An Efficient Approach for the Calculation of Eigenfrequencies and Mode Shapes of Tapered and Axially Functionally Graded Rayleigh Beams

作者：He, Min -Fan; Huang, Yong^*; Rong, Hai -Wu

来源：Acta Acustica United with Acustica, 2017, 103(2): 276-287.

DOI：10.3813/AAA.919056

• FREE-VIBRATION
• ELEMENTS

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.

• 出版日期2017-4
• 单位佛山科学技术学院