Dynamics behavior analysis of functionally graded blades under the trail excitation

Abstract

To investigate the effects of trail excitation on the vibration characteristics of rotating functionally graded blades, a dynamic model of rotating functionally graded blades with arbitrary presetting angles is established, and the dynamic behavior of the model is analyzed. The vibration displacement functions of rotating blades are fitted based on an improved Fourier series. A penalty function is adopted to realize the arbitrary boundary constraints of the blade. In addition, the trail excitation is expanded as sinusoidal harmonics. The vibration problem of rotating blades is solved using the Ritz method. By comparison with the results in the literature, the convergence and correctness of the present method are demonstrated, and new results of computation and key parameter analyses are given. The results show that the natural frequencies of the functionally graded blades can be adjusted by changing the distribution of components, and the natural frequencies of blades increase with the rotation rate, rotating radius, and presetting angle. Additionally, in a certain range of rotation speeds, the higher the harmonic order is, the higher the critical speed caused by the harmonic of wake exciting force.