Theoretical and Applied Mechanics Letters最新文献

Nonlinearity and randomness are both the essential attributes for the real world, and the case is the same for the models of infectious diseases, for which the deterministic models can not give a complete picture of the evolution. However, although there has been a lot of work on stochastic epidemic models, most of them focus mainly on qualitative properties, which makes us somewhat ignore the original meaning of the parameter value. In this paper we extend the classic susceptible-infectious-removed (SIR) epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic. Finally, in order to extend the meaning of parameters in the corresponding deterministic system, we tentatively introduce two new thresholds which then prove rational.

The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method. This paper studied the angular motion stability of a projectile system under random disturbances. The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion, the center manifold reduction, and the polar coordinates transformation. Then, an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation. From the results, the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength, which can be a reference for projectile design.

Two-dimensional time-resolved particle image velocimetry (TR-PIV) and stereographic particle image velocimetry (SPIV) techniques were used to investigate the effect of leading-edge tubercles on the flow over low-aspect-ratio wing models. The angle of attack is fixed at 10°, and the Reynolds number based on chord length is 5.8 × 10³. It is shown that the leading-edge tubercles can effectively mitigate flow separation in the model and also reduce the contribution of wake vortex to the fluctuating energy of flow. Counter-rotating vortex pairs (CVPs) initiated from the peak of leading-edge tubercles can promote nearby momentum exchange, enhance mixing of the flow and increase the energy contained in the boundary layer, which results in resisting the larger adverse pressure gradient. Therefore, it is concluded that CVPs play an important role in mitigating the flow separation for wings with leading-edge tubercles.

Metal additive manufacturing (MAM) is an emerging and disruptive technology that builds three-dimensional (3D) components by adding layer-upon-layer of metallic materials. The complex cyclic thermal history and highly localized energy can produce large temperature gradients, which will, in turn, lead to compressive and tensile stress during the MAM process and eventually result in residual stress. Being an issue of great concern, residual stress, which can cause distortion, delamination, cracking, etc., is considered a key mechanical quantity that affects the manufacturing quality and service performance of MAM parts. In this review paper, the ongoing work in the field of residual stress determination and control for MAM is described with a particular emphasis on the experimental measurement/control methods and numerical models. We also provide insight on what still requires to be achieved and the research opportunities and challenges.

Fully connected neural networks (FCNNs) have been developed for the closure of subgrid-scale (SGS) stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow. The FCNN-based SGS model trained using data with Mach number $Ma=3.0$ and Reynolds number $Re=3000$ was applied to situations with different Mach numbers and Reynolds numbers. The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point. The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43, with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model (DSM). In a posteriori test, the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles, mean temperature profiles, turbulent intensities, total Reynolds stress, total Reynolds heat flux, and mean SGS flux of kinetic energy, and outperformed the Smagorinsky model.

A mapping function between the Reynolds-averaged Navier-Stokes mean flow variables and transition intermittency factor is constructed by fully connected artificial neural network (ANN), which replaces the governing equation of the intermittency factor in transition-predictive Spalart-Allmaras (SA)-$\gamma$ model. By taking SA-$\gamma$ model as the benchmark, the present ANN model is trained at two airfoils with various angles of attack, Mach numbers and Reynolds numbers, and tested with unseen airfoils in different flow states. The a posteriori tests manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress and lift/drag/moment coefficient from the present two-way coupling ANN model almost coincide with those from the benchmark SA-$\gamma$ model. Furthermore, the ANN model proves to exhibit a higher calculation efficiency and better convergence quality than traditional SA-$\gamma$ model.

A new algorithm is proposed to solve the problems of shape-finding of suspension bridge with spatial cables what include tedious iteration, slow convergence speed and even no convergent under some circumstances. In this paper, the stress analysis of the main cable is carried out, and the relationship between the slope change and the coordinate change is found. This paper also discussed how to find the minimum slope point of symmetrical or asymmetric main cable, and the deformation compatibility equation is established and solved to obtain the shape of main cable. The algorithm in this paper can ensure the convergence of the solution for the suspension bridge with spatial cables. The calculation accuracy is high through the demonstration of the calculation examples.

Prediction of Lotka-Volterra equations has always been a complex problem due to their dynamic properties. In this paper, we present an algorithm for predicting the Lotka-Volterra equation and investigate the prediction for both the original system and the system driven by noise. This demonstrates that deep learning can be applied in dynamics of population. This is the first study that uses deep learning algorithms to predict Lotka-Volterra equations. Several numerical examples are presented to illustrate the performances of the proposed algorithm, including Predator nonlinear breeding and prey competition systems, one prey and two predator competition systems, and their respective systems. All the results suggest that the proposed algorithm is feasible and effective for predicting Lotka-Volterra equations. Furthermore, the influence of the optimizer on the algorithm is discussed in detail. These results indicate that the performance of the machine learning technique can be improved by constructing the neural networks appropriately.

This paper examines the influence of physical parameters on the collapse dynamics of a spherical bubble filled with diatomic gas ($\kappa =7/5$). The problem is formulated by the Rayleigh–Plesset dynamical equation, whose numerical solutions are carried out by Maple. Our studies show that each physical parameter affects the bubble collapse dynamics in different degree, which reveals that bubble collapse dynamics must considers all the parameters including liquid viscosity, surface tension, etc, else the outcome cannot be trusted.

A numerical model is presented in this article to investigate the interactions between laser generated ultrasonic and the microdefects (0.01 to 0.1 mm), which are on the surface of the laser powder bed fusion additive manufactured 316L stainless steel. Firstly, the influence of the transient sound field and detection positions on Rayleigh wave signals are investigated. The interactions between the varied microdefects and the laser ultrasonic are studied. It is shown that arrival time of reflected Rayleigh (RR) waves wave is only related to the location of defects. The depth can be checked from the feature point Q, the displacement amplitude and time delay of converted transverse (RS) wave, while the width information can be evaluated from the RS wave time delay. With the aid of fitting curves, it is found to be linearly related. This simulation study provides a theoretical basis for quantitative detection of surface microdefects of additive manufactured 316L stainless steel components.