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Dynamic response of clamped sandwich beams: analytical modeling

Lang Li, Bin Han, Qian-Cheng Zhang, Zhen-Yu Zhao, Tian Jian Lu

Uncorrected proof , doi: 10.1016/j.taml.2019.06.002

[Abstract] (16) [FullText HTML] (10) [PDF 2737KB] (2)

Abstract:
An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span. The clamped face sheets are simplified as a single-degree-of-freedom (SDOF) system, and the core is idealized using the rigid-perfectly-plastic-locking (RPPL) model. Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core. The model is validated with existing analytical predictions and FE simulation results, with good agreement achieved. Compared with existing analytical models, the proposed model exhibits superiority in two aspects: the deformation resistance of front face sheet during shock wave reflection is taken into account; the effect of pulse shape is considered. The practical application range of the proposed model is therefore wider.

Thermoelastic stability of closed cylindrical shell in supersonic gas flow

G.Y. Baghdasaryan, M.A. Mikilyan, I.A. Vardanyan, P. Marzocca

Uncorrected proof , doi: 10.1016/j.taml.2019.05.001

[Abstract] (43) [FullText HTML] (21) [PDF 2449KB] (6)

Abstract:
In this paper the problem of linear stability of a closed cylindrical shell under the action of both non-uniform temperature field and supersonic gas flow is considered. The stability conditions for the unperturbed state of the aerothermoelastic system are obtained. It is shown that, by the combined action of the temperature field and the ambient supersonic flow, the process of linear stability can be controlled and the temperature field affects significantly the critical flutter speed.

Thermoelastic waves in helical strands with Maxwell-Cattaneo heat conduction

Dansong Zhang, Martin Ostoja-Starzewski

Uncorrected proof , doi: 10.1016/j.taml.2019.05.003

[Abstract] (23) [FullText HTML] (21) [PDF 2631KB] (4)

Abstract:
Harmonic thermoelastic waves in helical strands with Maxwell-Cattaneo heat conduction are investigated analytically and numerically. The corresponding dispersion relation is a sixth-order algebraic equation, governed by six non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter, the ratio between extensional and torsional moduli, the Fourier number, and the dimensionless thermal relaxation. The behavior of the solutions is discussed from two perspectives with an asymptotic-numerical approach: (i) the effect of thermal relaxation on the elastic wave celerities, and (ii) the effect of thermoelastic coupling on the thermal wave celerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered. However, with large wavenumbers, the solutions behave differently depending on the thermal relaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from the classical result of the speed of second sound.

On time independent Schrödinger equations in quantum mechanics by the homotopy analysis method

Jyotirmoy Rana, Shijun Liao

Uncorrected proof , doi: 10.1016/j.taml.2019.05.006

[Abstract] (19) [FullText HTML] (15) [PDF 2551KB] (1)

Abstract:
A general analytic approach, namely the homotopy analysis method (HAM), is applied to solve the time independent Schrödinger equations. Unlike perturbation method, the HAM-based approach does not depend on any small physical parameters, corresponding to small disturbances. Especially, it provides a convenient way to gain the convergent series solution of quantum mechanics. This study illustrates the advantages of this HAM-based approach over the traditional perturbative approach, and its general validity for the Schrödinger equations. Note that perturbation methods are widely used in quantum mechanics, but perturbation results are hardly convergent. This study suggests that the HAM might provide us a new, powerful alternative to gain convergent series solution for some complicated problems in quantum mechanics, including many-body problems, which can be directly compared with the experiment data to improve the accuracy of the experimental findings and/or physical theories.

Generalized canonical transformation for second-order Birkhoffian systems on time scales

Y. Zhang, X. H. Zhai

Uncorrected proof , doi: 10.1016/j.taml.2019.06.004

[Abstract] (16) [FullText HTML] (11) [PDF 2389KB] (2)

Abstract:
The theory of time scales, which unifies continuous and discrete analysis, provides a powerful mathematical tool for the study of complex dynamic systems. It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems. In this paper, the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied, which extends the canonical transformation theory of Hamilton canonical equations. First, the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established. Second, based on this condition, six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given. Also, the relationships between new variables and old variables for each of these cases are derived. In the end, an example is given to show the application of the results.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Houzuo Guo, Cheng Su, Jianhua Xian

Uncorrected proof , doi: 10.1016/j.taml.2019.05.007

[Abstract] (16) [FullText HTML] (20) [PDF 2590KB] (2)

Abstract:
Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years. The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses. Therefore, it is reasonable to consider the variability of thermal environments while conducting thermal analysis. However, for ambient thermal excitations, only stationary random processes have been investigated thus far. In this study, the highly efficient explicit time-domain method (ETDM) is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems. The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body. Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses. A numerical example involving non-stationary stochastic internal heat generation rate is investigated. The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Creep relaxation in FGM rotating disc with nonlinear axisymmetric distribution of heterogeneity

Hodais Zharfi

Uncorrected proof , doi: 10.1016/j.taml.2019.05.005

[Abstract] (20) [FullText HTML] (11) [PDF 3389KB] (3)

Abstract:
Rotating discs are the vital part of many types of machineries. Usually there is a tendency to make use of them in higher rotational speeds, but ahead of their complete break down the incidence of vibration, plastic failure or creep relaxation can create serious damages which finally prevent the increase of the rotational speed. The invention of new materials has provided new opportunities to increase the loading capacity and speed of the discs. Functionally graded materials (FGMs) are a kind of new materials utilized in the construction of rotating discs. Consequently an important aspect in the analyses of heterogeneous FGM discs is the study of their creep relaxation. One of the well known constitutive equations for the modeling of creep phenomenon is known as the Sherby's law. Based on the steady state creep, the behavior of a variety of FGM rotating discs are studied. The analysis considers the conditions in which the distribution of volume fraction follows a power-law pattern. The required mathematical model and its solution for the analysis of stress and creep strain rate is represented. Some case studies are considered in which the effects of nonlinearly distributed volume fractions are studied. In the case studies, the analysis of rotating FGM discs made of Aluminum-Silicon Carbide compounds is considered. Besides, the analyses of discs with outside tractions are considered and the effects of typical material compositions upon the creep deformations are studied. For instance, the investigation discloses the significance of the use of FGM hubs in the turbine constructions.

Crack propagation simulation in brittle elastic materials by a phase field method

Xingxue Lu, Cheng Li, Ying Tie, Yuliang Hou, Chuanzeng Zhang

Accepted Manuscript , doi: 10.1016/j.taml.2019.06.001

[Abstract] (8) [FullText HTML] (1) [PDF 4131KB] (3)

Abstract:
To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations, the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable ϕ(x)∈[0,1] to characterize discontinuous cracks in brittle materials. This method can well describe the crack initiation and propagation without assuming the shape, size and orientation of the initial crack in advance. In this paper, a phase field method based on Miehe's approach [Miehe et al., Comp. Meth. App. Mech. Eng. (2010)] is applied to simulate different crack propagation problems in two-dimensional (2D), isotropic and linear elastic materials. The numerical implementation of the phase field method is realized within the framework of the finite element method (FEM). The validity, accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature. Several numerical examples are presented to show the effects of the loading type (tension and shear), boundary conditions, and initial crack location and orientation on the crack propagation path and force-displacement curve. Furthermore, for a single edge-cracked bi-material specimen, the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed. It is demonstrated that the phase field method is an efficient tool for the numerical simulation of crack propagation problems in brittle elastic materials, and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

Numerical investigations of fully nonlinear water waves generated by moving bottom topography

Mian Wang

Accepted Manuscript , doi: 10.1016/j.taml.2019.05.009

[Abstract] (8) [FullText HTML] (6) [PDF 3436KB] (2)

Abstract:
This paper is concerned with propagation of water waves induced by moving bodies with uniform velocity on the bottom of a channel, a simple model for prescribed underwater landslides. The fluid is assumed to be inviscid and incompressible, and the flow, irrotational. We apply this model to a variety of test problems, and particular attention is paid to long-time dynamics of waves induced by two landslide bodies moving with the same speed. We focus on the transcritical regime where the linear theory fails to depict the wave phenomena even in the qualitative sense since it predicts an infinite growth in amplitude. In order to resolve this problem, weakly nonlinear theory or direct numerical simulations for the fully nonlinear equations is required. Comparing results of the linear full-dispersion theory, the linear shallow water equations, the forced Korteweg-de Vries model, and the full Euler equations, we show that water waves generated by prescribed underwater landslides are characterized by the Froude number, sizes of landslide bodies and distance between them. Particularly, in the transcritical regime, the second body plays a key role in controlling the criticality for equal landslide bodies, while for unequal body heights, the higher one controls the criticality. The results obtained in the current paper complement numerical studies based on the forced Korteweg-de Vries equation and the nonlinear shallow water equations by Grimshaw and Maleewong (J. Fluid Mech. 2015, 2016).

Crashworthiness assessment of thin-walled double bottom tanker: A variety of ship grounding incidents

Aditya Rio Prabowo, Sukmaji Indro Cahyono, Jung Min Sohn

Accepted Manuscript , doi: 10.1016/j.taml.2019.05.002

[Abstract] (44) [FullText HTML] (23) [PDF 3100KB] (3)

Abstract:
This study addresses the issue of ship accidental grounding as an impact phenomenon, with the assumption that an interaction of its structure with the oceanic seabed (obstruction), idealized as rock topology, is capable of initiating a so-called hard ground scenario. This occurrence variation was considered by performing two main instances, encompassing raking and stranding, often experienced by oil/chemical tankers as thin-walled structures. In addition, a failure criterion was implemented on the structural geometry, in order to define its ultimate limit and possible damage, during interaction with the obstructions. Subsequently, the analysis results were compiled to assess structural crashworthiness as well as progressive failure of the double bottom part of the tanker, where energy criterion indicated the raking to be more destructive. Meanwhile, detailed observation of the failure sequence indicated the stranding to have successfully breached the inner bottom shell.

3D thermally induced analysis of annular plates of functionally graded materials

Yun-Fang Yang, Ding Chen, Bo Yang

Accepted Manuscript

[Abstract] (15) [FullText HTML] (17) [PDF 2903KB] (1)

Abstract:
Within the framework of three-dimensional elasticity theory, this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field. The present analytical solutions are validated through comparisons against those available in open literature. A parametric study is conducted to examine the effects of gradient distribution, different temperature fields, different diameter ratio and boundary conditions on the deformation and stress fields of the plate. The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials (FGM) annular plates.

Sensitivity analysis of the vane length and passage width for a radial type swirler employed in a triple swirler configuration

Foad Vashahi, Shahnaz Rezaei, Reza Alidoost Dafsari, Jeekeun Lee

Accepted Manuscript , doi: 10.1016/j.taml.2019.05.004

[Abstract] (16) [FullText HTML] (15) [PDF 3878KB] (1)

Abstract:
The design of axial or radial swirlers typically governs a number of geometrical parameters that are determined by the desired flow field. In the meantime, the number of unknown parameters increases with the number of concentrically mounted swirlers. The available literature is nonetheless limited, and designers are obligated to increase the number of initial assumptions. In this article, Three kinds of triple swirlers are employed and simulations are performed to determine the effect of each parameter on the swirler performance. Based on the correlation provided, over-lengthening the radial vane length could result in significant changes in the flow field from the jet-like pattern to a wide swirl-jet angle due to the Coanda effect. Passage width should also have the potential to alter the swirl-jet angle and velocity field at the exit of the swirler.

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

Feng Yue, Ziyan Wu, Haifeng Yang, Mengying Li

Accepted Manuscript , doi: 10.1016/j.taml.2019.04.007

[Abstract] (57) [FullText HTML] (32) [PDF 2786KB] (9)

Abstract:
In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thin plates on elastic foundations, the static problem of circular thin plates on Gibson elastic foundation is solved using an iterative method based on the modified Vlasov model. On the basis of the principle of minimum potential energy, the governing differential equations and boundary conditions for circular thin plates on modified Vlasov foundation considering the characteristics of Gibson soil are derived. The equations for the attenuation parameter in bending problem are also obtained, and the issue of unknown parameters being difficult to determine is solved using the iterative method. Numerical examples are analyzed and the results are in good agreement with those form other literatures. It proves that the method is practical and accurate. The inhomogeneity of modified Vlasov foundations has some influence on the deformation and internal force behavior of circular thin plates. The effects of various parameters on the bending of circular plates and characteristic parameters of the foundation are discussed. The modified model further enriches and develops the elastic foundations. Relevant conclusions that are meaningful to engineering practice are drawn.

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Letter

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

2019, 9(4): 215 -219. doi: 10.1016/j.taml.2019.04.001

[Abstract] (203) [FullText HTML] (75) [PDF 2585KB] (24)

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}

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

2019, 9(4): 220 -228. doi: 10.1016/j.taml.2019.03.006

[Abstract] (155) [FullText HTML] (78) [PDF 3251KB] (12)

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.

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

2019, 9(4): 229 -235. doi: 10.1016/j.taml.2019.03.005

[Abstract] (126) [FullText HTML] (61) [PDF 3294KB] (5)

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.

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

2019, 9(4): 246 -253. doi: 10.1016/j.taml.2019.04.003

[Abstract] (95) [FullText HTML] (52) [PDF 3027KB] (2)

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.

Direct method for a Cauchy problem with application to a Tokamak

Mohsen Tadi

2019, 9(4): 254 -259. doi: 10.1016/j.taml.2019.04.002

[Abstract] (110) [FullText HTML] (50) [PDF 2810KB] (8)

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.

Comparative numerical study on the child head injury under different child safety seat angles

Reza Razaghi, Hasan Biglari, Mojtaba Hasani, Alireza Karimi

2019, 9(4): 260 -263. doi: 10.1016/j.taml.2019.04.005

[Abstract] (150) [FullText HTML] (64) [PDF 2544KB] (7)

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.

Article

On the Weissenberg effect of turbulence

Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee

2019, 9(4): 236 -245. doi: 10.1016/j.taml.2019.03.004

[Abstract] (110) [FullText HTML] (40) [PDF 2579KB] (15)

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.

Analytical modeling for rapid design of bistable buckled beams

Wenzhong Yan, Yunchen Yu, Ankur Mehta

2019, 9(4): 264 -272. doi: 10.1016/j.taml.2019.04.006

[Abstract] (61) [FullText HTML] (29) [PDF 3000KB] (3)

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.