An Application Of The Φ-functions Series Method To The Integration Of Seismic Modelling
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A. Reyes, J. A. Reyes, M. Cortés-Molina, Y. Villacampa & F. García-Alonso
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.
seismic response, SDOF, 2DOF, numerical solutions, perturbed linear systems of ODEs