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Structural Engineering and Mechanics   Volume 25, Number 6, April20 2007, pages 717-732
DOI: https://doi.org/10.12989/sem.2007.25.6.717
 
An approximate formula to calculate the fundamental period of a fixed-free mass-spring system with varying mass and stiffness
Juwhan Kim, Kevin R. Collins and Yun Mook Lim

 
Abstract     [Buy Article]
    A formula to approximate the fundamental period of a fixed-free mass-spring varying mass and varying stiffness is formulated. The formula is derived mainly by taking parts from the general form of the characteristic polynomial, and adjusting the initial approximation coefficient derived from the exact solution of a uniform case. The formula is tested for a large randomly generated structures, and the results show that the approximated fundamental periods the error range of 4% with 90% of confidence. Also, the error is shown to be normally distributed zero mean, and the width of the distribution (as measured by the standard deviation) tends the total number of discretized elements in the system increases. Other possible extensions are discussed, including an extension to a continuous cantilever structure with distributed stiffness. The suggested formula provides an efficient way to estimate the fundamental period structures and other systems that can be modeled as mass-spring systems.
 
Key Words
    earthquake engineering; eigenvalue; eigensystem; fundamental period.
 
Address
Juwhan Kim; School of Civil & Environmental Engineering, College of Engineering, Yonsei University, Seoul 120-749, Korea
Kevin R. Collins; 5 Greystone Court Ledyard, CT 06339, USA
Yun Mook Lim; School of Civil & Environmental Engineering, College of Engineering, Yonsei University, Seoul 120-749, Korea
 

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