Volume 28, Issue 5 (September 2000)
Transverse Vibration of a Simply Supported Frustum of a Right Circular Cone
Presently, there is no efficient mechanical method in the United States to sort small-diameter logs. This paper explores the problem theoretically using transverse vibration as one such method. The numerical solution to the frequency equation for the transverse vibration of a simply-supported frustum of a right circular cone is found. We refer to this solid as a tapered cylinder with constant taper. The numerical solution is found as a function of cylinder taper, and an approximation to the solution of the frequency equation for slight taper is presented and compared with the numerical solution. This simple yet accurate approximation is most useful to determine the tapered cylinder's flexural stiffness or modulus of elasticity by freely vibrating a simply supported tapered cylinder.