Continious media vibrations of axially moving beams with small flexural stiffness

In this study, the axially moving flexible beam problem is considered. The equation ofmotion for axially moving beams is derived using Hamilton?s Principle. Equation and boundaryconditions are converted to nondimensional form. Thus equations become independent fromgeometry and material properties. Then the equation is optained by assuming small flexuralrigidity. At first, outer expansion solution optained using the Method of Multiple Scales, aperturbation technique. It is observed that this outer expansion solution does not satisfy theboundary conditions for momentum at simple-simple support and incline at fixed-fixed support.In order to eleminate this problem, inner expansion solution are obtained by making a secondexpansion in the neighborhood of extreme points. Then outer and iner expansion solitions arecombined to obtain composite solutions approximately satisfying all the boundary conditions. Atfirst, systems with two supports are considered and derieved solutions for simple-simple andfixed-fixed supports. Then, systems with three supports are considered and derieved solutionsfor simple-simple-simple and fixed-simple-fixed supports. And then, considered effects of axialspeed and flexural rigidity for first and second natural frequency of system for every conditions.