Browsing by Author "PAKDEMIRLI, M"

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    NONLINEAR VIBRATIONS OF A BEAM-SPRING-MASS SYSTEM
    PAKDEMIRLI, M; NAYFEH, AH
    The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system.
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    SIMILARITY ANALYSIS OF BOUNDARY-LAYER EQUATIONS OF A CLASS OF NON-NEWTONIAN FLUIDS
    PAKDEMIRLI, M
    A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluids in which the stress is an arbitrary function of rates of strain is made. It is shown that under scaling transformation, for an arbitrary stress function, only 90-degrees of wedge flow leads to similarity solutions, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. In the case of spiral group transformation, no similarity solutions exist if we force the stress function to remain arbitrary after the transformation, whereas for a specific more restricted form, similarity solutions exist for arbitrary wedge angles. For both transformations, similarity equations for power-law and Newtonian fluids are presented as special cases of the analysis. Finally the conditions for invariance and the form of the stress function for a two-dimensional case are also presented.