An Efficient Approach for the Calculation of Eigenfrequencies and Mode Shapes of Tapered and Axially Functionally Graded Rayleigh Beams
Free vibration of axially functionally graded Rayleigh beams with non-uniform cross-section is investigated by taking into account the effect of rotary inertia. By expanding the vibration mode into the shifted Chebyshev polynomials, the governing equation can be changed to a system
of linear algebraic equations. For various end conditions, we can obtain the characteristic polynomial equations in eigenvalues of natural frequency. Numerical results of the natural frequencies of homogeneous, non-uniform, and axially functionally graded Rayleigh beams are calculated for
different flexural rigidities, including polynomials, trigonometric and exponential functions. By comparison with the exact and previous results in open literatures, the correctness and effectiveness of the present approach is verified. We elucidate the effects of the rotary inertia, slenderness
ratio, taper ratio and gradient parameter on the natural frequency and vibration mode. The introduced method is of benefit to investigate the dynamic behaviors of axially non-uniform Rayleigh beams in engineering applications.
Document Type: Research Article
Publication date: 01 March 2017
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