Institute of Mechanics,
Chinese Academy of Sciences
2019 Vol.9(4)
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Theoretical and Applied Mechanics Letters 2019, 9(4): 215-219.
doi: 10.1016/j.taml.2019.04.001
Abstract:
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} ![]()
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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–
Theoretical and Applied Mechanics Letters 2019, 9(4): 220-228.
doi: 10.1016/j.taml.2019.03.006
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 229-235.
doi: 10.1016/j.taml.2019.03.005
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 246-253.
doi: 10.1016/j.taml.2019.04.003
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 254-259.
doi: 10.1016/j.taml.2019.04.002
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 260-263.
doi: 10.1016/j.taml.2019.04.005
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 236-245.
doi: 10.1016/j.taml.2019.03.004
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 264-272.
doi: 10.1016/j.taml.2019.04.006
Abstract:
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.
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.
Theoretical and Applied Mechanics Letters 2019, 9(4): 273-273.
doi: 10.1016/j.taml.2019.0c.001
Abstract:
Theoretical and Applied Mechanics Letters 2019, 9(4): 274-275.
doi: 10.1016/j.taml.2019.0c.002
Abstract:
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