In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

To solve the problem of detecting the damages of aero-engine blades in harsh environments, reduce the aviation safety hazards caused by visual reasons such as careless observation and delayed reporting of blade damages, the detection model of damages for aero-engine blades via deep learning algorithms is proposed in this paper. Firstly, the Gamma correction method is used to process the dataset captured by the borescope to enhance the characterization ability. Secondly, the improved Convolutional Block Attention Module (CBAM) is embed into the head and the end of backbone network of YOLOv7 model. Meanwhile, a branch is added to the channel attention module of CBAM to optimize its network structure. Finally, in order to improve the accuracy and convergence speed, CIOU is replaced by Alpha_GIOU as coordinate loss function in YOLOv7 model, and a new flow chart of detection for aero-engine blade damages is proposed. Detection experiment results demonstrate that the mean average precision (mAP) of improved YOLOv7 model in this paper is 96.1%, which is 1.0% higher than the original model. The improved YOLOv7 module has remarkable effects compared with YOLOv5s, YOLOv4, SSD and Faster R-CNN models. Meanwhile, the improved YOLOv7 model has better generalization performance, which provides a more reliable support for the real-time and visualization of damages detection of aero-engine blades.