Numerical investigation of the seismic response of a polar crane based on linear complementarity formulation

Abstract This paper numerically analyzes the seismic response of a polar crane operating at a nuclear plant, with derailment considered. In this case, the wheels and rails can no longer be treated as being bonded, and thus traditional methods in structural dynamics (e.g. response spectrum method) are no longer suitable for transient contact analysis. On the other hand, contact-impact analysis of flexible multibody systems will often face great difficulties attributed to the complexity of modeling and low computational efficiency. To overcome these problems, the wheel-rail interactions are modeled as multiple frictional unilateral constraints, and the resulting contact-impact problem is formulated as a linear complementarity problem (LCP). Later, a novel smoothing method is applied to smooth the LCP formulation by replacing the normal gap with the time-averaged normal gap over a short time period. A model smoothing method is then combined with modal synthesis to derive the equations of motion without high frequency components. Finally, the validity and feasibility of the proposed method are demonstrated through several numerical examples. The results show the different contact states during the seismic process, including smooth contact, detachment and re-contact.

[1]  Qi Wang,et al.  Modeling and simulation of planar multibody systems with revolute clearance joints considering stiction based on an LCP method , 2018, Mechanism and Machine Theory.

[2]  D. Xiang,et al.  A contact force model considering constant external forces for impact analysis in multibody dynamics , 2018, Multibody System Dynamics.

[3]  H. Nijmeijer,et al.  Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .

[4]  Gang Wang,et al.  Model smoothing method of contact-impact dynamics in flexible multibody systems , 2019, Mechanism and Machine Theory.

[5]  Cyril Feau,et al.  Experimental and numerical investigation of the earthquake response of crane bridges , 2015 .

[6]  Paulo Flores,et al.  Modeling and simulation of wear in revolute clearance joints in multibody systems , 2009 .

[7]  C. Glocker,et al.  Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems , 2012 .

[8]  Christoph Glocker,et al.  Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach , 2010 .

[9]  Hongping Zhu,et al.  A note on the Hertz contact model with nonlinear damping for pounding simulation , 2009 .

[10]  Rahmi Guclu,et al.  Self-tuning fuzzy logic control of a non-linear structural system with ATMD against earthquake , 2009 .

[11]  Mayya Tokman,et al.  Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods , 2006, J. Comput. Phys..

[12]  Jeffrey C. Trinkle,et al.  Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction , 1996, Math. Program..

[13]  Mohammad Mehdi Rashidi,et al.  A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems , 2015 .

[14]  Hamid M. Lankarani,et al.  A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems , 1989 .

[15]  Margarida F. Machado,et al.  On the continuous contact force models for soft materials in multibody dynamics , 2011 .

[16]  C. Glocker,et al.  Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics , 2005 .

[17]  Gang Wang,et al.  An efficient model for dynamic analysis and simulation of cable-pulley systems with time-varying cable lengths , 2017 .

[18]  Björn Engquist,et al.  A multiscale method for highly oscillatory ordinary differential equations with resonance , 2008, Math. Comput..

[19]  G. T. Rooney,et al.  Coulomb friction in mechanism sliding joints , 1982 .

[20]  Paulo Flores,et al.  A parametric study on the dynamic response of planar multibody systems with multiple clearance joints , 2010 .

[21]  Quang Tran,et al.  Effects of Boundary Condition Models on the Seismic Responses of a Container Crane , 2019 .

[22]  John McPhee,et al.  A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction , 2004 .

[24]  Jeffrey C. Trinkle,et al.  An implicit time-stepping scheme for rigid body dynamics with Coulomb friction , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[25]  Jacob Philippus Meijaard,et al.  Application of Runge–Kutta–Rosenbrock Methods to the Analysis of Flexible Multibody Systems , 2003 .

[26]  Ahmet Sagirli,et al.  Mathematical modelling of the container cranes under seismic loading and proving by shake table , 2013 .

[27]  Z. Ibrahim,et al.  Adaptive order of block backward differentiation formulas for stiff ODEs , 2017 .

[28]  Gang Wang,et al.  Hybrid modeling for dynamic analysis of cable-pulley systems with time-varying length cable and its application , 2017 .

[29]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .