M. K. Beirami and M. Ilaghi Hoseiny,
Volume 24, Issue 1 (7-2005)
Abstract
Forced hydraulic jump in a horizontal stilling basin with one and two continuous sills at the downstream end of an ogee standard weir was investigated. Experiments were completed on sills of five different heights which were fixed at two different distances from the toe of the weir. The main characteristics of the jump such as the sequent depth ratio, relative roller
length, and relative energy loss were analysed. Based on the momentum equation and using an experimental coefficient, a method was adopted to predict the sequent depth ratio. Using the results of the experiments, an analytical expression was developed for the prediction of the relative roller length. These methods agree well with the writers, and other investigators, experiments. The results of experiments on one and two prolonged sills showed that by increasing the height of the sill or shortering the distance of the sill from the toe of the weir, the reduction of the sequent depth and also the roller length obtains, but the energy loss increases
M. Rezaee, Sh. Amiri Jahed Amiri Jahed,
Volume 36, Issue 1 (9-2017)
Abstract
In the vibration of a cracked structure with small amplitude oscillations, the crack necessarily is not fully open or fully closed. Therefore, in order to provide a realistic model for the crack, one should relate the stiffness and damping at the crack location to the amount of the opening of the crack. In this study, a continuous model for vibration of a beam with a fatigue crack under low amplitude oscillations is presented in which the crack is not fully open or fully closed. By introducing a nonlinear model for the crack, the equation governing the vibration of the cracked beam is extracted. In order to consider the nonlinear behavior of the crack and to take into account the energy loss at the crack during the vibration, the bending moment at the crack location was considered as a nonlinear function of the angle of crack opening and its variations with respect to the time. The governing nonlinear equation is solved using the perturbation method. The solution reveals the dependency of the resonance frequency on the vibration amplitude. Analytical and explicit expressions are also derived for the nonlinear stiffness coefficient and the damping coefficient of the crack at the crack location. Finally, using the derived expressions for the crack parameters and experimental tests results for cracked beam, the nonlinear stiffness coefficient and the damping coefficient at the crack location is obtained.
