VALIDACION NUMÉRICA DEL AMORTIGUAMIENTO CRÍTICO PARA EL TERCER MODO DE VIBRACIÓN

Abstract

In this work, consists of two parts. One is the development and study of a modeling through the application of the theory for Euler-Bernoulli beam. And the other the simulation part of the crack is proposed by a pair of equations governing movement in the vertical and horizontal variation of stiffness in both axes. For the first part proposes the use of two beam elements, and to obtain solution of the model consists of two elements are introduced into the boundary conditions simulation of a disk in the center of both elements, which involve the effects caused by the rotational inertia, once the system is solved in solution which consists of the temporary system natural frequency and eigenvectors, we can obtain the mode shapes depending on the mass of the disk. The second part is the solution of a system of coupled equations, in which introduced as mentioned above, the phenomenon of breathing is defined by Mayes and Davies function, which is a smooth function of the “breathing cracked”. And which causes us a change in the rigidity of the system and therefore the system becomes unstable in other hand, there is a range where the system is unstable near the natural frequencies, this is due to the effect of the crack and for our model the damping is "zero" this is because the damping effect is very strong and causes us not to return unstable system. At the end of this work will areas of stability and instability and the effect damping in the system.