Diseño e implementación de un software para el análisis de vibraciones mecánicas mediante los métodos energéticos de RAYLEIGH-RITZ y MEF híbrido

Abstract

This Tesis deals with the implementation of the Rayleigh-Ritz method through a code developed in Matlab, solving practical examples as the deflection of a beam, and torsional vibration of bars and vibration of plates. Providing these codes in the Annexes to that future work can be changed and can be used by users interested in the area. In Chapter 1, "Analysis of mechanical vibrations" different concepts of importance for the study of mechanical vibrations and their evolution in the time where the vibration phenomenon is beginning to seek an explanation and to modern times cited, where the analysis by means of computers has facilitated the solution to more complex problems. In Chapter 2 "linear mechanical vibrations" the theoretical basis for the study of vibrations from the simplistic concept such as mass-spring model to the analysis of membranes where complexity increases without passing unnoticed concepts more developed cited literature and studies such as vibration analysis of frames, beams and bars. The structural analysis that is discussed in Chapter 3 are of great importance since many current studies have been developed either civil structures (buildings, bridges etc.) and mechanical (machinery, automotive, aerospace, etc. ) in this chapter the theoretical basis for the structures cited, applying the theory of Rayleigh-Ritz. The finite element method has been a mainstay in the development of engineering in modern times and why vibration analysis by this method is mentioned in Chapter 4 where the analysis of beams, shafts, frames, along with studying the deduction of the variational formulation of hyperbolic problems. Finally in Chapter 5 the results and conclusions of the implementation problems are obtained and some observations are made for future work can resume the issue.