2023 Vol.13(2)

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Characterization methods for additive manufacturing
Huimin Xie, Zhongwei Li, Zhanwei Liu
Theoretical and Applied Mechanics Letters  13 (2023) 100415. doi: 10.1016/j.taml.2022.100415
[Abstract](1463) [PDF 515KB](31)
Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester
Di Liu, Shen Xu, Jinzhong Ma
Theoretical and Applied Mechanics Letters  13 (2023) 100412. doi: 10.1016/j.taml.2022.100412
[Abstract](280) [PDF 1775KB](18)
In this paper, the approximate Bayesian computation combines the particle swarm optimization and sequential Monte Carlo methods, which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system. Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed, which verifies the effectiveness of the proposed method. Finally, a partial response sample of the regular and chaotic responses, determined by the maximum Lyapunov exponent, is applied to detect whether chaotic motion occurs in them by a 0–1 test. This paper can provide a reference for data-based parameter identification and chaotic prediction of chaotic vibration energy harvester systems.
Hopf bifurcation of nonlinear system with multisource stochastic factors
Xinyu Bai, Shaojuan Ma, Qianling Zhang, Qiyi Liu
Theoretical and Applied Mechanics Letters  13 (2023) 100417. doi: 10.1016/j.taml.2022.100417
[Abstract](271) [PDF 1734KB](8)
The article mainly explores the Hopf bifurcation of a kind of nonlinear system with Gaussian white noise excitation and bounded random parameter. Firstly, the nonlinear system with multisource stochastic factors is reduced to an equivalent deterministic nonlinear system by the sequential orthogonal decomposition method and the Karhunen–Loeve (K-L) decomposition theory. Secondly, the critical conditions about the Hopf bifurcation of the equivalent deterministic system are obtained. At the same time the influence of multisource stochastic factors on the Hopf bifurcation for the proposed system is explored. Finally, the theorical results are verified by the numerical simulations.
Path integral solutions for n-dimensional stochastic differential equations under α-stable Levy excitation
Wanrong Zan, Yong Xu, Jürgen Kurths
Theoretical and Applied Mechanics Letters  13 (2023) 100430. doi: 10.1016/j.taml.2023.100430
[Abstract](259) [PDF 5719KB](9)
In this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with -stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of -stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
In-situ 3D contour measurement for laser powder bed fusion based on phase guidance
Yuze Zhang, Pan Zhang, Xin Jiang, Siyuan Zhang, Kai Zhong, Zhongwei Li
Theoretical and Applied Mechanics Letters  13 (2023) 100405. doi: 10.1016/j.taml.2022.100405
[Abstract](252) [PDF 2522KB](10)
In-situ layerwise imaging measurement of laser powder bed fusion (LPBF) provides a wealth of forming and defect data which enables monitoring of components quality and powder bed homogeneity. Using high-resolution camera layerwise imaging and image processing algorithms to monitor fusion area and powder bed geometric defects has been studied by many researchers, which successfully monitored the contours of components and evaluated their accuracy. However, research for the methods of in-situ 3D contour measurement or component edge warping identification is rare. In this study, a 3D contour measurement method combining gray intensity and phase difference is proposed, and its accuracy is verified by designed experiments. The results show that the high-precision of the 3D contours can be achieved by the constructed energy minimization function. This method can detect the deviations of common geometric features as well as warpage at LPBF component edges, and provides fundamental data for in-situ quality monitoring tools.
Linear logistic regression with weight thresholding for flow regime classification of a stratified wake
Xinyi L.D. Huang, Robert F. Kunz, Xiang I.A. Yang
Theoretical and Applied Mechanics Letters  13 (2023) 100414. doi: 10.1016/j.taml.2022.100414
[Abstract](247) [PDF 4165KB](8)
A stratified wake has multiple flow regimes, and exhibits different behaviors in these regimes due to the competing physical effects of momentum and buoyancy. This work aims at automated classification of the weakly and the strongly stratified turbulence regimes based on information available in a full Reynolds stress model. First, we generate a direct numerical simulation database with Reynolds numbers from 10,000 to 50,000 and Froude numbers from 2 to 50. Order (100) independent realizations of temporally evolving wakes are computed to get converged statistics. Second, we train a linear logistic regression classifier with weight thresholding for automated flow regime classification. The classifier is designed to identify the physics critical to classification. Trained against data at one flow condition, the classifier is found to generalize well to other Reynolds and Froude numbers. The results show that the physics governing wake evolution is universal, and that the classifier captures that physics.
Slip boundary effect on the critical Reynolds number of subcritical transition in channel flow
Yue Xiao, Linsen Zhang, Jianjun Tao
Theoretical and Applied Mechanics Letters  13 (2023) 100431. doi: 10.1016/j.taml.2023.100431
[Abstract](274) [PDF 1092KB](11)
In this letter, the effect of slip boundary on the origin of subcritical transition in two-dimensional channel flows is studied numerically and theoretically. It is shown that both the positive and the negative slip lengths will increase the critical Reynolds number of localized wave packet and hence postpone the transition. By applying a variable transformation and expanding the variables about a small slip length, it is illustrated that the slip boundary effect only exists in the second and higher order modulations of the no-slip solution, and hence explains the power law found in simulations, i.e. the relative increment of the critical Reynolds number due to the slip boundary is proportional to the square of the slip length.
Modeling cell contractility responses to acoustic tweezing cytometry
Suyan Zhang, Zhenzhen Fan
Theoretical and Applied Mechanics Letters  13 (2023) 100400. doi: 10.1016/j.taml.2022.100400
[Abstract](285) [PDF 5990KB](5)
Acoustic tweezing cytometry (ATC) is a recently developed method for cell mechanics regulation. Targeted microbubbles, which are attached to integrins and subsequently the actin cytoskeleton, anchor, amplify and transmit the mechanical energy in an acoustic field inside the cells, eliciting prominent cytoskeleton contractile force increases in various cell types. We propose that a mechanochemical conversion mechanism is critical for the high efficiency of ATC to activate cell contractility responses. Our models predict key experimental observations. Moreover, we study the influences of ATC parameters (ultrasound center frequency, pulse repetition frequency, duty cycle, and acoustic pressure), cell areas, the number of ATC stimuli, and extracellular matrix rigidity on cell contractility responses to ATC. The simulation results suggest that it is large molecules, rather than small ions, that facilitate global responses to the local ATC stimulation, and the incorporation of visible stress fiber bundles improves the accuracy of modeling.
On the structure of the turbulent/non-turbulent interface in a fully developed spatially evolving axisymmetric wake
Weijun Yin, YuanLiang Xie, Xinxian Zhang, Yi Zhou
Theoretical and Applied Mechanics Letters  13 (2023) 100404. doi: 10.1016/j.taml.2022.100404
[Abstract](257) [PDF 2800KB](9)
In this work, we numerically study the structure of the turbulent/nonturbulent (T/NT) interface in a fully developed spatially evolving axisymmetric wake by means of direct numerical simulations. There is a continuous and contorted pure shear layer (PSL) adjacent to the outer edge of the T/NT interface. The local thickness of the PSL exhibits a wide range of scales (from the Kolmogorov scale to the Taylor microscale) and the conditional mean thickness with being the centerline Kolmogorov scale is the same as the viscous superlayer. In the viscous superlayer, the pure shear motions without rotation are overwhelmingly dominant. It is also demonstrated that the physics of the turbulent sublayer is closely related to the PSL with a large thickness. Another significant finding is that the time averaged area of the rotational region , and the pure shear region at different streamwise locations scale with the square of the wake-width . This study opens an avenue for a better understanding of the structures of the T/NT interface.
Noise color influence on escape times in nonlinear oscillators - experimental and numerical results
Thomas Breunung, Balakumar Balachandran
Theoretical and Applied Mechanics Letters  13 (2023) 100420. doi: 10.1016/j.taml.2022.100420
[Abstract](242) [PDF 3221KB](5)
The interplay between noise and nonlinearites can lead to escape dynamics. Associated nonlinear phenomena have been observed in various applications ranging from climatology to biology and engineering. For reasons of computational ease, in most studies, Gaussian white noise is used. However, this noise model is not physical due to the associated infinite energy content. Here, the authors present extensive experimental investigations and numerical simulations conducted to examine the impact of noise color on escape times in nonlinear oscillators. With a careful parameterization of the numerical simulations, the authors are able to make quantitative comparisons with experimental results. Through the experiments and simulations, it is illustrated that the noise color can drastically influence escape times and escape probability.