일단은 일반적인 지지조건을 갖고 타단은 집중질량을 갖는 변단면 보의 자유진동

Free Vibrations of Tapered Beams with General Boundary Condition at One End and Mass at the Other End

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. 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 and the corresponding mode shapes are calculated over a wide range of section ratio, dimensionless spring constant, and mass ratio.