# A novel algorithm for solving MDOF systems with clearances

Kranjčević, Nenad and Stegić, Milenko and Vranković, Nikola (2013) A novel algorithm for solving MDOF systems with clearances. = A novel algorithm for solving MDOF systems with clearances. In: The 2013 World Congress on Advances in Structural Engineering and Mechanics (ASEM13), 8-12.09.2013., Jeju, Južna Koreja.

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## Abstract

A novel algorithm for solving MDOF systems with clearances Nenad Kranjcevic 1), Milenko Stegic2) and *Nikola Vrankovic3) 1), 2 ), 3) Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia 3) nvrankov@fsb.hr ABSTRACT The behavior of vibration systems with clearances is essential from the viewpoint of dynamic design, and a noise and vibration control. Clearance type nonlinearities possess non- smooth force–deflection characteristics (usually modeled as piecewise linear) and generally require a special treatment compared with other types of nonlinearities (Babitsky 2001). There is no general analysis method that can be applied to all nonlinear systems in all instances. In this paper, a novel algorithm for calculating steady state responses of multi- degree-of-freedom (MDOF) systems with clearances is presented. The algorithm is a new developed semi-analytical procedure of explicit integration based on piecing together the local linear equations of motion (Kranjcevic 2003). The accuracy of the algorithm does not significant depend on a magnitude of the integration step since the local linear equations of motion are being solved analytically. The time step has to be sufficiently small for a reliable numerical determination of the switching points between linear equations of motion. It is a remarkable advantage with respect to other numerical integration methods The procedure is applied to obtain the frequency response of the three-degree-of-freedom semi-definite system with two clearances under periodic excitations. The numerical results are validated considering standard numerical integration software (MATLAB). Close agreement is found between the frequency responses resulting from both approaches. REFERENCES Babitsky, V. I. and Krupenin, V. L. (2001), Vibrations of Strongly Nonlinear Discontinuous Systems, Springer, Berlin. Kranjcevic, N., Stegic, M. and Vrankovic, N. (2003), “The piecewise full decoupling method for dynamic problems”. Proc. App. Math. Mech., PAMM, Vol. 3(1), 112-113.

Item Type: Conference or Workshop Item (Lecture) MDOF piecewise linear system, clearance, numerical integration TECHNICAL SCIENCE > Mechanical Engineering 100 Department of Design > 120 Chair of Machine Elements200 Department of Engineering Mechanics > 230 Chair of Mechanical Systems Dynamics No No 18 Mar 2016 10:27 24 Mar 2016 11:10 http://repozitorij.fsb.hr/id/eprint/5262