Computation of Rayleigh Damping Coefficients for Large Systems

 

Indrajit Chowdhury

Chief Discipline Supervisor, Civil & Structural Engineering,
Petrofac International Limited, Sharjah, U.A.E.

and

Shambhu P. Dasgupta

Professor, Department of Civil Engineering,
Indian Institute of Technology, Kharagpur, India
e-mail: dasgupta@civil.iitkgp.ernet.in

 

TECHNICAL NOTE

For systems with large degrees of freedom, it is difficult to guess meaningful values of Rayleigh damping coefficients a and b at the start of an analysis of systems with multi-degree of freedom. A number of general-purpose commercially available software have the provision of providing the value of a and b for calculation of Rayleigh damping matrix for dynamic analysis. Since an engineer may not be in a position to pre-assess the same at the beginning, has no option but to assume an unrealistic constant damping ratio for all modes. Based on the present technique it is very simple to develop a spreadsheet and arrive at a rational value of a and b which develops a damping ratio sequence increasing progressively with each of the subsequent modes and one can furnish input data for the dynamic analysis.

The present paper outlines a procedure, which ensures a rational estimate of a and b even for a system with large degrees of freedom. The results obtained have been checked against different class of real life structure and foundation systems and the results are presented graphically.

Keywords: Dynamics, damping, eigen values, finite element method, natural frequency, soil-foundation system.

 

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