Nonlinear vibrations of multi-supported fluid conveying beam

In this study, nonlinear vibrations of the fluid carrying, the different types of continuous media will discuss. We will accept those fluid carrying beam are connected to the ground with fixed supports. During vibration, with softening or loosening of the ground connection point for various reasons, or flexion at the support points, amplitude is composed at connection points. In this study, this case will be modeled as flexible bearing at the support points. Flow velocity will be taken as harmonically varying about a mean velocity. By considering extension of beam, nonlinear terms will add to the equations of motion. The equations of motion will derived beams by using Hamilton's principle. The obtained equations of motion will be independence from material and geometric structure by nondimensionalization. Approximate solutions were obtained using the Method of Multiple Scales, a perturbation method. Located in the middle part of the support of different locations, with different stiffness of the spring, the amount of different mass, different beam coefficient values for different occupancy rates and the fluid velocity is calculated natural frequencies exactly. Also the fluid velocity variation of the frequency zero and natural frequencies than double the far as the fluid velocity variation frequency is close to zero, and the fluid velocity variation frequency natural frequency doubled is close to the conditions have been examined separately.