 2017
, “Force and Displacement Transmissibility of a Quasi-Zero Stiffness Vibration Isolator With Geometric Nonlinear Damping
,” Nonlinear Dyn.
, 87
(4
), pp. 2267
–2279
. 31.
Huang
, X. L.
, and Shen
, H. S.
, 2004
, “Nonlinear Vibration and Dynamic Response of Functionally Graded Plates in Thermal Environments
,” Int. J. Solids Struct.
, 41
(9–10
), pp. 2403
–2427
. 32.
Chen
, L.-Q.
, and Yang
, X. D.
, 2005
, “Steady-State Response of Axially Moving Viscoelastic Beams With Pulsating Speed: Comparison of Two Nonlinear Models
,” Int. J. Solids Struct.
, 42
(1
), pp. 37
–50
. 33.
Zu
, J. W. Z.
, and Han
, R. P. S.
, 1992
, “Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions
,” ASME J. Appl. Mech.
, 59
(2S
), pp. S197
–S204
. 34.
Israr
, A.
, Cartmell
, M. P.
, Manoach
, E.
, Trendafilova
, I.
, Krawczuk
, M.
, and Arkadiusz
, L.
, 2009
, “Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading
,” ASME J. Appl. Mech.
, 76
(1
), p. 011005
. 35.
Ding
, H.
, Li
, Y.
, and Chen
, L.-Q.
, 2018
, “Nonlinear Vibration of a Beam With Asymmetric Elastic Supports
,” Nonlinear Dyn.
pp. 1
–12
. 36.
Mao
, X.-Y.
, Ding
, H.
, and Chen
, L.-Q.
, 2017
, “Vibration of Flexible Structures Under Nonlinear Boundary Conditions
,” ASME J. Appl. Mech.
, 84
(11
), p. 111006
. 37.
Ding
, H.
, Dowell
, E. H.
, and Chen
, L.-Q.
, 2018
, “Transmissibility of Bending Vibration of an Elastic Beam
,” ASME J. Vib. Acoust.
, 140
(3
), p. 031007
. 38.
Ding
, H.
, Lu
, Z.-Q.
, and Chen
, L.-Q.
, 2019
, “Nonlinear Isolation of Transverse Vibration of Pre-Pressure Beams
,” J. Sound Vib.
, 442
, pp. 738
–751
. 39.
Ding
, H.
, and Chen
, L.-Q.
, 2018
, “Nonlinear Vibration of a Slightly Curved Beam With Quasi-Zero-Stiffness Isolators
,” Nonlinear Dyn.
pp. 1
–16
. 40.
Nayfeh
, A. H.
, and Mook
, D. T.
, 1979
, Nonlinear Oscillations
, John Wiley & Sons
, New York
.41.
Mao
, X.-Y.
, Ding
, H.
, and Chen
, L.-Q.
, 2017
, “Dynamics of a Super-Critically Axially Moving Beam With Parametric and Forced Resonance
,” Nonlinear Dyn.
, 89
(2
), pp. 1475
–1487
. 42.
Mao
, X.-Y.
, Ding
, H.
, and Chen
, L.-Q.
, 2017
, “Forced Vibration of Axially Moving Beam With Internal Resonance in the Supercritical Regime
,” Int. J. Mech. Sci.
, 131
, pp. 81
–94
. 43.
Mao
, X.-Y.
, Ding
, H.
, Lim
, C. W.
, and Chen
, L.-Q.
, 2016
, “Super-Harmonic Resonance and Multi-Frequency Responses of a Super-Critical Translating Beam
,” J. Sound Vib.
, 385
, pp. 267
–283
. 44.
Wang
, Y. L.
, Wang
, X. W.
, and Zhou
, Y.
, 2004
, “Static and Free Vibration Analyses of Rectangular Plates by the New Version of the Differential Quadrature Element Method
,” Int. J. Numer. Methods Eng.
, 59
(9
), pp. 1207
–1226
. 45.
Wang
, X. W.
, and Wang
, Y. L.
, 2013
, “Free Vibration Analysis of Multiple-Stepped Beams by the Differential Quadrature Element Method
,” Appl. Math. Comput.
, 219
(11
), pp. 5802
–5810
. 46.
Shu
, C.
, Chew
, Y. T.
, and Richards
, B. E.
, 1995
, “Generalized Differential and Integral Quadrature and Their Application to Solve Boundary Layer Equations
,” Int. J. Numer. Methods Fluids
, 21
(9
), pp. 723
–733
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