Iterative method for frequency updating of simple vibrating system

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.