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Modeling dynamic behavior of MDOF systems with multiple bilinear springs

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Abstract

A computational scheme is presented in this paper to simulate dynamical behavior of multiple degrees of freedom (MDOF) systems with multiple bilinear springs. In the proposed scheme, a bilinear spring is modeled using by two parallel springs - a primary spring and a secondary spring. The primary spring is an ordinary linear spring having identical stiffness in tension and compression, and is active for tension and compression. The secondary spring, whose stiffness characterizes the bilinearity, is active only during compression. It is employed in connection with the Newmark integration method and the linear complementarity problem (LCP) formulation to obtain time-domain responses of dynamical systems with bilinear springs due to initial disturbances and harmonic excitations. The scheme described in this paper is effective in dealing with the sudden transition from tension to compression and vice versa simultaneously for all bilinear springs. Numerical results for bilinear oscillators with finite bilinearity ratios and impact oscillators with an infinite bilinearity ratio show that the proposed bilinear spring model is accurate, generic and valid for bilinearity ratios ranging from zero to infinity. Orderly and chaotic behavior of viscously damped 3-DOF system under harmonic excitation is studied for a wide range of excitation frequencies and bilinear ratios to demonstrate the effectiveness and applicability of the proposed model for MDOF bilinear systems.

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Yali Ma, Shudong Yu & Delun Wang

  2. Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, M5B 2K3, Canada

    Shudong Yu

Authors
  1. Yali Ma
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  2. Shudong Yu
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  3. Delun Wang
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Corresponding author

Correspondence to Yali Ma.

Additional information

Recommended by Associate Editor Jin Woo Lee

Yali Ma obtained her Bachelor’s degree, Master’s degree and Ph.D. in Mechanical Engineering from Dalian University of Technology. She is a Professor of Mechanical Engineering at Dalian University of Technology, a member of China Mechanical Design Institute Committee. She was a visiting researcher at the Department of informatics at King's College London, UK in 2006. Her research interests include behaviors analysis and modeling, digital design, optimization design and innovation design of mechanical systems.

Shudong Yu obtained his Bachelor’s degree in Mechanical Engineering from Jiangxi University of Technology in 1982, Master’s degree in Mechanics from Northeastern University in 1984, Ph.D. in Mechanical Engineering from the University of Toronto in 1995. He is a Professor of Mechanical Engineering at Ryerson University, Toronto, Canada. His research interests include nuclear fuel design and modeling, non-linear vibration, friction, contact, multi-body dynamics, and flow-induced vibration.

Delun Wang obtained his Bachelor’s degree from Jiangxi University of Technology in 1982, Master’s degree and Ph.D. in Mechanical Engineering from Dalian University of Technology. He is a Professor of Mechanical Engineering at Dalian University of Technology, a Co-chair of Consultancy Committee of Teaching for Basic Program of Mechanical Engineering, Ministry of Education of China, a Chair of Teaching and Researching Committee of Theory of Mechanisms and Machine of China. He was an Associate Editor of Journal of Mechanisms and Robotics, ASME, 2009–2013. His research interests include kinematic geometry of mechanisms, methodology of machine design, accuracy design of machinery.

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Ma, Y., Yu, S. & Wang, D. Modeling dynamic behavior of MDOF systems with multiple bilinear springs. J Mech Sci Technol 32, 4057–4069 (2018). https://doi.org/10.1007/s12206-018-0805-5

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  • DOI: https://doi.org/10.1007/s12206-018-0805-5

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