Free Vibrations of Arbitrary Tapered Beams with Static Deflections due to Arbitrary Distributed Dead Loads

임의분포 사하중에 의한 정적처짐을 고려한 임의 변단면 보의 자유진동

A numerical method is presented to obtain natural frequencies and mode shapes of the arbitrary tapered beams with static deflections due to arbitrary distributed dead loads. The differential equation governing the free vibration is derived and solved numerically. In the numerical example, the linearly tapered beams and both the triangular and sinusoidal distributed dead loads are chosen. The lowest three natural frequencies are reported and typical mode shapes are presented in the figure.