Iterative method for frequency updating of simple vibrating system

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Iterative method for frequency updating of simple vibrating system
M. R. Tabeshpour
Center of Excellence in Hydrodynamics and Dynamics of Marine Vehicles
Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran
E-mail: tabeshpour@sharif.edu
(Received 29 May 2012; accepted 4 September 2012)
Abstract. Iterative methods for modification of vibratory characteristics of dynamic systems
have attracted a lot of attention as a convenient and more economical way when compared to
the traditional and costly structural dynamic optimization processes. Many complicated
structures, such as telecommunication towers, chimneys and tall buildings, may be modeled as
simple spring-mass systems. This paper presents an iterative method for modification of the
frequencies of simple vibrating system consisting of springs and masses. The proposed
algorithm may be used to adjust any of the vibration frequencies of a simple vibrating system to
the target values within the desired level of accuracy. The method based on the variation of
mass and/or stiffness properties of the system is simple yet efficient and needs less
computational effort. The efficiency of the method is demonstrated using a numerical example.
It is demonstrated that there is a faster convergence for adjustment of the lower frequencies and
for the case with stiffness variation of the system rather than mass variation.
Keywords: iterative, frequency updating, simple, vibrating system.

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