Free Vibrations of Uniform Pipes Made From Composite Materials at an Internal Flow Under Effect of Additional Boundary Conditions


In this paper the approximate method of Raleigh method can be used to study the effect of additional boundary conditions (clamped – free & clamped – clamped ) on the free transverse vibrations of uniform pipes which have length, L (1m) , inner radius, "Ri" (1cm) & thickness, "t" (1mm) made from composite materials, where the resin of unsaturated polyester represented the matrix material reinforced by aligned (E-fibers glass) in the first case and used aligned fiber (Kevlar-49) in the second case. The length of fibers is in the two types, the first type is long fibers (continuous) and the second is short fibers (discontinuous) for different length all at volume fraction of fibers, "f" (0.15 & 0.25). At any construction of the pipe in composite material the natural frequency decreased when the velocity of flow increased from zero to critical velocity also can be observed the pipe at clamped – clamped boundary conditions predicts natural frequency & critical velocity greater than that pipe at clamped – free. The natural frequency and critical velocity increase with increasing volume fraction and length of discontinuous fiber. The value of natural frequency for pipes which have continuous fibers is constant at certain velocity of flow while are variable in pipes which have discontinuous fibers according to ratio between length of short fiber to critical length of discontinuous fiber whereas the natural frequency increase with increasing this ratio. Finally the pipes with Kevlar fiber have high critical velocity and natural frequency compare with pipes for fiber glass.