Parameter studies on impact in a lap joint

Abstract

To represent a loose lap joint, a beam impacting four springs with gaps is modeled. Modal analysis with base excitation is solved, and time histories of contact points are closely monitored. Using the impulse during steady state response, six influential parameters are studied: damping ratio, contact stiffness, intermediate contact position, gap, excitation amplitude and beam height. For all parameters, the system response is highly controlled by modes with two contacting springs. Each parameter’s effect on system response is presented including unstable regions, unique trend behaviours result. Recommendations for structural designers are also noted.

Graphical abstract

Keywords

impact mechanics / contact / joint behaviour / modal analysis / parameter study

References

[1] Gilardi G, Sharf I. Literature survey of contact dynamics modelling. Mechanism and Machine Theory, 2002, 37(10): 1213–1239

[2] Davies H G. Random vibration of a beam impacting stops. Journal of Sound and Vibration, 1980, 68(4): 479–487

[3] Pun D, Lau S L, Liu Y B. Internal resonance of an L-shaped beam with a limit stop: Part I, Free vibration. Journal of Sound and Vibration, 1996, 193(5): 1023–1035

[4] Pun D, Lau S L, Liu Y B. Internal resonance of an L-shaped beam with a limit stop: Part II, Forced vibration. Journal of Sound and Vibration, 1996, 193(5): 1037–1047

[5] Metallidis P, Natsiavas S. Vibration of a continuous system with clearance and motion constraints. International Journal of Non-linear Mechanics, 2000, 35(4): 675–690

[6] Chattopadhyay S. Dynamics of vibrating beams impacting around a clearance gap. In: Proceedings of IMAC-XIX: A Conference on Structural Dynamics. Kissimmee, 2001

[7] Dumont Y, Kuttler K L, Shillor M. Analysis and simulations of vibrations of a beam with a slider. Journal of Engineering Mathematics, 2003, 47(1): 61–82

[8] Ervin E K, Wickert J A. Repetitive impact response of a beam structure subjected to harmonic base excitation. Journal of Sound and Vibration, 2007, 307(1–2): 2–19

[9] Ervin E K. Vibro-impact behavior of two orthogonal beams. Journal of Engineering Mechanics, 2009, 135(6): 529–537

[10] Moorthy R I K, Kakodkar A, Srirangarajan H R, Finite element simulation of chaotic vibrations of a beam with non-linear boundary conditions. Computers & Structures, 1993, 49(4): 589–596

[11] van de Vorst E L B, Heertjes M F, van Campen D H, Experimental and numerical analysis of the steady state behaviour of a beam system with impact. Journal of Sound and Vibration, 1998, 212(2): 321–336

[12] Wagg D J, Bishop S R. Application of non-smooth modelling techniques to the dynamic of a flexible impacting beam. Journal of Sound and Vibration, 2002, 256(5): 803–820

[13] Vyasarayani C P, Sandhu S S, McPhee J. Nonsmooth modeling of vibro-impacting Euler-Bernoulli beam. Advances in Acoustics and Vibration, 2012, 2012: 1–9

[14] Mackerle J. Finite element analysis of fastening and joining: A bibliography (1990–2002). International Journal of Pressure Vessels and Piping, 2003, 80(4): 253–271

[15] Kim J, Yoon J C, Kang B S. Finite element analysis and modeling of structure with bolted joints. Applied Mathematical Modelling, 2007, 31(5): 895–911

[16] Salih E L, Gardner L, Nethercot D A. Numerical study of stainless steel gusset plate connections. Engineering Structures, 2013, 49(0): 448–464

[17] Zang M, Gao W, Lei Z. A contact algorithm for 3d discrete and finite element contact problems based on penalty function method. Computational Mechanics, 2011, 48(5): 541–550

[18] Yang T, Fan S H, Lin C S. Joint stiffness identification using FRF measurements. Computers & Structures, 2003, 81(28–29): 2549–2556

[19] Barhorst A A. Modeling loose joints in elastic structures-variable structure motion model development. Journal of Vibration and Control, 2008, 14(11): 1767–1797

[20] Barhorst A A. Modeling loose joints in elastic structures simulation algorithm and results. Journal of Vibration and Control, 2009, 15(1): 3–24

[21] Jalali H, Ahmadian H, Mottershead J E. Identification of nonlinear bolted lap-joint parameters by force-state mapping. International Journal of Solids and Structures, 2007, 44(25–26): 8087–8105

[22] Ahmadian H, Jalali H. Identification of bolted lap joints parameters in assembled structures. Mechanical Systems and Signal Processing, 2007, 21(2): 1041–1050

[23] Iranzad M, Ahmadian H. Identification of nonlinear bolted lap joint models. Computers & Structures, 2012, 96–97: 1–8

[24] Barhorst A A. Modeling loose joints in elastic structures momentum transfer model development. Journal of Vibration and Control, 2008, 14(12): 1803–1841

[25] Foster J T, Barhorst A A, Wong C N S, et al. Modeling loose joints in elastic structures experimental results and validation. Journal of Vibration and Control, 2009, 15(4): 549–565

[26] Rahmani A M, Ervin E K. Frequency response of an impacting lap joint. Journal of Nonlinear Dynamics, 2014, 2014: 1–10

[27] HIS, Inc. Engineering Sciences Data Unit, IHS ESDU 91001: Structural parameters used in response calculations. Estimation of numerical values. 2012

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg