This paper proposes a semi-analytical solution via the differential quadrature method (DQM) for stability analysis of linear multi-degree-of-freedom second-order systems with multiple delays. The vibration systems are reformulated as a delayed differential equation (DDE) in state–space form. With the derivative of the state vector with respect to time at an arbitrary discrete-time point being expressed as a linear weighted sum of the values of the state vector, the original DDE is approximated by a set of algebraic equations, leading to the Floquet transition matrix. Based on Floquet theory, the stability of the systems is then determined by checking the eigenvalues of the transition matrix. The computational accuracy and efficiency are demonstrated through comparison with existing methods via numerical examples. As an application, the proposed method is employed to predict chatter stability in simultaneous machining operations, providing a reference for the choice of machining parameters.
Differential Quadrature Method for Stability Analysis of Dynamic Systems With Multiple Delays: Application to Simultaneous Machining Operations
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 19, 2014; final manuscript received October 11, 2014; published online November 14, 2014. Assoc. Editor: Philip Bayly.
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Ding, Y., Niu, J., Zhu, L., and Ding, H. (April 1, 2015). "Differential Quadrature Method for Stability Analysis of Dynamic Systems With Multiple Delays: Application to Simultaneous Machining Operations." ASME. J. Vib. Acoust. April 2015; 137(2): 024501. https://doi.org/10.1115/1.4028832
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