This paper reviewed the research on the vibration of orthotropic circular membrane. We applied the large deflection theory of membrane and principle of virtual displacement to derive the governing vibration equations of circular membrane, solved it, and obtained the power series formula of nonlinear vibration frequency of circular membrane with all edges fixed. The paper gave the computational example and compared the frequency with different initial displacements, respectively. Results obtained from this paper provide some theoretical foundation for the research of orthotropic composite materials; meanwhile, the results provide some theoretical foundation for the research of nonlinear vibration of membrane.

In this paper, a novel parameter recognition method of mode-converted wave in single-source ultrasound is put forward and applied to the estimation of axial stresses in bolts. To overcome the distortion and aliasing of the mode-converted wave in single-source ultrasonic signal, a time-frequency parameter recognition method based on the Gabor transform is introduced to recognize the accurate time of flight (TOF) of the mode-converted wave. Based on the mode conversion of the single-source longitudinal ultrasound, a new nonlinear evaluation model based on acoustoelastic equation is derived to determine the axial stress of bolt. The performance of the proposed method is evaluated by comparing it with the commonly used TOF ratio method of longitudinal wave and shear wave (L-S). The experiment result shows that the proposed method is more effective in detecting the connection status of bolted joints than the traditional L-S method.

Nonlinear vibration computational problem of isotropic thin plates in large amplitude was investigated here. We applied the Von Kármán’s theory of thin plates to derive the governing equations of nonlinear free vibration of isotropic thin plates, and solved the governing equations by direct integration method combined with power series expansion method. We obtained the power series solution of the nonlinear vibration frequency of the rectangular thin plates with four edges simply supported. Finally, the paper gave the computational example and compared the two results from the large amplitude theory and the small one, respectively. Results obtained from this paper provide a new analytical computational approach for calculating the frequency of nonlinear free vibration of isotropic thin plates in large amplitude, and provide more accurate theoretical basis for the vibration control and dynamic design of plate structures.

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