Effects of Rotating on Hygro-Mechanical Vibration Analysis of Functionally Graded Beams Based on Euler-Bernouli Beam Theory

This paper investigates free vibration characteristics of a rotating functionally graded (FG) beam in hygro environments. In the present study, Material properties of the FG beam vary continuously through thickness direction according to the power-law, which approximates material properties of FG beam.The governing differential equations of motion are derived based on Euler-Bernouli beam theory and using the Hamilton’s principle which solved utilizing a semi-analytical technique called the Differential Transform Method (DTM). In order to verify the competency and accuracy of the current analysis, a comparative study with previous researches are performed and a good agreement is observed. Influences of several important parameter such as power-law exponent, hygro environment, rotational speed and slenderness ratio on natural frequencies are investigated and discussed in detail. It is concluded that these effects play significant role on dynamic behavior of rotating FG beam in hygro environments. Numerical results are tabulated in several tables and figures that can be serve as benchmarks for future analyses of rotating FG beams in the hygro environments.Some novelties of the present study are stated as follows:  There was no work that considers moisture environments with a rotating functionally graded beam until this paper is written. Moisture distribution is considered as linear moisture rise. It is for the first time that a semi-analytical technique is used to solve the differential equations in such field. This method which previously stated as DTM reduces the computational difficulties of the other traditional methods and all the calculations can be made simple manipulations. In many cases, the series solutions obtained with DTM can be written in exact closed form. And even comparison between the results of DT and analytical methods reveals the accuracy of DT method.

Keywords:

vibration analysis , FG beam , hygro environments , DTM