A semi-analytical method is presented to calculate the dynamic responses of a rectangular plate due to a moving oscillator. In previous analytical solutions of the moving oscillator problem, the elastic distributed structure has usually been modeled by an elastic beam structure. This restrictive assumption is removed in this study by assuming a general plate as two-dimensional elastic distributed structure. The method can be applied for any arbitrary path on the plate. A combination of the Fourier and Laplace transformation as well as the convolution theorem is used to solve the governing differential equations of the problem. A modified integration technique is then presented to solve the coupled governing differential equations of motion. An adaptive finite element model of the system has been developed. In order to avoid the inaccurate results of the off-nodal position of the moving object, an adaptive mesh strategy is developed, thus the finite element mesh is ceaselessly adapted to follow the moving object trajectory. Illustrative examples are then shown for three different paths. Comparisons between the simulation results of the presented semi-analytical method, for specific cases, with the results of the adaptive mesh finite element method and also with the available results in the literature demonstrate the validity of the methodology.
Abstract. In the present work, the spray characteristics of bio-ethanol and its blends have been experimentally and theoretically investigated. To have a comprehensive study, the e ects of ambient condition and injection pressure on the spray of di erent blends have been considered. Macroscopic and microscopic characteristics of spray such as tip penetration length, cone angle, projected area, volume, Sauter Mean Diameter (SMD), and Ohnesorge number are investigated precisely. Besides, air entrainment and atomization analyses have been carried out to improve mixture formation process. Using curve tting and least squares method, theoretical correlations have been suggested in such a way to predict experimental results with the accuracy of 9.9%. To have a good estimation of the calculated parameters, uncertainty analysis has been performed. The results demonstrate that enhancing the injection pressure or decreasing the ambient pressure improves the atomization characteristics of spray. Moreover, outcomes of this study indicate that spray tip penetration is enhanced by increasing the injection pressure or bio-ethanol percentage in the blend, while spray cone angle showing the opposite behavior.
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