The phenomena of sub- and super-harmonic responses make up one of the prominent nonlinear characteristics of a beam with a breathing crack. In order to fully understand the behaviors of sub- and super-harmonic resonances, it is necessary to analyze the nonlinear vibration of a beam-like structure with a breathing crack. In this study, a new stiffness model that considers the influence of the partial crack closure is proposed to model the stiffness variation of the cracked beam. Based on the finite element model of a beam with a breathing crack, the multiple-scale method is proposed to analyze the nonlinear vibration of a cracked beam subjected to harmonic excitation, and the relation between the nonlinear vibration of the cracked beam and the system parameters is obtained. An experiment is conducted to validate the analytical results. The study shows that the nonlinear responses of a beam with a breathing crack are affected by both the structural parameters and the crack parameters.

Tetracalcium phosphate (TTCP), a potential biological scaffold material, has attracted increasing interest for bone regeneration applications due to its good biodegradability and biocompatibility. In this research, three-dimensional porous TTCP scaffolds were manufactured via selective laser sintering (SLS), and an in-depth and meticulous study on the influence of laser power on the microstructure and mechanical properties of TTCP scaffolds was performed. The results showed that the TTCP particles fused together and formed a solid object due to the decrease in the number of micro-pores in the scaffold as the laser power increased from 6 W to 9 W. The maximum compressive strength that the scaffold could withstand and the strength of the fracture toughness were 11.87 ± 0.64 MPa and 1.12 ± 0.1 MPa·m^1/2, respectively. When the laser power increased from 9 W to 10 W, the TTCP grains grew abnormally, resulting in diminished mechanical properties. The bioactivity tests showed that the surfaces of the scaffolds were entirely covered by bone-like apatite layers after soaking in simulated body fluid (SBF) for three days, indicating that the scaffolds exhibit excellent bioactivity. Moreover, cell experiments showed that the TTCP scaffolds had good biocompatibility. This study indicated that SLS-fabricated TTCP scaffolds may be a promising candidate for bone regeneration applications.

A new model is presented for studying the effects of crack parameters on the dynamics of a cracked beam structure. The model is established by the finite element displacement method. In particular, the stiffness matrix of the cracked beam element is firstly derived by the displacement method, which does not need the flexibility matrix inversion calculation compared with the previous local flexibility approaches based on the force method. Starting with a finite element model of cracked beam element, the equation of strain energy of a cracked beam element is formed by the displacement method combined with the linear fracture mechanics. Then, based on the finite element method, the dynamic model of the cracked beam structure is obtained. The results show that the dynamic model discovers the internal relation between the dynamic characteristics of cracked beam structure and structural parameters, material parameters, and crack parameters. Finally, an example is presented to validate the proposed dynamic model.

This paper presents a novel model for calculating the dynamic stress of a beam structure in a vibrating screen. The proposed model employs a dynamic screen box model as a foundation and utilizes the flow method to establish the mass of the screening materials within the screen box. By considering the motion characteristics of beam structures, the dynamic model for the beam structure of a vibrating screen is derived. The results indicate that the dynamic model can reveal the internal relationship between the dynamic characteristics of beam structures and the structural and material parameters. Finally, a validation example is presented to demonstrate the effectiveness of the proposed dynamic model. The presented model not only contributes to the understanding of the dynamic behavior of beam structures in vibrating screens but also provides a reliable and accurate method for predicting the dynamic stress in beam structures. The proposed model can be applied to optimize the design and performance of vibrating screens, which have wide applications in mining, metallurgy, and other industries. Further research can be conducted to explore the potential of the proposed model for other types of structures subjected to dynamic loads.

Aiming at the problem of inaccurate fault diagnosis caused by limited fault samples and challenging feature extraction in helicopter planetary gear trains, this study proposes a fault diagnosis method based on Bispectrum and Attention Mechanism Deep Convolutional Generative Adversarial Networks (BAMDCGAN). First, to enhance the sample quality generated by the Attention Mechanism Deep Convolutional Generative Adversarial Network (AMDCGAN), bispectral features are adopted as input samples, forming the proposed BAMDCGAN framework. Secondly, by utilizing the experimental data of the planetary gear train, bispectral feature samples under three load conditions and five fault states were constructed. These samples were used as the training data for BAMDCGAN, enabling the adversarial generation of enhanced fault samples. Finally, the Convolutional Neural Network (CNN) and Vision Transformer (VIT) are trained on the augmented dataset respectively for planetary gear train fault diagnosis. Comparative experiments with Envelope Spectrum + AMDCGAN + CNN, Time Domain + AMDCGAN + CNN, Short-Time Fourier Transform (STFT) + AMDCGAN + CNN, Envelope Spectrum + AMDCGAN + VIT and Hilbert-Huang Transform (HHT) + AMDCGAN + CNN methods demonstrate that the proposed BAMDCGAN-based fault diagnosis method achieves the highest diagnostic accuracy, exceeding 97.8% across varying load conditions. Compared to non-augmented samples, diagnostic accuracy is improved by 2.1%.