VIBRATIONS OF NON-UNIFORM CONTINUOUS BEAMS UNDER MOVING LOADS (original) (raw)

Dynamics Analysis of a Damped Non uniform Beam subjected to Loads moving with Variable Velocity

Aims/ objectives : To obtain the analytical solutions of the governing fourth order partial differential equations with variable and singular coefficients of non-uniform elastic beams under constant and harmonic variable loads travelling at varying velocity. Methodology: The governing equation of the problem is a fourth order partial differential equation. In order to solve this problem, elegant technique called Galerkin's Method is used to reduce the governing fourth order partial differential equations with variable and singular coefficients to a sequence of second order ordinary differential equations. Results: The results show that response amplitudes of the non uniform beam decrease as the value of the axial force N increases. Furthermore, for fixed value of axial force N, the displacements of the simply supported non uniform beam resting on elastic foundations decrease as the foundation modulus K increases. The results further show that, for fixed N and K, it is observed that higher values of the load longitudinal frequency produce more stabilizing effects on the elastic beam. Conclusion: Higher values of axial force N and foundation moduli K reduce the risk factor of resonance in a vibrating system. Also higher load longitudinal frequency produce more stabilizing effects on the elastic beam thereby reduce resonance in a vibrating system.