A Generalized Method For The Optimal Design Of Beams Under Flexural Vibration

A generalized method is developed for the design of a cantilever of circular cross-section in flexural vibration. The dynamic rigidity of the overhang bar can be increased if the root portion of the bar is made of high elastic modulus material while the free end portion is composed of low density material. Hence, the method developed is for a beam composed of two materials at different ends, but the method applies to a beam of a single material as well. The variational statement is written, and a set of non-linear boundary value equations are obtained. By solving these equations, the shape of the bar and the material length ratio (length of the material at root portion over total overhang length) which would result in a highest first mode natural frequency is determined. The optimal shape, material length ratio and flexural rigidity of the overhang bar composed of two materials under various constraints are discussed. © 1993 Academic Press LImited.