Dynamic analysis of a spinning functionally graded material shaft by the p - version of the finite element method

Abstract

This paper is concerned with the dynamic behavior of the spinning Functionally Graded Material (FGM) shaft on rigid bearings. A pversion, hierarchical finite element is employed to define the model. A theoretical study allows the establishment of the kinetic energy and the strain energy of the shaft, necessary to the result of the equations of motion. In this model the transverse shear deformation, rotary inertia and gyroscopic effects have been incorporated. A hierarchical beam finite element with six degrees of freedom per node is developed and used to model the shaft. A program is elaborate for the calculation of the natural frequencies of a spinning FGM shaft. To verify the present model, the results are compared with those available in the literature. The efficiency and accuracy of the methods employed are discussed.

Dynamic analysis of functionally graded shaft

“…Rao et al [13] came up with the idea of a mathematical model using power law and TMBT for FE modelling. Boukhalfa et al [14] analyzed FG rotor shaft by using P-version of FEM with trigonometric shape functions and studied whirling frequencies, natural frequency response, and the whirling speeds of the rotating FG shaft. Further they also employ hpversion of FEM in to study vibrations of composite shaft by using kinetic and strain energy equations to formulate the equation of motion [15].…”

Generalized Differential Quadrature Method for Free Vibration Analysis of a Rotating Composite Thin-Walled Shaft

“…Alwan et al [15] analyzed solid shafts and composite tube shafts using ANSYS. Boukhalfa [16] considered the dynamic behavior of the spinning Functionally Graded Material (FGM) shaft on rigid bearings. A p-version hierarchical finite element was employed to define the model.…”

Characterization of Functionally Graded Timoshenko Beams with Variable Rotational Speed

“…From a mechanics viewpoint, the main advantages of material property grading appear to be improving bonding strength, toughness, wear and corrosion resistance, and reduced residual and thermal stresses. Therefore, now-a-days, an FGM has been a promising candidate for many engineering applications where a high temperature gradient field is the main concern [9][10][11]. Effects of rotary inertia and shear deformation are not negligible for thick beams or even thin beams that are vibrating at high frequencies.…”