Application of -Transform Method for Dynamic Analysis of Periodic Shear Structures
Publication: Journal of Engineering Mechanics
Volume 140, Issue 5
Abstract
The governing dynamic equilibrium equation of -story periodic shear structure with arbitrary top-story mass, arbitrary base-story stiffness, and that is subjected to base excitation is given in the form of a constant coefficient second-order finite-difference equation. The first integration of the governing difference equation for the eigenanalysis results in the Volterra difference equation of convolution type and yields the first boundary condition. The -transform method is applied to the equation to obtain the general solution for displacement mode shapes. Applying the second boundary condition to the general solution results in the characteristic equation in which the frequencies are obtained by solving it. The general form of the characteristic equation for eigenfrequencies is presented, and analytical solutions for some special cases are derived. Displacement and drift mode shape functions are obtained. All the modal parameters, including modal mass, excitation factor, participation factor, and effective modal mass, are derived using the sum and the sum of the square modal displacements and are presented as closed-form solutions.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abramowitz, M., and Stegun, I. A. (1970). Handbook of mathematical functions, U.S. Dept. of Commerce, National Bureau of Standards, Washington, DC.
Biggs, J. M. (1964). Introduction to structural dynamics, McGraw Hill, New York.
Elaydi, S. (2005). An introduction to difference equations, 3rd Ed., Springer, New York.
FEMA. (2004). NEHRP recommended provisions, Building Seismic Safety Council, National Institute of Building Sciences, Washington, DC.
Grigorian, M. (1993). “On the dynamic analysis of regular shear structures.” Earthq. Spectra, 9(1), 55–66.
Jennings, P. C. (1997). “Earthquake response of tall regular buildings.” Rep. No. EERL 97-01, California Institute of Technology, Earthquake Engineering Research Laboratory, Pasadena, CA.
Jennings, P. C. (2003). “An introduction to the earthquake response of structures.” International handbook of earthquake and engineering seismology—Part B, W. H. K. Lee, H. Kanamori, P. C. Jennings, and C. Kisslinger, Academic Press, Burlington, MA, 1097–1125.
Lin, Y. K. (1976). Probabilistic theory of structural dynamics, Robert E. Krieger, Malabar, FL.
Maple R14 [Computer software]. Waterloo, ON, Canada, Maplesoft.
Meirovitch, L., and Engels, R. C. (1977). “Response of periodic structures by the -transform method.” AIAA J., 15(2), 167–174.
Stephen, N. G. (1999). “On the vibration of one-dimensional periodic structures.” J. Sound Vib., 227(5), 1133–1142.
Thompson, T. T. (1993). Theory of vibration with applications, Prentice Hall, Englewood Cliffs, NJ.
Timoshenko, S. (1971). Theory of structures, McGraw Hill, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 5 • May 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 25, 2012
Accepted: Sep 9, 2013
Published online: Sep 11, 2013
Published in print: May 1, 2014
Discussion open until: Jun 16, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.