Abstract:
Free vibration study represents one of the most important studies for complex structure such as wing structure. In this search, a new model for wing structure was created including changing in the airfoil shape. The wing of airfoil Naca 2414 of aluminum 2024 alloy was used to construct the wing. Four case studies were accomplished for different airfoil shape so that the location of the airfoil is change from location to other at the chord. Free vibration analysis for five modes was performed to obtain the vibration characteristics such as natural frequency and mode shapes. From the results, it was found that, in general the change in the airfoil leads to (keeping same weight so the thickness and wing length remain constant) increase the vibration characteristics. A numerical program include the analysis was achieved and added to ANSYS milieu as a new motivation.

1.1 Introduction:
In 1999, Joseph W Clement* and Diann Breit[1] create an active rotor blade flap system to reduce the vibrations in rotorcraft. In his search, he used added flaps to the wing to change the aerodynamic characteristics which in turn lead to increase the frequency of the wing. It was appeared that the researcher add a new masses to the structure so that the total weight was increased.In 2001, William (Wei) Cai and Pragasen Pillay [2] obtain the resonant frequencies and mode shapes of the SRM stator to decrease the acoustic noise. He solved the differential equation using finite element method and elasticity theory .they concluded that resonant frequency of the stator stack was decreased roughly linearly with increased of the yoke radius when the yoke thickness is kept unchanged. Furthermore, the existence of the stator poles were reduced the frequencies of the first few order modes and increased the higher order natural frequencies so that the geometry of the poles effects on the resonant frequencies of the SRM.
In 2009, Meng-chun Yu and Chyanbin Hwu [3] studied the free vibration on the tapered composite wings employing the Hamilton’s principle and finite element formulation. They observed that the divergence dynamic pressure was increased and
NUMERICAL INVESTIGATION OF FREE Ahmad Saddy Mohamad
VIBRATION ON NEW STEPPED WING MODEL
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the fundamental natural frequency was decreased when the taper ratio was increased. In August 2009(Xavier Mauclère) [4] founded a new airfoil design based on direct numerical optimization of a B-spline representation of airfoil shape ,which allowed to reproduced different airfoils with various geometries with maximal geometry difference less than 0.5% . That means existed different mass with the same thickness of the new airfoil design. In February 2011, B. Sobhani Aragh · M. H. Yas[5] investigated three-dimensional free vibration analysis of four-parameter continuous grading fiber reinforced (CGFR) cylindrical panels resting on Pasternak foundations using generalized power-law distribution. From This research they concluded that the non-dimensional natural frequency decreases with increasing the R/L ratio .that means decreased in length to diameter ratio for the cylinder to increasing natural frequency and reduced vibration.