끝단 질량과 일반적인 단부조건을 갖는 변단면 보의 자유진동

Free Vibrations of Tapered Beams with General Boundary Conditions and Tip Masses

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.