An Efficient Approximation for Optimal Damping in Mechanical Systems

This paper is concerned with an efficient algorithm for damping optimization in mechanical systems with a prescribed structure. Our approach is based on the minimization of the total energy of the system which is equivalent to the minimization of the trace of the corresponding Lyapunov equation. Thus, the prescribed structure in our case means that a mechanical system is close to a modally damped system. Although our approach is very efficient (as expected) for mechanical systems close to modally damped system, our experiments show that for some cases when systems are not modally damped, the proposed approach provides efficient approximation of optimal damping.

[1]  Peter Benner,et al.  Semi‐active damping optimization of vibrational systems using the parametric dominant pole algorithm , 2016 .

[2]  Ninoslav Truhar,et al.  On some properties of the Lyapunov equation for damped systems , 2004 .

[3]  K. Veselic,et al.  Passive Control of Linear Systems , 2011 .

[4]  Ninoslav Truhar,et al.  An Efficient Method for Estimating the Optimal Dampers' Viscosity for Linear Vibrating Systems Using Lyapunov Equation , 2009, SIAM J. Matrix Anal. Appl..

[5]  Ninoslav Truhar,et al.  Damping optimization over the arbitrary time of the excited mechanical system , 2016, J. Comput. Appl. Math..

[6]  Peter Benner,et al.  Dimension reduction for damping optimization in linear vibrating systems , 2011 .

[7]  Mark H. Milman,et al.  Optimization methods for passive damper placement and tuning , 1992 .

[8]  Peter Benner,et al.  Optimal damping of selected eigenfrequencies using dimension reduction , 2013, Numer. Linear Algebra Appl..

[9]  William H. Paulsen,et al.  Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix , 2015 .

[10]  Pierre E. Dupont,et al.  CONSTRAINED OPTIMAL CONTROL OF VIBRATION DAMPERS , 1998 .

[11]  Ninoslav Truhar,et al.  Damping optimization in mechanical systems with external force , 2015, Appl. Math. Comput..

[12]  Ninoslav Truhar,et al.  An efficient algorithm for damper optimization for linear vibrating systems using Lyapunov equation , 2004 .

[13]  Ninoslav Truhar,et al.  Bounds on the trace of a solution to the Lyapunov equation with a general stable matrix , 2007, Syst. Control. Lett..

[14]  K. Veselic On linear vibrational systems with one dimensional damping II , 1990 .