Free Vibration Analysis of an Axially Functionally Graded Rotating Tapered Rayleigh Beam Using Differential Transform and Variational Iteration Methods
Keywords:
Rotating Tapered Beam, Free Vibration, Functionally Graded Beam, Variational Iteration Method, Differential Transform MethodAbstract
The free vibration response of an axially functionally graded rotating cantilever tapered Rayleigh beam based on Rayleigh Beam Theory (RBT) is studied using the Differential Transform Method (DTM) and Variational Iteration Method (VIM). Firstly, the governing partial differential equations of motion are simplified into ordinary differential equations through the separation of variables. Then, dimensionless parameters are integrated into the equations of motion to derive a set of recurrence equations. Utilising MAPLE 18 computer codes, the dimensionless frequencies and mode shapes are computed through direct algebraic operations and derived equations. The competency of DTM and VIM in determining the frequency parameters and the vibration modes of a rotating cantilever tapered Rayleigh beam composed of gradient materials is examined, and the influences of taper ratio, inverse of the slenderness ratio and rotational speed on the dimensionless frequencies are analysed. The first eight dimensionless frequencies' convergence and the associated vibration modes are displayed in graphs. For validation of results, a comparison is carried out between the methods adopted in this study. The outcomes reveal that the two semi-analytical techniques are effective and reliable and can be easily employed to examine functionally graded beams' free vibration. The results obtained show that there is excellent agreement between the two methods used.
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