Two Dimensional Transverse Vibration of a Packet Blade

Ching-I Chen ； Chin-Yu Nee

《中華民國振動與噪音工程學會論文集》 1999 (1999/05) Pp. 20-28

https://doi.org/10.30028/CSSVANNUAL.199905.0020

並列摘要

This study performs the derivation of mathematical model to two dimensional of a packet taper blade structure, in which the pertinent transverse free vibration characteristics are investigating for their dynamics behavior. The blades were considered as rectangular cross-section area with constant width and linearly taper in thickness and with double equal-taper in thickness and width. Based on the Bernoulli-Euler beam theory, the equations of motion are derived by the standard variational statement of Hamilton's Principle in continuous approach. An exact solution is solved in terms of Bessel functions and the boundary conditions lead to the matrix form of frequency equation that can be numerically solved by false position method. An example of four blades is performed in the numerical simulation. The natural frequencies of the first two cantilever modes and the first group of three fixed-supported modes are derived for both types of taper blade with taper ratio between 0.7 and 1.3. The number of natural frequency in each cantilever mode depends on the number of blade with very small variation in their value. According to the results, one concludes (1) the natural frequency exists in group manner for both cantilever and fixed-supported mode, (2) the fundamental cantilever natural frequency decreases when the taper ratio increases for both single taper and double taper blade, (3) the second cantilever natural frequency increase when the taper ratio increases for both single taper and double taper blade, (4) the tendency of the first group of three fixed-supported natural frequencies is similar to the second cantilever mode, (5) there are N modes in each cantilever mode and N-1 modes in the first group of fixed- supported mode.