Abstract
The research reported here deals with the non-linear vibration and the static and flutter instabilities of a uniform beam that is elastically supported by a horizontal and vertical spring at each of the two ends of the member. The beam is also subjected to axial and transverse restraints. The axial compressive restraint is applied at the horizontal springs by an initial displacement x 0, and the transverse restraint is composed of an initial static displacement y st . The equations of motion take into consideration the rotary and shear effects, but damping is neglected. Deflection variations before and after buckling have been examined by varying the axial and vertical restraints x 0 and y st , respectively. The effects of these restraints on the vibration of the beam are also examined in detail for a wide range of values of the spring constants, and the creation of regions of static and flutter instabilities, as well as the location of double points of instability, are investigated in detail.
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