Abstract
This paper explores nonlinear dynamic behavior of vibro-impacting tapered cantilever with tip mass with regard to frequency response analysis. A typical frequency response curve of vibro-impacting beams displays well-known resonance frequency shift along with a hysteric jump and drop phenomena. We did a comprehensive parametric analysis capturing the effects of taper, tip-mass, stop location, and gap on the non-smooth frequency response. Analysis is presented in a non-dimensional form useful for other similar cases. Simulation results are further validated with corresponding experimental results for a few cases. Illustrative comparison of simulation results for varying parameters brings out several interesting aspects of variation in the nonlinear behavior.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. J. Fegelman and K. Grosh, Dynamics of a flexible beam contacting a linear spring at low frequency excitation: Experiment and analysis, J. of Vibration and Acoustics, 124 (2002) 237–249.
I. R. P. Krishna and C. Padmanabhan, Experimental and numerical investigations of impacting cantilever beams part 1: first mode response, Nonlinear Dynamics, 67 (2012) 1985–2000.
F. C. Moon and S. W. Shaw, Chaotic vibrations of a beam with non-linear boundary conditions, Int. J. of Non-Linear Mechanics, 18 (6) (1983) 465–477.
S. W. Shaw and P. J. Holmes, A periodically forced piecewise linear oscillator, J. of Sound and Vibration, 90 (1) (1983) 129–155.
S. W. Shaw, Forced vibrations of a beam with one-sided amplitude constraint: Theory and experiment, J. of Sound and Vibration, 99 (2) (1985) 199–212.
A. B. Nordmark, Non-periodic motion caused by grazing incidence in an impact oscillator, J. of Sound and Vibration, 145 (2) (1991) 279–297.
D. Wagg and S. Bishop, Application of non-smooth modeling techniques to the dynamics of a flexible impacting beam, J. of Sound and Vibration, 256 (5) (2002) 803–820.
S. R. Bishop, M. G. Thompson and S. Foale, Prediction of period-1 impacts in a driven beam, Proceedings of Royal Society: Mathematical, Physical and Engineering Sciences, 452 (1954) (1996) 2579–2592.
D. Wagg, G. Karapodinis and S. R. Bishop, An experimental study of the impulse response of a vibro-impacting cantilever beam, J. of Sound and Vibration, 228 (2) (1999) 243–264.
A. Fathi and N. Popplewell, Improved approximations for a beam impacting a stop, J. of Sound and Vibration, 170 (3) (1994) 365–375.
D. J. Wagg, A note on co-efficient of restitution models including the effects of impact induced vibration, J. of Sound and Vibration, 300 (2007) 1071–1078.
P. Gandhi and A. Badkas, On the nonlinear dynamics of a vibro-impacting cantilever with end mass, ASME 2012 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers (2012) 253–261.
H. Abbas, H. Hai, J. Rongong and Y. Xing, Damping performance of metal swarfs in a horizontal hollow structure, J. of Mechanical Science and Technology, 28 (1) (2014) 9–13.
S. Chen, J. Tang and Z. Hu, Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form, J. of Mechanical Science and Technology, 29 (9) (2015) 3563–3569.
L. D. Viet, N. B.Nghi, N. N. Hieu, D. T. Hung, N. N. Linh and L. X. Hung, On a combination of ground-hook controllers for semi-active tuned mass dampers, J. of Mechanical Science and Technology, 28 (6) (2014) 2059–2064.
S. Wang, Y. Wang, Z. Huang and T. X. Yu, Dynamic behavior of elastic bars and beams impinging on ideal springs, J. of Applied Mechanics, 83 (3) (2016) 031002.
X. Long, J. Liu and G. Meng, Nonlinear dynamics of two harmonically excited elastic structures with impact interaction, J. of Sound and Vibration, 333 (5) (2014) 1430–1441.
I. R. P. Krishna and C. Padmanabhan, Experimental and numerical investigation of impacting cantilever beams: Second mode response, International J. of Mechanical Sciences, 92 (2015) 187–193.
M. Elmegard, B. Krauskopf, K. M. Osinga, J. Starke and J. J. Thomsen, Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment, Nonlinear Dynamics, 77 (3) (2014) 951–966.
K. Vijayan, M. I. Friswell, H. H. Khodaparast and S. Adhikari, Non-linear energy harvesting from coupled impacting beams, International J. of Mechanical Sciences, 96 (2015) 101–109.
J. Y. Yoon and B. Kim, Analysis of vibro-impacts in a torsional system under both wide open throttle and coast conditions with focus on the multi-staged clutch damper, J. of Mechanical Science and Technology, 29 (12) (2015) 5167–5181.
S. H. Ho and C. K. Chen, Analysis of general elastically end restrained nonuniform beams using differential transform, Applied Mathematical Modeling, 22 (1998) 1219–234.
A. Mirzabeigy, Semi-analytical approach for free vibration analysis of variable cross-section beams resting on elastic foundation and under axial force, International J. of Engineering, 26 (3) (2014) 385–394.
M. Malik and H. H. Dang, Vibration analysis of continuous systems by differential transformation, Applied Mathematics and Computation, 96 (1998) 17–26.
C. Y. Wang, Vibration of a tapered cantilever of constant thickness and linearly tapered width, Arch. Appl. Mech., 83 (2013) 171–176.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Eung-Soo Shin
P. S. Gandhi received his Ph.D. from Rice University, Houston, TX. He is currently a Professor at Indian Institute of Technology-Bombay, Mumbai, India. His research interests are in nonlinear dynamics and control, MEMS fabrication, robotics and mechatronics.
Vishal Vyas is a Ph.D. student in the Mechanical Engineering Department, Indian Institute of Technology-Bombay, Mumbai, India. His research interests are in nonlinear vibrations of continuous systems and vibration energy harvesting.
Rights and permissions
About this article
Cite this article
Gandhi, P.S., Vyas, V. On the dynamics of tapered vibro-impacting cantilever with tip mass. J Mech Sci Technol 31, 63–73 (2017). https://doi.org/10.1007/s12206-016-1208-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-016-1208-0