Addressing the challenge of accurately solving unstable stick-slip vibration problems in non-smooth dynamics, this paper proposes a solution algorithm based on Physics-informed Neural Networks (PINN). Firstly, the classical stick-slip vibration problem is dynamically modeled using the linear complementarity theory under unilateral constraints. Then, the linear complementarity relationship is designed as a loss function to guide the training of the neural network, constructing a PINN algorithm for solving multi-point friction-induced stick-slip vibration problems. The accurate simulation of complex responses of multiple sliders'stick-slip vibrations in frictional systems is conducted. By comparing the numerical results with the Switching Model method that includes event detection and the traditional Time-Stepping method without event detection, the accuracy of the PINN algorithm is verified. The proposed PINN algorithm transforms the traditional optimization problem calculation into network training of the machine learning algorithm, making it suitable for stick-slip vibration analysis with multiple contact points. This method achieves accurate nonsmooth state transitions and provides a convenient and easy-to-use new approach for the accurate simulation of complex nonlinear vibration responses in multi-degree-of-freedom frictional systems.

Structural condition assessment is crucial for ensuring the safe services of structures, with structural damage detection (SDD) being a core component. In this paper, a novel SDD method is proposed based on the adaptive grasshopper algorithm and sparse regularization. It aims to tackle accuracy decline of SDD results and instability involving uncertainties and incomplete measurement, thereby achieving sparse-regularization-based structural condition assessment. Firstly, adaptive Lévy flight and elite opposition-based learning strategies are incorporated into the adaptive grasshopper algorithm to prevent the SDD process from falling into local optima and to enhance the stability of SDD results. Secondly, a modal parameter-based objective function with sparse regularization is formulated to increase the sparsity of SDD results, thereby improving SDD accuracy and robustness. The optimization results of competition-based evolutionary computation benchmark functions show that the adaptive grasshopper algorithm exhibits better global convergence and identification stability compared with its standard version. Numerical and experimental results for simply-supported beams indicate that the proposed method can ensure reliable SDD accuracy even in the case of incomplete measurements, and it possesses good noise robustness as well.

The calculation of the probability distribution of performance functions is a core issue in uncertainty quantification and reliability design, and the recently proposed equivalent expectation method (EEM) is an effective way to solve this problem. This paper proposes an improved EEM. Putting forward an empirical calculation formula for the standard deviation coefficient of auxiliary random variablesand obtaining a more accurate probability distribution of the auxiliary function. Meanwhile, aiming at the accuracy issue in calculating the probability distribution of theperformance function is proposed, the calculation formula for the PDF of the performance function is derived using only one auxiliary function. In the process of calculating the PDF, proposing an exact theoretical transformation of probability distribution from auxiliary functions to performance functions is proposed, resulting in a more accurate PDF of the performance function. Finally, the effectiveness and accuracy of the method are verified through three numerical examples. The results indicate that this method is suitable for computing the probability distribution of high-dimensional nonlinear or implicit performance functions.

In order to investigate the effect of cable damage on in-plane free vibration characteristics of cable-beam composite structures, three dimensionless parameters of cable damage intensity, extent and position are introduced in this paper to establish an in-plane dynamic model of single-cable cantilever beam composite structures with cable damage. The eigenvalue problem of in-plane free vibration of a single cable-cantilever beam model is solved by the method of separation of variables. At the same time, the finite element models under undamaged and damaged conditions of the cable are established for verification, and the results are in good agreement with the theoretical results. The results show that the frequency of the combined structure will decrease obviously only when the sag or damage intensity and extent of the cable are large. When the damage intensity and extent of the cable increase to a certain value, 1∶1 in-mode resonance phenomena tend to appear for high order frequencies. The asymmetric initial configuration caused by damage can increase the frequency of the combined structure, and some mixed modes of the combined structure change to local modes, while some local modes change to mixed modes.

Research on acoustic propagation in multiple fluids has important application values in naval architecture and ocean engineering, such as sound propagation in pipelines filled with water and air, and the detection of buried objects. There are two difficulties in solving such problems with the use of the classical finite element method: one is the serious numerical dispersion error in the finite element solutions under medium and high wave numbers; the other is the need to use refined mesh grids to discretize the fluids near the coupling interface. These difficulties lead to a large computational cost for the finite element method, and the manual intervention to generate refined grids. Compared with the finite element method, the weak-form meshfree method does not require traditional grids, and the dispersion error effect in its solution is much weaker, ensuring good computational accuracy and efficiency. However, the meshfree shape functions are usually discontinuous in the problem domain, resulting in the inability of the continuity condition of the acoustic particle velocity to be naturally satisfied on the interface. Therefore, this paper uses the penalty function method to reconstruct the continuity condition of the acoustic particle velocity on the interface, and proposes a Galerkin weak form suitable for meshfree methods for sound propagation in multiple fluids. Numerical analysis shows that the meshfree solutions is consistent with the reference solutions, and the computational accuracy and efficiency of the meshfree method can be higher than the finite element solutions.

This paper presents an analytical method, namely interface stiffness transfer method, for evaluating the responses of multilayered elastic structures. Based on the Love function and general solutions, the stiffness matrix relationship of the displacement-stress state vectors is introduced to obtain the interface stiffness transfer matrix equation between adjacent layers, which satisfies an algebraic Riccati matrix equation. When the elastic layer is a half-space, an explicit solution is obtained directly for the interface stiffness matrix. The interface stiffness transfer matrix method starts from the bottom layer with a known stiffness, and then deals with one layer at a time until the uppermost layer is reached, obtaining the interface stiffness of the multilayered structure. Finally, by solving the symmetric equilibrium equations of the boundary conditions, the displacement-stress state vector of an arbitrary layer is obtained. This method keeps the advantages of the classical transfer matrix method, but naturally excludes its exponential growth terms. In particular, the proposed method is a powerful candidate for efficiently solving the algebraic Riccati equation for the optimal control problems. Numerical examples show the properties of the interface stiffness transfer method.

Accurately constructing the nonlinear hysteresis loop model at the bolt connection is crucial for the vibration reduction and safety performance evaluation of a satellite load-carrying structure. Traditional time-domain analysis methods of computational models require substantial time costs, and typical data-driven models struggle to construct high-precision hysteresis models. To address these challenges, a novel Residual Improvement Deep Learning Algorithm (RIDLA) is proposed for constructing the hysteresis loop model of displacement and force at the bolt connection. The algorithm fully leverages the capacity of Long Short-Term Memory (LSTM) neural networks to fit nonlinear relationships in time series. It adopts an innovative approach by creating a multi-level residual improvement deep learning model that iteratively refines predictions based on measured responses, resulting in highly accurate modeling of hysteresis at bolt connections. The performance of the RIDLA method is validated using experimental data from cyclic loading of a subcomponent of a satellite load carrying structure. The findings demonstrate that RIDLA achieves highly accurate predictions of the displacement and force hysteresis loop at the bolt connection. Additionally, the RIDLA method could be applied to predict the dynamic responses of other complex non-linear systems.

The discontinuous Galerkin (DG) method has been widely adopted due to its excellent properties such as high accuracy and ease of parallelization. The adaptive mesh refinement (AMR) technique has been widely adopted to improve computational efficiency with much less computational cost compared with uniform global refinement to the same level with AMR. This paper combines the advantages of DG and AMR, and a new hybrid limiter is applied to the DG method on adaptive Cartesian grid based on p4est, an open-source library. The limiter exhibits advantages of high precision, compactness, robustness, and ease of implementation. The shock wave is captured with a shock indictor and the performance of the new hybrid limiter is compared with that of the total variational bounded (TVB) limiter in this paper. The result shows that the performance of the former is significantly better than that of the latter. A series of numerical examples for Euler equations and Navier-Stokes equations are used to verify the feasibility and efficiency of the proposed method. The results show that the new hybrid limiter performs very well in the AMRDG method, it has lower dissipation and great shock capture ability, and the computational efficiency is greatly improved while the accuracy is guaranteed.

A surrogate model is a new research idea direction of aerodynamic data generation. A traditional surrogate model relies on a large number of high-precision simulation sample points and their responses values to ensure the accuracy of the model. A multi-credibility surrogate model can reduce the computational cost while maintaining a certain accuracy by integrating multi-layer high and low credibility models, which is of great significance for reducing a missile development cycle. In this paper, the influence of different numbers of low-confidence sample points on the multi-confidence model and the optimal ratio of high-low-confidence sample points are studied, and a multi-confidence sampling method suitable for aerodynamics data is proposed. It is applied to the construction of three multi-credibility surrogate models in the prediction of missile aerodynamic data, among which the Co-Kriging model has the best comprehensive prediction effect. The recommended ratio of high and low confidence sample size is between 1: 4 and 1: 3.

The formation of porous media is influenced by a number of factors, including the deposition and fragmentation of particles, which result in the formation of interlayers with varying structures. These interlayers exert a significant influence on the mechanical behavior of porous media. This paper presents a systematic investigation into the influence of the inclination angle and thickness of the interlayer on the mechanical behavior of porous media, employing the discrete element method. The results demonstrate that the stress intensity of porous media containing interlayers is between those of the two homogeneous porous media and varies with changes in the inclination angle and thickness of the interlayers. The average coordination number between grains is found to be significantly affected by the thickness of the interlayer at the beginning of loading, but stabilized at the end of loading. The variation of the coordination number affects the distribution of strong and weak force chains, while the inclination angle and thickness of the interlayer determine the magnitude and direction of stress transfer in the force chains. Furthermore, the contact unit normal force and normal contact force are deflected with the increase of the inclination angle of the interlayer, demonstrating significant anisotropy. This study advances our understanding of the intricate mechanical behavior of porous media containing interlayers in strata, offering invaluable insights for optimization and practical application in geological engineering.