NONLINEAR VIBRATIONS OF TIMOSHENKO BEAMS CARRYING A CONCENTRATED MASS

Transverse vibrations of Timoshenko type beams carrying a concentrated mass have been investigated. Both ends of this mass-beam system have simply supports. Hamilton Principle has been used in order to derive equation of motion . For this coupled differential equations, approximately solutions have been searched by means of Method of Multiple Scales(a perturbation method). These solutions consist of two orders/parts; linear problem and nonlinear problem. One of them gives us natural frequency, and other one gives forced vibration solution. New symplectic method has been used to solve these coupled differential equations. Dynamic properties of the mass-beam system have been investigated using different control parameters; location and magnitude of the concentrated mass, rotational inertia and shear deformation effects.