Research Papers

Methods of Identification of Definite Degenerated and Nonlinear Dynamic System Using Specially Programmed Nonharmonic Enforce

[+] Author and Article Information
Miroslaw Bocian

Department of Mechanics, Materials Science
and Engineering,
Wroclaw University of Science and Technology,
Smoluchowskiego 25,
Wroclaw 50-370, Poland
e-mail: miroslaw.bocian@pwr.edu.pl

Krzysztof Jamroziak

Department of Mechanics, Materials Science
and Engineering,
Wroclaw University of Science and Technology,
Smoluchowskiego 25,
Wroclaw 50-370, Poland
e-mail: krzysztof.jamroziak@interia.pl

Mariusz Kosobudzki

General Tadeusz Kosciuszko Military Academy
of Land Forces,
Czajkowskiego 109,
Wroclaw 51-150, Poland
e-mail: m.kosobudzki@wso.wroc.pl

Maciej Kulisiewicz

Faculty of Technology and Engineering,
Wroclaw University of Science and Technology,
Armii Krajowej 78,
Walbrzych 58-302, Poland
e-mail: maciej.kulisiewicz@pwr.edu.pl

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 25, 2016; final manuscript received February 8, 2017; published online May 31, 2017. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 139(8), 081012 (May 31, 2017) (6 pages) Paper No: DS-16-1367; doi: 10.1115/1.4036080 History: Received July 25, 2016; Revised February 08, 2017

The paper presents the new way of identification of complex nonlinear dynamic systems. The method has been explained with the use of a dynamic structure (degenerated one) with 1.5 degrees-of-freedom and some nonlinear restitution force. The applied method allows for the assessment of the dynamic behavior of material in a wide range of dynamic loads. The equation of energy balance when oscillations are set harmonic is applicable to the solution. It is possible when the loading force is adjustable. The method has been computer verified using a system with cubic spring characteristic.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Geradin, M. , and Rixen, D. J. , 2015, Mechanical Vibration (Theory and Applications to Structural Dynamics) 3rd ed., Wiley, Hoboken, NJ.
Osinski, Z. , 1998, Damping of Vibrations, Balkema, Rotterdam, The Netherlands.
Bialas, K. , and Sekala, A. , 2013, “ Vibration Analysis of Mechanical Systems With the Discrete-Continuous Distribution of Parameters,” Solid State Phenom., 198, pp. 698–703. [CrossRef]
Borkowski, L. , Perlikowski, P. , Kapitaniak, T. , and Stefanski, A. , 2015, “ Experimental Observation of Three-Frequency Quasiperiodic Solution in a Ring of Unidirectionally Coupled Oscillators,” Phys. Rev. E, 91(6), p. 062906. [CrossRef]
Buchacz, A. , and Placzek, M. , 2010, “ Development of Mathematical Model of a Mechatronic System,” Solid State Phenom., 164, pp. 319–322. [CrossRef]
Kosobudzki, M. , 2014, “ The Use of Acceleration Signal in Modeling Process of Loading an Element of Underframe of High Mobility Wheeled Vehicle,” Ekspl. Niezawodnosc Maint. Reliab., 16(4), pp. 595–599.
Krason, W. , and Malachowski, J. , 2015, “ Multibody Rigid Models and 3D FE Models in Numerical Analysis of Transport Aircraft Main Landing Gear,” Bull. Pol. Acad. Sci.: Tech. Sci, 63(3), pp. 745–757.
Placzek, M. , 2015, “ Modelling and Investigation of a Piezo Composite Actuator Application,” Int. J. Mater. Prod. Technol., 50(3/4), pp. 244–258. [CrossRef]
Rusinski, E. , Moczko, P. , Odyjas, P. , and Pietrusiak, D. , 2013, “ Investigations of Structural Vibrations Problems of High Performance Machines,” FME Trans., 41(4), pp. 305–310.
Rusinski, E. , Moczko, P. , and Pietrusiak, D. , 2014, “ Low Frequency Vibrations of the Surface Mining Machines Caused by Operational Loads and Its Impact on Durability,” International Conference on Noise and Vibration Engineering (ISMA2014) and International Conference on Uncertainty in Structural Dynamics (USD2014), Leuven, Belgium, pp. 683–694.
Uhl, T. , and Mendrok, K. , 2005, The Use of Identification to Determine the Forces on Mechanical Structures, Publisher Institute for Sustainable Technologies—National Research Institute, Radom, Poland (in Polish).
Warminski, J. , 2015, “ Frequency Locking in a Nonlinear MEMS Oscillator Driven by Harmonic Force and Time Delay,” Int. J. Dyn. Control, 3(2), pp. 122–136. [CrossRef]
Zolkiewski, S. , 2013, “ Diagnostics and Transversal Vibrations Control of Rotating Beam by Means of Campbell Diagrams,” Key Eng. Mater., 588, pp. 91–100. [CrossRef]
Louca, L. S. , Stein, J. L. , and Hulbert, G. M. , 2010, “ Energy-Based Model Reduction Methodology for Automated Modeling,” ASME J. Dyn. Syst., Meas., Control, 132(6), p. 061202. [CrossRef]
Zhang, Q. , and Bodony, D. J. , 2016, “ Numerical Investigation of a Honeycomb Liner Grazed by Laminar and Turbulent Boundary Layers,” J. Fluid Mech., 792, pp. 936–980. [CrossRef]
Bocian, M. , Jamroziak, K. , and Kulisiewicz, M. , 2014, “ An Identification of Nonlinear Dissipative Properties of Constructional Materials at Dynamical Impact Loads conditions,” Meccanica, 49(8), pp. 1955–1965. [CrossRef]
Bocian, M. , Jamroziak, K. , and Kulisiewicz, M. , 2014, “ An Identification of the Mechanical Properties of the Systems Subjected to the Shock Loads Using the Non-Linear Dynamic Models,” Eighth European Nonlinear Dynamics Conference (ENOC 2014), Institute of Mechanics and Mechatronics, Vienna University of Technology, Vienna, Austria, Pleminary USB-Stick Version Final CD-ROM Volume, Paper No. 172.
Bocian, M. , Jamroziak, K. , and Kulisiewicz, M. , 2009, “ Determination of the Chain-Like Non-Linear Multi-Degree-of-Freedom Systems Constant Parameters Under Dynamical Complex Loads,” Proc. Appl. Math. Mech., 9(1), pp. 397–398. [CrossRef]
Jamroziak, K. , and Bocian, M. , 2014, “ Analysis of Non-Classical Models Which Have Been Subjected to Percussive Loads Using Equations of Energy and Power,” Adv. Mater. Res., 1036, pp. 608–613. [CrossRef]
Lenci, S. , 2004, “ Elastic and Damage Longitudinal Shear Behaviour of Highly Concentrated Long Fibre Composites,” Meccanica, 39(5), pp. 415–439. [CrossRef]
Kulisiewicz, M., Bocian, M., and Jamroziak, K. 2008, “ Criteria of Material Selection for Ballistic Shields in the Context of Chosen Degenerated Models,” J. Achiev. Mater. Manuf. Eng., 31(2), pp. 505–509.
Jamroziak, K. , 2015, “ Parametric Identification of the Degenerate Model With a Dissipative-Elastic Element Dispersing Impact Energy,” Solid State Phenom., 220–221, pp. 213–217. [CrossRef]
Jamroziak, K. , Bocian, M. , and Kulisiewicz, M. , 2013, “ Energy Consumption in Mechanical Systems Using a Certain Nonlinear Degenerate Model,” J. Theor. Appl. Mech., 51(4), pp. 827–835.
Kulisiewicz, M. , 1987, “ Experimental Technique of Testing the Parallel Spring-Damper Configuration of the Dynamic Mechanical Systems With a Single Degrees-of-Freedom,” Modell., Simul. Control B, 11(1), pp. 15–28.
Kulisiewicz, M. , and Piesiak, S. , 2002, “ Identification of Dynamical Systems With Degenerated Elements Under Complex Nonharmonic Loading,” Mech. Mech. Eng., 6(3), pp. 163–172.
Cunniff, P. M. , 1992, “ An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact,” Text. Res. J., 62(9), pp. 495–509. [CrossRef]
Ben-Dor, G. , Dubinsky, A. , and Elperin, T. , 2006, Applied High-Speed Plate Penetration Dynamics, Springer, Dordrecht, The Netherlands.
Chen, X. , ed., 2016, Advanced Fibrous Composite Materials for Ballistic Protection, Woodhead Publishing, Elsevier, Amsterdam, The Netherlands.
Liu, G. R. , Tan, V. B. C. , and Han, X. , eds., 2006, Computational Methods, Springer, Dordrecht, The Netherlands.
Dwivedi, A. K. , Dalzell, M. W. , Fossey, S. A. , Slusarski, K. A. , Long, L. R. , and Wetzel, E. D. , 2016, “ Low Velocity Ballistic Behavior of Continuous Filament Knit Aramid,” Int. J. Impact Eng., 96, pp. 23–34. [CrossRef]
Sun, C. T. , and Potti, S. V. , 1996, “ A Simple Model to Predict Residual Velocities of Thick Composite Laminates Subjected to High Velocity Impact,” Int. J. Impact Eng., 18(3), pp. 339–353. [CrossRef]
Mazurkiewicz, L. , Malachowski, J. , and Baranowski, P. , 2015, “ Optimization of Protective Panel for Critical Supporting Elements,” Compos. Struct., 134, pp. 493–505. [CrossRef]
Kulisiewicz, M. , Piesiak, S. , and Bocian, M. , 2001, “ Identification of Nonlinear Damping Using Energy Balance Method With Random Pulse Excitation,” J. Vib. Control, 7(5), pp. 699–710. [CrossRef]
Bocian, M. , and Kulisiewicz, M. , 2014, “ Method of Identifying Nonlinear Characteristic of Energy Dissipation in Dynamic Systems With One Degrees-of-Freedom,” Arch. Civ. Mech. Eng., 14(3), pp. 354–359. [CrossRef]
Bocian, M. , Jamroziak, K. , and Kulisiewicz, M. , 2014, “ The Identification of Nonlinear Damping of the Selected Components of MDOF Complex Vibratory Systems,” Ninth International Conference on Structural Dynamics (EURODYN 2014), A. Cunha , E. Caetano, P. Ribeiro, G. Müller eds., Porto, Portugal, pp. 3365–3372.
Shim, V. P. W. , Tan, V. B. C. , and Tay, T. E. , 1995, “ Modelling Deformation and Damage Characteristics of Woven Fabric Under Small Projectile Impact,” Int. J. Impact Eng., 16(4), pp. 585–605. [CrossRef]
Iwan, W. D. , 1967, “ On a Class of Models for the Yielding Behavior of Continuous and Composite Systems,” ASME J. Appl. Mech., 34(3), pp. 612–617. [CrossRef]
Beliveau, J. G. , 1976, “ Identification of Viscous Damping in Structures From Modal Information,” ASME J. Appl. Mech., 43(2), pp. 335–339. [CrossRef]
Abrate, S. , 2005, Impact on Composite Structures, Cambridge University Press, Cambridge, UK.
Silberschmidt, V. V. , ed., 2016, Dynamic Deformation, Damage and Fracture in Composite Materials and Structures, Woodhead Publishing, Elsevier, Amsterdam, The Netherlands.
Abrate, S. , Ferrero, J. F. , and Navarro, P. , 2015, “ Cohesive Zone Models and Impact Damage Predictions for Composite Structures,” Meccanica, 50(10), pp. 2587–2620. [CrossRef]
Baranowski, P. , Malachowski, J. , Niezgoda, T. , and Mazurkewicz, L. , 2015, “ Dynamic Behaviour of Various Fibre Systems During Impact Interaction – Numerical Approach,” Fibres Text. East. Eur., 6(114), pp. 72–81. [CrossRef]
Wang, C. L. , Su, Z. B. , and Martino, F. , 1986, “ Bipolaron Dynamics in Nearly Degenerate Quasi-One-Dimensional Polymers,” Phys. Rev. B, 33(2), pp. 1512–1515. [CrossRef]
Coppolino, R. N. , 2015, “ Structural Dynamics Modeling: Tales of Sin and Redemption,” Special Topics in Structural Dynamics, Volume 6 (Conference Proceedings of the Society for Experimental Mechanics Series (CPSEMS)), Springer International Publishing, Springer-Verlag, New York, pp. 63–73.
Jamroziak, K. , Bocian, M. , and Kulisiewicz, M. , 2016, “ Identification of a Subsystem Located in the Complex Dynamical Systems Subjected to Random Loads,” ASME J. Comput. Nonlinear Dyn., 12(1), p. 014501. [CrossRef]
Kulisiewicz, M. , 2005, Modeling and Identification of Nonlinear Mechanical Systems Under Dynamic Complex Loads, Publishing House of Wroclaw University of Technology, Wroclaw, Poland.
Hayashi, C. , 1964, Nonlinear Oscillations in Physical Systems, McGraw-Hill, New York.


Grahic Jump Location
Fig. 1

The diagram of (a) the real system and (b) the model

Grahic Jump Location
Fig. 2

The diagram of the method applied to force harmonic oscillations of system (4)

Grahic Jump Location
Fig. 3

The concept of the extortion of harmonic oscillations

Grahic Jump Location
Fig. 4

The main idea of the presented identification method

Grahic Jump Location
Fig. 5

An example of the displacement from the place of the experiment for q(x) = c3x3: (a) the extortion of harmonic oscillations, (b) before the introduction of the corrective feedback, and (c) when the system is stabilized

Grahic Jump Location
Fig. 6

Examples of loops for intermittent vibrations of the system calculated with the use of the energy balance equation: (a), (d), (g), and (j) before the introduction of the corrective feedback; (b), (e), (h), and (k) during stabilizing the system when the correction of the control system is switched on; and (c), (f), (i), and (l) the system is stabilized after introducing the correction to control the system of excitation p(t)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In