Free vibration analysis of rotating axially functionally graded-tapered beams using Chebyshev–Ritz method

Abstract

The modal analysis of rotating axially functionally graded tapered Euler–Bernoulli beams with various boundary conditions is studied. The Chebyshev polynomials multiplied by boundary functions are chosen as the admissible functions in the Ritz minimisation procedure, which is called the Chebyshev–Ritz method. The Chebyshev polynomials guarantee the numerical robustness while the boundary functions satisfy the geometric boundary conditions and the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the method is verified through the convergence and comparative studies. The effects of hub radius ratio, dimensionless rotational speed ratio, taper ratios for height and breadth and gradient parameters of material on natural frequencies and mode shapes are studied in detail.

Keywords:

• Rotating tapered beams
• Chebyshev–Ritz method
• Axially functionally graded material
• Free vibration
• Frequency
• Parameterized analysis