An Application Of The Φ-functions Series
Method To The Integration Of Seismic Modelling
Author(s)
A. Reyes, J. A. Reyes, M. Cortés-Molina, Y. Villacampa
& F. García-Alonso
Abstract
The interest to improve the response of structures in front of an earthquake has
increased in recent years, leading to the investigation of different calculation
methods, especially those based on static non-linear analysis to increase
accuracy. The non-linear calculation can be approached by means of discrete or
continuous models. The discrete models represent the structure by a finite
number of degrees of freedom; in this case the movement equations are ordinary
differential equations which are resolved by numerical methods.
This paper applies a new method for the numerical integration of SDOF and
2DOF, which is developed from the Scheifele methods. The algorithm integrates
the unperturbed problem without truncation error, which represents an advantage
in front of the Taylor series. The new method calculates the exact solution of the
perturbed problem through a series of functions, whose coefficients are obtained
by simple algebraic recurrences involving the perturbation function.
To illustrate the application of the algorithm the resolution of two linear
systems is shown; the first one with a single degree of freedom and the second
with two degrees of freedom.
Keywords: seismic response, SDOF, 2DOF, numerical solutions, perturbed
linear systems of ODEs.
Keywords
seismic response, SDOF, 2DOF, numerical solutions, perturbed
linear systems of ODEs
Related Book
Other papers in this volume
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