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Abstract: Abstract The coupled thermo-mechanical contact between a rotating sphere made of one-dimensional hexagonal quasicrystal materials, and a layer-substrate system with interfacial imperfections, is investigated by applying the discrete convolution-fast Fourier transform (DC-FFT) algorithm. The effects of dislocation-like interface defects, friction coefficient, coating thickness and rotation velocity on the thermoelastic field are discussed. The effect of vertical imperfection on the phason normal displacement is opposite to that of horizontal imperfections. The discontinuity of the horizontal displacement plays a limiting role on the effect of the vertical discontinuities on the phason normal stress. The peak value of the normal phason displacement decreases, and the peak point obviously moves in the negative direction of the x-axis with the increase of friction coefficient, while the change of the phason normal stress is negligible. The numerical results may provide theoretical help for the design of quasicrystal coatings. PubDate: 2023-02-01
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Abstract: Abstract This work presents a global surrogate modelling of mechanical systems with elasto-plastic material behaviour based on support vector regression (SVR). In general, the main challenge in surrogate modelling is to construct an approximation model with the ability to capture the non-smooth behaviour of the system under interest. This paper investigates the ability of the SVR to deal with discontinuous and high non-smooth outputs. Two different kernel functions, namely the Gaussian and Matèrn 5/2 kernel functions, are examined and compared through one-dimensional, purely phenomenological elasto-plastic case. Thereafter, an essential part of this paper is addressed towards the application of the SVR for the two-dimensional elasto-plastic case preceded by a finite element method. In this study, the SVR computational cost is reduced by using anisotropic training grid where the number of points are only increased in the direction of the most important input parameters. Finally, the SVR accuracy is improved by smoothing the response surface based on the linear regression. The SVR is constructed using an in-house MATLAB code, while Abaqus is used as a finite element solver. PubDate: 2023-02-01
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Abstract: Abstract We study the stagnation point boundary layer flow in a three-dimensional space with forced convection heat transfer in a porous medium. The local thermal non-equilibrium (LTNE) model is considered due to a hot (cold) fluid flowing in cold (hot) porous medium for which we take two different but coupled heat transport equations. The governing equations that describe the physical mechanism are solved numerically using the Chebyshev collocation method, and the results are qualitatively confirmed by predicting their far-field asymptotic analysis. In the asymptotic analysis, the governing equations are linearized about the edge of boundary layers and using the computational linear algebraic approach, and the solutions are expressed using the confluent hypergeometric functions of first kind. The results show that the thicknesses of both momentum and thermal boundary layers are found to be thinning for the three-dimensionality and porous parameters. The temperature of fluid and solid medium is identical at pore level when the interface heat transfer rate and porosity scaled are held large, and for an opposite case, the LTNE influences are rather strong. Due to lack of comparison of the present results, the stability analysis is performed on LTNE three-dimensional boundary layer solutions to show all the obtained solutions are practically feasible. The physical dynamics behind these interesting mechanisms are discussed in detail. PubDate: 2023-02-01
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Abstract: Abstract This work investigates the planar motion of a dynamical model with two degrees-of-freedom (DOF) consisting of a connected tuned absorber with a simple pendulum. It is taken into account that the pendulum’s pivot moves in a Lissajous trajectory with stationary angular velocity in the presence of a harmonic excitation moment. In terms of the model’s generalized coordinates, Lagrange’s equations are used to derive the motion’s controlling system. The approximate solutions of this system, up to a higher order of approximation, are achieved utilizing the approach of multiple scales (AMS). Resonance cases are all classified, in which two of them are examined simultaneously to gain the corresponding equations of modulation. The solutions at the steady-state are studied in terms of solvability conditions. According to the Routh-Hurwitz criteria, all potential fixed points at steady and unsteady states are determined and graphed. The dynamical behavior of the motion's time-histories and the curves of resonance are drawn. Regions of stability are examined by inspecting their graphs in order to assess the favorable impact of various parameters on the motion. The achieved outcomes are regarded as novel because the used methodology is applied to a specific dynamical system. The importance of this model under study can be seen from its numerous applications in disciplines like engineering and physics. Furthermore, pendulum vibration absorbers are commonly employed to reduce the vibrations in engineering constructions such as chimneys, bridges, television towers, high buildings, auto-balancing shafts, and antennas. PubDate: 2023-02-01
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Abstract: Abstract Energy harvesting represents one of the recent challenging subjects related to vibration and control. The scale of energy harvesters and storage can involve a wide power range, and the scale of some milliwatt is the elective field of piezoelectric applications. This paper investigates the power frontiers of the piezoelectric-based harvesters applied to automotive units. The analysis, supported by experimental data, aims at estimating the upper bound of the specific power of this technology for powering small devices on board cars. Passive optimally tuned piezoelectric harvester and semi-active controlled ones are compared, based on a new control strategy named VFC-Variational Feedback Control, recently developed by the authors. This new technique makes it possible to increase the total energy storage drained from car vibrations. However, the real advantage for their use relies on a sharp balance between the harvested power and the costs for the additional hardware mass transport. Numerical simulations of circuitry and experimental vibration data provides references to assess the energy convenience in installing this type of devices on board. PubDate: 2023-02-01
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Abstract: Abstract The bending problems of fully clamped orthotropic/isotropic rectangular plates with different thicknesses are uniformly solved by the symplectic superposition method. Firstly, the equilibrium equations of orthotropic rectangular moderately thick plates (RMTPs) are transformed into a Hamiltonian system. Then, by analyzing the boundary conditions and loads of the plates, the bending problems of the orthotropic RMTPs with four clamped edges are decomposed into two sub-problems under the condition of two opposite edges simply supported. The general solutions of the two subproblems are obtained by using the variable separation method in the Hamiltonian system. Finally by superposing the general solutions of the two subproblems, we get the bending symplectic superposition solutions of the fully clamped orthotropic RMTPs. PubDate: 2023-02-01
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Abstract: Abstract Drop dynamics is often used to study liquid-fluid interfacial problems. Also, oscillatory pendent drops are a suitable and alternative tool to study non-linear dynamical systems. According to the paper by Ghorbanifar et al. (J Appl Fluid Mech 1:234, 10.47176/jafm.14.01.31313, 2021) it was predicted numerically that elastic force excreted by a pendent drop is a complete cubic polynomial function. The present work deals with the analytical analysis and proof of the force–displacement function of a pendent drop (which was realized by Ghorbanifar et al.) and using this function the bifurcation of drop was investigated. The oscillatory pendent drop equation of motion (OPDEM) presented here, can completely describe the force–displacement and damping functions of the pendent drop. In this article, the equation of motion of a pendent drop is presented, which paves the way for analytical investigations of drop dynamics. The presented novel dynamical model allows following the oscillation, growth, and detachment of a pendent drop and studying its elastic and non-linear behavior. Here, a drop was modeled as a combination of an elastic rod and a dashpot simulating the drop related surface tension and viscous damping forces, respectively. The displacement of the drop mass center was then related to the rod elongation. Then, the damped OPDEM was derived. It was found that the forcing and damping terms of OPDEM are complete cubic and quadratic polynomials, respectively. Using Lyapunov's method for stability analysis, non-linear dynamics of pendent drop was studied. It was shown the drop growth condition is that the displacement should lie between the local extrema of the forcing term of OPDEM. Exploiting the results presented by Ghorbanifar et al. effects of changing Bond and Capillary numbers on the bifurcation of the governing ODE of drop oscillations were investigated. It was realized that for the Bond numbers greater than about 0.11 saddle-point bifurcation occurs. This causes equilibrium points of OPDEM vanish and system becomes unstable. Also, increasing Capillary number to the values higher than 1.8E−5 causes transcritical bifurcation which leads to the removal of one of the balance points. For this case, by increasing Capillary number the system tends towards one equilibrium point. These results open a way to relate some dimensionless numbers in fluid flow to the dynamics of non-linear systems described by OPDEM and help in studying their stability. PubDate: 2023-02-01
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Abstract: Abstract Bursting oscillations in a system with low-frequency excitation by introducing a new approach of time-varying asymmetric potential is considered. The paper shows that this complex type of oscillations occurs as a combination of double imperfect and double saddle-node bifurcation during each cycle. Furthermore, such a mechanism of generating bursting oscillations is reflected in the complete symmetrization of the bifurcation diagram, which represents a new result. In line with this is the original representation of the catastrophe surface. Such a new shape of catastrophe surface and its connection with bursting oscillations are analyzed in detail. A new way of explanation of bursting oscillations based on the analogy with the motion of a particle in extended potential which alternates from bistable to the monostable case is also provided. With this new concept, it is shown why there is no lower limit of the excitation frequency to generate bursting oscillations. Also, the authors believe that with such an approach, subharmonic oscillations, as they have been treated in this class of nonlinear oscillations, should be observed in a new way. The approach is illustrated on a simple real mechanical model, the functionality and effectiveness of which are strongly dependent on parameters of systems and the relations between them. PubDate: 2023-02-01
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Abstract: Abstract The paper deals with the study of the influence of the homogeneous finite initial strains in a highly elastic plate which is in contact with a compressible inviscid fluid on the dispersion of the axisymmetric waves propagating in the “plate + fluid” and “plate + fluid + rigid wall” systems. It is assumed that the homogeneous finite initial strains in the plate are caused by the radial forces acting at infinity, and the motion of the plate is described by the three-dimensional linearized equations and relations of elastic waves in bodies with initial stresses. The fluid flow is formulated by the linearized Navier–Stokes equations for compressible barotropic inviscid fluids. Elasticity relations for the plate material are presented through the harmonic potential. It is established that as a result of the difference between the initial strain states appearing in the axisymmetric and plane-strain states in the plate, the dispersion equation obtained for the studied dynamic problem does not coincide with the dispersion equation obtained for the corresponding plane-strain state. The dispersion curves are constructed for various values of the initial strains in the case where the material of the plate is soft-rubber, and the fluid is taken as water. From analysis of these curves, in particular, it is established that the initial strains not only quantitatively, but also qualitatively influence the dispersion of the axisymmetric waves propagating in the hydro-elastic system under consideration. PubDate: 2023-02-01
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Abstract: Abstract In the manufacturing of micro-electromechanical, geotectonic, nuclear devices, etc., mathematical modeling of thermoelastic diffusion phenomenon has significant importance. In this light, the present problem studies two-dimensional thermodiffusive elastic half-space with variable thermal conductivity and diffusivity. Adopting hyperbolic two-temperature dual-phase-lag thermoelastic diffusion model based on memory-dependent derivatives augments the novelty of the present work. Initially, the medium is kept quiescent and the bounding surface of half-space is subjected to thermal, mechanical, and concentration loadings. Linearizing heat conduction and mass diffusion equations using Kirchhoff’s transformation method, the problem is solved using eigenvalue approach in Laplace–Fourier transformed domain with initial and boundary restrictions. To obtain the results in space-time domain, numerical inversion technique is applied. The impact of various parameters on dimensionless field variables involved in the study is analyzed graphically. The results reveal that nonlinear kernel function and greater values of time delay contribute to smoother flow of temperature change and concentration in the medium. With classical two-temperature theory, physical quantities attain comparatively lower magnitudes than with one-temperature or hyperbolic two-temperature theories. The variable thermal conductivity and diffusivity have an increasing impact on temperature change and concentration, respectively. PubDate: 2023-02-01
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Abstract: Abstract In this study, torsional buckling behavior of a laminated composite cylindrical shell panel reinforced with graphene nano-sheets is analyzed. Using the theory of linear three-dimensional elasticity and based on the principle of virtual work and finite element method, equilibrium equations are extracted. Buckling loads are obtained based on a generalized geometric stiffness concept. Halpin-Sai equations are also used to obtain the mechanical properties of the composite material. The effects of weight fractions and graphene distribution pattern along the thickness of the shell, and zigzag and armchair layup of graphene platelets on the torsional buckling loads are investigated. Five graphene distribution patterns FG-X, FG-O, FG-Ʌ, FG-V and UD are utilized in this study. The 15 models of GPL distribution and arrangement of composite layers are investigated. PubDate: 2023-02-01
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Abstract: Abstract In mechanical industry, most mechanical systems contain lubrication clearance joints. Consequently, to analyze the dynamic response errors and accuracy reliability for mechanisms with lubrication clearance joints is very necessary. So far majority studies have focused on kinematic accuracy reliability for mechanism, but few on dynamic response errors and accuracy reliability. Moreover, the only studies on dynamic accuracy reliability mainly focus on mechanisms with dry contact clearance joint, while the studies on dynamic accuracy reliability for mechanisms with lubrication clearance joint are very few. This paper presents an analysis method of dynamic response errors and accuracy reliability for mechanism with lubrication clearance joints. Firstly, the lubrication clearance joint model and dry contact clearance joint model are established, respectively. The dynamic model of nine-bar mechanism with multiple lubrication clearance joints is developed according to Lagrangian multiplier method. And then, the dynamic accuracy reliability model for mechanism is derived by first-order second-moment method. Finally, the influences of lubrication clearance and dry contact clearance on dynamic response errors and accuracy reliability for mechanism are compared and analyzed at different driving speeds. And the influences of dynamic viscosity and clearance values on dynamic response errors and accuracy reliability for mechanism with lubrication clearance joints are researched. This research offers the theory foundation for design of reliability for mechanism. PubDate: 2023-02-01
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Abstract: Abstract The buckling and postbuckling behavior of thin toroidal shell segments composed of auxetic core and graphene-reinforced face sheets under radial loads is reported in the present research combining exiting analytical solutions with the new material designs. Three types of graphene distribution of laminated face sheets and the lattice auxetic core are considered for convex, concave toroidal shell segments and cylindrical shells. The honeycomb lattice auxetic core can be modeled applying a homogenization technique. The Stein and McElman approximation can be used for longitudinally shallow shells to establish the nonlinear equilibrium equations in the framework of the Donnell shell theory with geometrically nonlinearities taking into account the two-parameter foundation model. The expressions of the radial load-maximal deflection postbuckling curves are achieved using the Galerkin method. The numerical investigations indicate the remarkably positive effects of honeycomb auxetic core and graphene-reinforced face sheets on nonlinear buckling responses of shells. PubDate: 2023-02-01
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Abstract: Abstract The capillary-driven flow is an essential portion of liquid behavior under microgravity. Capillary-driven flows in eccentric annuli under microgravity are deeply analyzed in this paper. A second-order differential equation for the climbing height of liquid is derived. It can be solved with the Runge–Kutta method with appropriate initial conditions. The influences of the dynamic angle, the friction force on the annulus wall and the liquid meniscus in the reservoir on liquid behaviors are all considered in this paper. Moreover, effects of eccentricity on flow resistance and flow speed are discussed. This study has been verified by numerical simulation with the volume of fluid method. PubDate: 2023-02-01
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Abstract: Abstract The relaxation process of viscoelastic materials has the memory-dependent effect, while integer-order thermo-viscoelastic models may be challenged to predict precise thermal–mechanical behaviors in solving transient problems of viscoelastic materials in a heat transfer environment. It is found that the fractional-order viscoelastic models fit well with the experimental data from creep and relaxation tests. Additionally, the size-dependent effect on elastic deformation is becoming an issue of great importance recently due to the development of small-scale devices. To capture the memory-dependent and size-dependent effects, the present work aims to formulate a modified fractional-order thermo-viscoelastic model at small-scale for the first time by simultaneously incorporating the effects of the unified definition of the fractional-order parameter, the unified definition of the fractional-order strain parameter and the nonlocal parameter based on the generalized thermo-viscoelastic theory. Then the dynamic response of a viscoelastic microplate under a thermal shock is studied by using the modified fractional-order thermo-viscoelastic model. The corresponding governing equations are formulated and solved by the Laplace transform and its numerical inversion. In conclusion, the influences of the fractional-order parameters, the fractional-order strain parameters and the nonlocal parameters on the variations of the considered quantities are presented and discussed in detail. The obtained results show that these parameters significantly influence the variations of all the considered quantities. PubDate: 2023-02-01
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Abstract: Abstract This paper focuses mainly on developing single-step explicit integration algorithms considering the implicit treatment of velocity. A novel explicit algorithm (GSSI) is proposed and recommended as a self-starting dissipative alternative to the central difference methods in transient analysis. GSSI not only shares the same advantages as the central difference methods, such as second-order accuracy and computational cost, but also achieves flexible dissipation control and self-starting property. Remarkably, GSSI provides a significantly larger stability bound than the central difference methods in the damped case. GSSI imposes two algorithmic parameters ( \( \rho _s \) and \( \rho _b \) ) to flexibly adjust numerical dissipation at the bifurcation point. In general, the \( \rho _b \) controls numerical dissipation at the bifurcation point, while the \(\rho _s \) further adjusts the amount of dissipation in the low-frequency range. Spectral analysis and numerical examples are given solved to show the superiority of GSSI over the existing single-step explicit methods with respect to accuracy, stability, and dissipation control. PubDate: 2023-02-01
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Abstract: Abstract A developing approach for solving equations of a trapped motion of small satellite near the secondary planet mplanet (Earth) in case of the elliptic restricted problem of three bodies, ER3BP, is presented hereby. In ordinary way, this problem includes consideration of two primaries, MSun and mplanet (mplanet < < MSun), both are orbiting around their center of mass on Keplerian orbits. Eccentricity of orbit for the aforementioned mplanet is considered to be quasiperiodically variable depending on long-term Milankovitch cycles or various types of seasonal irradiation processes influencing onto orbit of planet (hereafter, Earth). Our aim is first to establish and second to investigate a novel type of ER3BP with variable eccentricity of secondary planet stemming from long-term Milankovitch cycles where in the formulation of above problem, small satellite will always maintain its orbit located near the secondary planet, mplanet. Indeed, Milankovitch cycles govern the dynamics of slow changing the eccentricity of the secondary planet orbit quasiperiodically during a long-time period of secondary planet’s motion around the primary. This planet moves on quasi-stable elliptic orbit with negligible deviations from purely elliptical motion. Semi-analytical solutions and numerical findings with graphical plots are presented accordingly. PubDate: 2023-02-01
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Abstract: Abstract Elliptical cracks are common in practice engineering. Non-Fourier heat conduction law assumed that the speed of heat propagation in a body is finite. When the length size of materials reduces to micro/nanoscale or the thermal shock time reduces to ps/fs scale, the theory is more exact to evaluate the thermal shock resistance. In this paper, non-Fourier thermal fracture and thermal shock resistance of a ceramic plate with an embedded elliptical crack are evaluated. Firstly, the non-Fourier temperature is analytically solved by the standard separation of variables method. Secondly, the thermal stress is obtained for the ceramic plate without crack by temperature-stress constitutive equation. Thirdly, the thermal stress intensity factor is given by the thermal stress. Finally, the thermal shock resistance is evaluated by the strength and fracture toughness failure criteria. PubDate: 2023-02-01
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Abstract: Abstract This paper deals with the analytical investigation of the steady-state heat conduction within a semi-infinite medium embedding an insulating penny-shaped crack and subjected to a disk heat source of an arbitrary heat flux distribution. This axisymmetric heat conduction problem is formulated as a mixed boundary value problem, which is then converted to dual integral equations using the Hankel integral transform technique. A solution approach based on the Gegenbauer addition formula is employed to directly reduce the resulting integral equations into an infinite set of simultaneous equations. Closed-form expressions for temperature, heat flux, heat flux intensity factor near the crack tip, and constriction resistance are subsequently derived. Moreover, four practical configurations of heat flux conditions are further investigated and discussed. Sets of dimensionless plots are provided to show the effect of the size and depth of the crack on the thermal fields, heat flux intensity factor, and constriction resistance. Additionally, the validity of the obtained results is tested by comparison with numerical simulations and shows a good agreement. PubDate: 2023-02-01
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