2019 Vol.9(4)

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Analysis on nasal airway by using scale-adaptive simulation combined with standard $ k-\omega $ model and 3D printing modeling physical experiment
Jiemin Zhan, Yangyang Xi, Kay Lin, Weiguang Yu, Wenqing Hu
Theoretical and Applied Mechanics Letters  2019, 9(4): 215-219. doi: 10.1016/j.taml.2019.04.001
[Abstract](1206) [FullText HTML] (669) [PDF 2585KB](40)
The physiological structure of the upper respiratory tract is complex and varies with each individual, and the circulating air has turbulent performance. In this paper, based on computed tomography (CT) medical images published online and the three-dimensional (3D) printing technology, a 3D model of the human upper respiratory tract was reconstructed and an experimental device of the upper respiratory tract was made. We implemented the respiratory experiment and measured the flow rate, and a scale-adaptive k\begin{document}$ \omega $\end{document} model is applied for numerical simulation, the results are in good agreement. The flow field during respiratory was analyzed by coronal velocity cross section, vortex line and particle tracks. We found that the relatively strong shear effect happens at the areas of nasal valve and nasopharynx. In the middle and upper nasal tract, vortex line separation occurs and there is significant passage effect. The results indicate that SAS method is effective in studying upper respiratory airflow.
Numerical analysis of a simplest fractional-order hyperchaotic system
Dong Peng, Kehui Sun, Shaobo He, Limin Zhang, Abdulaziz O. A. Alamodi
Theoretical and Applied Mechanics Letters  2019, 9(4): 220-228. doi: 10.1016/j.taml.2019.03.006
[Abstract](1268) [FullText HTML] (413) [PDF 3251KB](60)
In this paper, a simplest fractional-order hyperchaotic (SFOH) system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system, which possesses seven terms without any quadratic or higher-order polynomials. The numerical solution of the SFOH system is investigated based on the Adomian decomposition method (ADM). The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics. Dynamics of this system are demonstrated by means of phase portraits, bifurcation diagrams, Lyapunov exponent spectrum (LEs) and Poincaré section. The results show that the system has a wide chaotic range with order change, and large Lyapunov exponent when the order is very small, which indicates that the system has a good application prospect. Besides, the parameter a is a partial amplitude controller for the SFOH system. Finally, the system is successfully implemented by digital signal processor (DSP). It lays a foundation for the application of the SFOH system.
Pendulum systems for harvesting vibration energy from railroad tracks and sleepers during the passage of a high-speed train: A feasibility evaluation
Franco E. Dotti, Mauricio D. Sosa
Theoretical and Applied Mechanics Letters  2019, 9(4): 229-235. doi: 10.1016/j.taml.2019.03.005
[Abstract](1125) [FullText HTML] (393) [PDF 3294KB](16)
We evaluate the feasibility of recovering energy from the vibrations of track and sleepers, during passage of a high-speed train, by means of a pendulum harvester. A simple mathematical model of the parametric pendulum is employed to obtain numerical predictions, while measured data of vibration tests during the passage of a Thalys high-speed train are considered as input forcing. Since a sustained rotation is the most energetic motion of a pendulum, the possibility of achieving such state is evaluated, taking into account the influence of initial conditions, damping and other factors. Numerical simulations show that rotating pendulum harvesters with sufficiently low viscous damping could be able to generate a usable average power on the order of 5–6 W per unit. Considering a modular arrangement of devices, such energy is enough to feed variety of rail-side equipment, as wireless sensors or warning light systems. However, a suitable choice of initial conditions could be a difficult task, leading to the need of a control action.
Thermal explosion and irreversibility of hydromagnetic reactive couple stress fluid with viscous dissipation and Navier slips
S.O. Salawu, M.S. Dada, O.J. Fenuga
Theoretical and Applied Mechanics Letters  2019, 9(4): 246-253. doi: 10.1016/j.taml.2019.04.003
[Abstract](783) [FullText HTML] (424) [PDF 3027KB](20)
The study examines the thermal explosion branched-chain and entropy generation as a result of irreversibility of hydromagnetic reactive couple stress liquid with viscous heating and Navier slips. The reactive fluid flow is enhanced by heat dependent pre-exponential factor and axial pressure gradient in a porous wall. The flow equations for the non-Newtonian couple stress fluid model and heat transfer are solved by employing a semi-analytical collocation weighted residual method (CWRM). The efficiency and validity of the obtained results was verified with the existing results. The results reveal that at low hysteresis magnetic and viscous dissipation the irreversibility process is minimized and thermodynamic equilibrium is improved. The results from this study can assist in understanding the relationship between thermal and thermal explosions branched-chain.
Direct method for a Cauchy problem with application to a Tokamak
Mohsen Tadi
Theoretical and Applied Mechanics Letters  2019, 9(4): 254-259. doi: 10.1016/j.taml.2019.04.002
[Abstract](723) [FullText HTML] (356) [PDF 2810KB](15)
This note is concerned with a new direct (non-iterative) method for the solution of an elliptic inverse problem. This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition. Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations. Four examples are used to study the applicability of the method with the presence of noise.
Comparative numerical study on the child head injury under different child safety seat angles
Reza Razaghi, Hasan Biglari, Mojtaba Hasani, Alireza Karimi
Theoretical and Applied Mechanics Letters  2019, 9(4): 260-263. doi: 10.1016/j.taml.2019.04.005
[Abstract](889) [FullText HTML] (398) [PDF 2544KB](13)
It has been shown that annually around 1250 children younger than 15 years old die in traffic accident. The number of children who also injured as a consequence of car accidents is noticeably higher. According to the ECE-R44 regulation the safety of children in the cars, the use of a child safety seat (CSS) is highly recommended. Using a CSS would dramatically diminish the injuries of traffic accidents. However, the posture, especially the angle, of a child when seating on a seat may also affect the amount of injury occurs during the accident. It has been revealed that during the accident only few children remained seated in the standard position, and most of them whether slouched or slanted and turned their head to the side-support of the CSS. Extreme positions, such as leaning forward, escaping from the harness or holding feet were also observed. This study aimed to perform a finite element (FE) study to figure out what angle of seating would result in the least amount of injury to the child head in a typical car crash under the speed of 47 km/h. To do that, a 1.5 years old child dummy (a dummy representing the anthropometry of a 1.5 years old child) has been accommodated on a seat under the angles of 15°, 30°, and 45°. The results revealed. The resulted displacements in the head after the accident were also calculated at X, Y, and Z directions. The results in this regard indicated a higher displacement at X direction whereas the lowest one was seen at Y direction. The results have implications not only for understanding the amount of injury to the child head after the accident under different seating angles, but also for giving an insight to the CSS industries and families to choose the right seating posture for the child in the car to reduce the severity of injury.
On the Weissenberg effect of turbulence
Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee
Theoretical and Applied Mechanics Letters  2019, 9(4): 236-245. doi: 10.1016/j.taml.2019.03.004
[Abstract](1898) [FullText HTML] (965) [PDF 2579KB](87)
Within the framework of the Navier–Stokes equations, the Weissenberg effect of turbulence is investigated. We begin with our investigation on the elastic effect of homogeneous turbulent shear flow. First, in the sense of Truesdell (Physics of Fluids, 1964) on the natural time of materials, we derive the natural time of turbulence, and use it together with the natural viscosity of turbulence derived in the article of Huang et al. (Journal of Turbulence, 2003) to define the natural Weissenberg number of turbulence as a measure of the elastic effect of homogeneous turbulence. Second, we define a primary Weissenberg number of turbulence, which in laminar flow reduces to the Weissenberg number widely applied in rheology to characterize the elasticity of visco-elastic fluids. Our analysis based on the experimental results of Tavoularis and Karnik (Journal of Fluid Mechanics, 1989) indicates that the larger is the Weissenberg number of turbulence, the more elastic becomes the turbulent flow concerned. Furthermore, we put forth a general Weissenberg number of turbulence, which includes the primary Weissenberg number of turbulence as a special case, to measure the overall elastic effects of turbulence. Besides, it is shown that the general Weissenberg number can also be used to characterize the elastic effects of non-Newtonian fluids in laminar flow.
Analytical modeling for rapid design of bistable buckled beams
Wenzhong Yan, Yunchen Yu, Ankur Mehta
Theoretical and Applied Mechanics Letters  2019, 9(4): 264-272. doi: 10.1016/j.taml.2019.04.006
[Abstract](791) [FullText HTML] (369) [PDF 3000KB](16)
Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics, energy harvesting, and microelectromechanical system (MEMS). However, their design often requires time-consuming and expensive computations. In this work, we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force. Based on the Euler–Bernoulli beam theory, we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties. This model is verified against the results from a finite element analysis (FEA) model, with maximum discrepancy less than 7%. By analyzing and simplifying our theoretical model, we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam. These behavioral values include critical force, critical displacement, and travel, which are generally sufficient for characterizing the snap-through properties of a bistable buckled beam. Based on these analytical formulas, we investigate the influence of a bistable buckled beam's key design parameters, including its actuation position and precompression, on its critical behavioral values, with our results validated by FEA simulations. Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.
Comment and Response
Comment on the paper “Theoretical & Applied Mechanics Letters 7 (2017) 235–242”
Asterios Pantokratoras
Theoretical and Applied Mechanics Letters  2019, 9(4): 273-273. doi: 10.1016/j.taml.2019.0c.001
[Abstract](535) [FullText HTML] (341) [PDF 2234KB](12)
Response to (Comment on the paper "Theoretical & Applied Mechanics Letters 7 (2017) 235–242”)
Yahaya Shagaiya Daniel, Zainal Abdul Aziz, Zuhaila Ismail, Faisal Salah
Theoretical and Applied Mechanics Letters  2019, 9(4): 274-275. doi: 10.1016/j.taml.2019.0c.002
[Abstract](595) [FullText HTML] (339) [PDF 2291KB](15)