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In this paper, vortex induced vibration of simply supported viscoelastic beam were investigated using semi-analytical method. By applying the general form of the viscoelastic model, the nonlinear partial differential equations of motion based on the Euler Bernoulli beam’s theory and displacement coupling fluid-structure interaction model were obtained via the Newton’s second law. A classical nonlinear van der Pol equation was taken as the governing equation for one component of the vortex shedding force on the beam. Employing the Galerkin discretization method, the equations of motion are reduced to a set of nonlinear ordinary differential equations with coupled terms and then there have been solved numerically by Runge-Kutta method. Finally, the effect of system parameters on the time response, phase plane and maximum amplitude of the beam are investigated. The results indicate that the viscoelastic behavior have a significant influence on the dynamic characteristics of the system and causes to change the Lock-in phenomenon with respect to corresponding elastic system. For example, for E2=10E1 the viscoelastic behavior can change the position of the locking area, and the maximum amplitude of the beam is increased by 45%. Lock-in from of vortex-induced vibrations was considered as a possible source of increased fatigue and damage. Therefore, by using viscoelastic materials the maximum amplitude of the system is reduced and the Lock-in condition can be changed. Additionally, based on the significant influence of viscoelastic behavior on the dynamic characteristics of the system, viscoelastic behavior should be considered in the mathematical model of the systems.

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Evaluation of pressure oscillation of solid rocket motors in actual conditions requires static tests. These test have a large application in evaluation of motor various parameters effect on its operation. Using of these tests are very limited due to their high costs and so, evaluation of various parameters is nearly impossible. To solve this problem, sub scaled solid rocket motor must be designed. In this paper, designing process of space shuttle sub scaled solid boosters, called 1881, with scale 1:31 has been proposed. Space shuttle and ariane 5 boosters have been argued to modeling and simulation. Sub scaled motor modeling and design parameters using Buckingham’s Pi theorem and then, operation and dimensional properties have been presented. Three tests for evaluation of designed motor were done successfully and pressure and thrust history and its oscillations have been evaluated. Results show that for facility of fitting and reduction of test cost in subscale motors, using of Tan-Cu in throat instead of graphite and flange design of joints are very useful. Despite of using Buckingham’s Pi theorem in solid motor scaling, propellant chemistry and its burning rate are affected of Crawford bomb and real flow of combustion products and in many case, error correction between Crawford and motor data is inevitable. On the other hand, existence of empty volume in forward segments and others, plays an important role in pressure oscillations and after end of burning or reducing, oscillations will be uniform.

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This study aims to evaluate the effect of gender identity on loyalty emphasizing on personal identity, consumption patterns, and Purchase decision making styles. This study is considered an applied research, and according to the method of gathering data is considered to be descriptive-survey research. The data of this research was gathered from a sample of 492 participants who were users of home appliances in city of Tehran through simple cluster sampling method. Questionnaires were used as data gathering tool. The data were analyzed by structural equation modeling via Lisrel software. The findings indicate that gender identity affects brand loyalty, personal identity, purchase decision making styles, and consumption patterns. Also, loyalty is affected by personal identity, purchase decision making styles, and consumption patterns. Finally, personal identity and consumption patterns affect purchase decision making styles.