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Research Papers

Stick-Slip Vibrations of Layered Structures Undergoing Large Deflection and Dry Friction at the Interface

[+] Author and Article Information
Hamid M. Sedighi

e-mail: h-msedighi@phdstu.scu.ac.ir;
hmsedighi@gmail.com

Kourosh H. Shirazi

Associate Professor
e-mail: k.shirazi@scu.ac.ir

Khosro Naderan-Tahan

Associate Professor
e-mail: Naderan_k@scu.ac.ir
Department of Mechanical Engineering,
Shahid Chamran University,
Ahvaz 61357-43337, Iran

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received September 30, 2012; final manuscript received March 31, 2013; published online June 19, 2013. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 135(6), 061006 (Jun 19, 2013) (12 pages) Paper No: VIB-12-1273; doi: 10.1115/1.4024218 History: Received September 30, 2012; Revised March 31, 2013

The present study focuses on the nonlinear analysis of the dynamical behavior of layered structures, including interfacial friction in the presence of the stick-slip phenomenon and large deformation. To achieve a proper outlook for the two-layer structure's behavior, it is essential to precisely realize the mechanisms of motion. Taking the dry friction into account, coupled equations of the transversal and longitudinal large vibration of two-layers are derived and nondimensionalized. Furthermore, the free and forced vibration of the aforementioned system is investigated. From the results of the numerical simulation, it is observed that there exist quasi-periodic and stick–slip chaotic motions in the system. The results demonstrate that the single mode method usually utilized may lead to incorrect conclusions and, instead, the higher order mode method should be employed. A comparative study with ANSYS is developed to verify the accuracy of the proposed approach.

Copyright © 2013 by ASME
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References

Jei, Y. G., Kim, J. S., and HongS. W., 1999, “A New Lateral Vibration Damper Using Leaf Springs,” ASME J. Vibr. Acoust., 121(3), p. 343. [CrossRef]
Osipenko, M. A., Nyashin, Yu. I., and Rudakov, R. N., 2003, “A Contact Problem in the Theory of Leaf Spring Bending,” Int. J. Solids Struct., 40(12), pp. 3129–3136. [CrossRef]
Oh, S. D., Jung, W. W., Bae, D. H., Lee, Y. Z., 2005, “Friction and Wear Characteristics for Automotive Leaf Spring Materials Due to the Influence of the Residual Stress,” Key Eng. Mater., 297–300, pp. 1388–1394. [CrossRef]
Chen, W., and Deng, X., 2005, “Structural Damping Caused by Micro-Slip Along Frictional Interfaces,” Int. J. Mech. Sci., 47, pp. 1191–1211. [CrossRef]
Goodman, L. E., and Klumpp, J. H., 1956, “Analysis of Slip Damping With Reference to Turbine Blade Vibration,” ASME J. Appl. Mech., 23, pp. 421–429.
Badrakhan, F., 1994, “Slip Damping in Vibrating Layered Beams and Leaf Springs: Energy Dissipated and Optimum Considerations,” J. Sound Vib., 174(1), pp. 91–103. [CrossRef]
Damisa, O., Olunloyo, V. O. S., Osheku, C. A., and Oyediran, A. A., 2008, “Dynamic Analysis of Slip Damping in Clamped Layered Beams With Non-Uniform Pressure Distribution at the Interface,” J. Sound Vib., 309, pp. 349–374. [CrossRef]
Olunloyo, V. O. S., Damisa, O., Osheku, C. A., and Oyediran, A. A., 2010, “Analysis of the Effects of Laminate Depth and Material Properties on the Damping Associated With Layered Structures in a Pressurized Environment,” Trans, Can. Soc. Mech. Eng.,34(2), pp. 165–196.
Li, Q., and Li, W., 2004, “A Contact Finite Element Algorithm for the Multileaf Spring of Vehicle Suspension Systems,” Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.), 218, pp. 305–314. [CrossRef]
Krys'ko, V. A., Koch, M. I., Zhigalov, M. V., and Krys'ko, A. V., 2012, “Chaotic Phase Synchronization of Vibrations of Multilayer Beam Structures,” J. Appl. Mech. Tech. Phys., 53(3), pp. 451–459. [CrossRef]
Ibrahim, R. A., 1994, “Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling,” Appl. Mech. Rev., 47, pp. 227–253. [CrossRef]
Brockley, C. A., and Ko, P. L., 1970, “Quasi-Harmonic Friction-Induced Vibration,” ASME J. Lubr. Technol., 89, pp. 550–556. [CrossRef]
Kang, J., Krousgrill, C. M., and Sadeghi, F., 2009, “Oscillation Pattern of Stick-Slip Vibrations,” Int. J. Non-Linear Mech., 44, pp. 820–828. [CrossRef]
Awrejcewicz, J., and Sendkowski, D., 2005, “Stick-Slip Chaos Detection in Coupled Oscillators With Friction,” Int. J. Solids Struct., 42, pp. 5669–5682. [CrossRef]
Han, Q., and Zheng, X., 2005, “Chaotic Response of a Large Deflection Beam and Effect of the Second Order Mode,” Eur. J. Mech. A/Solids, 24, pp. 944–956. [CrossRef]
Heuer, R., and Adam, C., 2000, “Piezoelectric Vibrations of Composite Beams With Interlayer Slip,” Acta Mech., 140, pp. 247–263. [CrossRef]
Ames, W. F., 1977, Numerical Methods for Partial Differential Equations, 2nd ed., Academic, New York.
Shampine, L. F., Gladwell, I., and Thompson, S., 2003, Solving ODEs With MATLAB, Cambridge University Press, Cambridge, UK.
Stefanski, A., and Kapitaniak, T., 2000, “Using Chaos Synchronization to Estimate the Largest Lyapunov Exponent of Nonsmooth Systems,” Discrete Dyn. Nat. Soc., 4, pp. 207–215. [CrossRef]
ANSYS® Academic Research, Release 14.0, “Help System, Coupled Field Analysis Guide,” Ansys, Inc.

Figures

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Fig. 1

Configuration of the layered structure under dynamic loading

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Fig. 2

Free-body diagram of an infinitesimal element of the deformed layered beam

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Fig. 3

Interlayer slip definition in the deformed element

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Fig. 4

Time history of the layered beam free vibration in the lateral direction for μ = 0.2,rt = 0.2,α = 1.5 × 10-3: (a) p* = 2 × 10-5, and (b) p* = 2.75 × 10-5

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Fig. 5

Details of the bifurcation diagram showing the initial slip occurrence for p* = 8 × 10-4,μ = 0.2,rt = 0.1, and α = 0.03

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Fig. 6

The impact of the excitation amplitude on the nonlinear behavior of the layered structure for rt = 0.9, p* = 1.5 × 10-5, and α = 1 × 10-2: (a) f0 = 1 × 10-2, (b) f0 = 2 × 10-2, (c) f0 = 17.14 × 10-2, (d) f0 = 30 × 10-2, and (e) f0 = 49.54 × 10-2

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Fig. 7

The diagram of the disturbance value |z| versus the convergence parameter ks and the time history of the disturbance value in (a) the lateral direction, and (b) the axial direction

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Fig. 8

The Poincaré projections for different interlayer pressures rt = 0.8,f0 = 20 × 10-2, and α = 1.5 × 10-2: (a) p* = 0, (b) p* = 1 × 10-8, (c) p* = 1×10-5, (d) p* = 2×10-5, (e) the phase portrait for p* = 2.95 × 10-5, and (f) the corresponding Poincaré section for p* = 3 × 10-5

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Fig. 9

The Poincaré projections for f0 = 20 × 10-2, α = 1.5 × 10-2, (a) p* = 1 × 10-5, rt = 0.5, (b) p* = 2.5 × 10-5, rt = 0.5, (c) p* = 1.1 × 10-5,rt = 0.7, (d) p* = 2.15 × 10-5,rt = 0.7, (e) p* = 1 × 10-5,rt = 0.9, and (f) p* = 2.5 × 10-5,rt = 0.9

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Fig. 10

Variation of the interface friction for μ = 0.3, p* = 5 × 10-5,α = 1.5 × 10-2, and f0 = 10 × 10-2: (a) rt = 0.1, (b) rt = 0.3, f0 = 20 × 10-2, (c) rt = 0.1, (d) rt = 0.3, f0 = 30 × 10-2, (e) rt = 0.1, and (f) rt = 0.3

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Fig. 11

Variation of the interface friction by varying the beam's location for μ = 0.3, p* = 1 × 10-5,α = 1.5 × 10-2, and f0 = 1 × 10-1 at (a) x* = 1, (b) x* = 0.9, (c) x* = 0.7, and (d) x* = 0.4

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Fig. 12

Schematics of the 3D FE mesh used for ANSYS simulations of the two-layer beam

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Fig. 13

Comparison between the time histories of the present modeling and the FEM results for rt = 0.8,f0 = 10 × 10-2,α = 1.5 × 10-2,p* = 5 × 10-5, and μ = 0.2

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Fig. 14

Comparison between the time histories of the present modeling and the FEM results for rt = 0.9,f0 = 20 × 10-2,α = 1.5 × 10-2,p* = 8 × 10-5, and μ = 0.2

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Fig. 15

Comparison between the time histories of the present modeling and the FEM results for rt = 1,f0 = 20 × 10-2,α = 1.5 × 10-2,p* = 1.5 × 10-5, and μ = 0.3

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