Table of Content

01 February 2020, Volume 41 Issue 2

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Articles

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

X. WANG, W. T. ANG, H. FAN

2020, 41(2):  193-206.  doi:10.1007/s10483-020-2563-8

Abstract ( 445 )   HTML ( 24)   PDF (651KB) ( 149 )  

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The current work models a weak (soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes.

Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model

Peng JIANG, Hai QING, Cunfa GAO

2020, 41(2):  207-232.  doi:10.1007/s10483-020-2569-6

Abstract ( 375 )   HTML ( 9)   PDF (547KB) ( 122 )  

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Several studies indicate that Eringen's nonlocal model may lead to some inconsistencies for both Euler-Bernoulli and Timoshenko beams, such as cantilever beams subjected to an end point force and fixed-fixed beams subjected a uniform distributed load. In this paper, the elastic buckling behavior of nanobeams, including both EulerBernoulli and Timoshenko beams, is investigated on the basis of a stress-driven nonlocal integral model. The constitutive equations are the Fredholm-type integral equations of the first kind, which can be transformed to the Volterra integral equations of the first kind. With the application of the Laplace transformation, the general solutions of the deflections and bending moments for the Euler-Bernoulli and Timoshenko beams as well as the rotation and shear force for the Timoshenko beams are obtained explicitly with several unknown constants. Considering the boundary conditions and extra constitutive constraints, the characteristic equations are obtained explicitly for the Euler-Bernoulli and Timoshenko beams under different boundary conditions, from which one can determine the critical buckling loads of nanobeams. The effects of the nonlocal parameters and buckling order on the buckling loads of nanobeams are studied numerically, and a consistent toughening effect is obtained.

Nonlinear primary resonance analysis of nanoshells including vibrational mode interactions based on the surface elasticity theory

A. SARAFRAZ, S. SAHMANI, M. M. AGHDAM

2020, 41(2):  233-260.  doi:10.1007/s10483-020-2564-5

Abstract ( 339 )   HTML ( 5)   PDF (1299KB) ( 69 )  

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The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency should be accounted for in the mechanical behaviors of nanoscale structures. In the current investigation, the influence of free surface energy on the nonlinear primary resonance of silicon nanoshells under soft harmonic external excitation is studied. In order to obtain more accurate results, the interaction between the first, third, and fifth symmetric vibration modes with the main oscillation mode is taken into consideration. Through the implementation of the Gurtin-Murdoch theory of elasticity into the classical shell theory, a size-dependent shell model is developed incorporating the effect of surface free energy. With the aid of the variational approach, the governing differential equations of motion including both of the cubic and quadratic nonlinearities are derived. Thereafter, the multi-time-scale method is used to achieve an analytical solution for the nonlinear size-dependent problem. The frequency-response and amplitude-response of the soft harmonic excited nanoshells are presented corresponding to different values of shell thickness and surface elastic constants as well as various vibration mode interactions. It is depicted that through consideration of the interaction between the higher symmetric vibration modes and the main oscillation mode, the hardening response of nanoshell changes to the softening one. This pattern is observed corresponding to both of the positive and negative values of the surface elastic constants and the surface residual stress.

Nonlocal and strain gradient effects on nonlinear forced vibration of axially moving nanobeams under internal resonance conditions

Jing WANG, Yilin ZHU, Bo ZHANG, Huoming SHEN, Juan LIU

2020, 41(2):  261-278.  doi:10.1007/s10483-020-2565-5

Abstract ( 335 )   HTML ( 9)   PDF (321KB) ( 109 )  

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Based on the nonlocal strain gradient theory (NSGT), a model is proposed for an axially moving nanobeam with two kinds of scale effects. The internal resonanceaccompanied fundamental harmonic response of the external excitation frequency in the vicinities of the first and second natural frequencies is studied by adopting the multivariate Lindstedt-Poincaré (L-P) method. Based on the root discriminant of the frequencyamplitude equation under internal resonance conditions, theoretical analyses are performed to investigate the scale effects of the resonance region and the critical external excitation amplitude. Numerical results show that the region of internal resonance is related to the amplitude of the external excitation. Particularly, the internal resonance disappears after a certain critical value of the external excitation amplitude is reached. It is also shown that the scale parameters, i.e., the nonlocal parameters and the material characteristic length parameters, respectively, reduce and increase the critical amplitude, leading to a promotion or suppression of the occurrence of internal resonance. In addition, the scale parameters affect the size of the enclosed loop of the bifurcated solution curves as well by changing their intersection, divergence, or tangency.

Merging phononic crystals and acoustic black holes

Xiaofei LYU, Qian DING, Tianzhi YANG

2020, 41(2):  279-288.  doi:10.1007/s10483-020-2568-7

Abstract ( 398 )   HTML ( 9)   PDF (1479KB) ( 80 )  

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Phononic crystals (PCs) have recently been developed as effective components for vibration suppression and sound absorption. As a typical design of PCs, wave attenuation occurs in the so-called stop-band. However, the structural response is still significantly large in the pass-band. In this paper, we combine PCs and acoustic black holes (ABHs) in a unique device, achieving a versatile device that can attenuate vibration in the stop-band, while suppress vibration in the pass-band. This approach provides a versatile platform for controlling vibration in a multiband with a simple design.

Magnetic field effects on the nonlinear vibration of a rotor

M. EFTEKHARI, A. DASHTI-RAHMATABADI, A. MAZIDI

2020, 41(2):  289-312.  doi:10.1007/s10483-020-2567-6

Abstract ( 458 )   HTML ( 6)   PDF (1432KB) ( 62 )  

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The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated, resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.

Effects of thermo-magneto-electro nonlinearity characteristics on the stability of functionally graded piezoelectric beam

Haohao BI, Bo WANG, Zichen DENG, Shuodao WANG

2020, 41(2):  313-326.  doi:10.1007/s10483-020-2570-9

Abstract ( 383 )   HTML ( 8)   PDF (491KB) ( 70 )  

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Due to the increasing interests in using functionally graded piezoelectric materials (FGPMs) in the design of advanced micro-electro-mechanical systems, it is important to understand the stability behaviors of the FGPM beams. In this study, considering the effects of geometrical nonlinearity, temperature, and electricity in the constitutive relations and the effect of the magnetic field on the FGPM beam, the Euler-Bernoulli beam model is adopted, and the nonlinear governing equation of motion is derived via Hamilton's principle. A perturbation method, which can decompose the deflection into static and dynamic components, is utilized to linearize the nonlinear governing equation. Then, a dynamic stability analysis is carried out, and the approximate analytical solutions for the nonlinear frequency and boundary frequencies of the unstable region are obtained. Numerical examples are performed to verify the present analysis. The effects of the static deflection, the static load factor, the temperature change, and the magnetic field flux on the stability behaviors of the FGPM beam are discussed. From the proposed analytical solutions and numerical results, one can easily and clearly find the effects of various controlled parameters, such as geometric and physical properties of the system, on the mechanical behaviors of structures, and the conclusions are very important and useful for the design of micro-devices.

A numerical investigation of CO₂ dilution on the thermochemical characteristics of a swirl stabilized diffusion flame

S. VAKILIPOUR, Y. TOHIDI, J. AL-ZAILI, R. RIAZI

2020, 41(2):  327-348.  doi:10.1007/s10483-020-2571-6

Abstract ( 323 )   HTML ( 6)   PDF (1541KB) ( 119 )  

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The turbulent combustion flow modeling is performed to study the effects of CO₂ addition to the fuel and oxidizer streams on the thermochemical characteristics of a swirl stabilized diffusion flame. A flamelet approach along with three well-known turbulence models is utilized to model the turbulent combustion flow field. The k-ω shear stress transport (SST) model shows the best agreement with the experimental measurements compared with other models. Therefore, the k-ω SST model is used to study the effects of CO₂ dilution on the flame structure and strength, temperature distribution, and CO concentration. To determine the chemical effects of CO₂ dilution, a fictitious species is replaced with the regular CO₂ in both the fuel stream and the oxidizer stream. The results indicate that the flame temperature decreases when CO₂ is added to either the fuel or the oxidizer stream. The flame length reduction is observed at all levels of CO₂ dilution. The H radical concentration indicating the flame strength decreases, following by the thermochemical effects of CO₂ dilution processes. In comparison with the fictitious species dilution, the chemical effects of CO₂ addition enhance the CO mass fraction. The numerical simulations show that when the dilution level is higher, the rate of the flame length reduction is more significant at low swirl numbers.

Magnetic nanoparticle drug targeting to patient-specific atherosclerosis: effects of magnetic field intensity and configuration

Xuelan ZHANG, Mingyao LUO, Peilai TAN, Liancun ZHENG, Chang SHU

2020, 41(2):  349-360.  doi:10.1007/s10483-020-2566-9

Abstract ( 412 )   HTML ( 8)   PDF (857KB) ( 63 )  

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Nanoparticle-mediated drug delivery is recognized as a promising option for targeted treatment of atherosclerosis. In this paper, the Eulerian-Lagrangian technique is adopted to simulate the delivery of drug-loaded nanoparticles to patient-specific atherosclerotic plaque with the aid of an external magnetic field. Plaques and vascular walls are introduced as porous media formulated by the Darcy-Forchheimer model in this targeted transport process. The results demonstrate that the delivery efficiency of particles to atherosclerosis depends on the external magnetic field, such as configuration and intensity, in which the configuration angle of the current wire is a key factor and the double current wires have advantages over the single current wire. Meanwhile, the delivery efficiency gradually decreases as the distance between the plaque cap and the current wire increases. Further, although augmenting the current or magnetic susceptibility can generally improve the delivery efficiency of nanoparticles, this increase is not apparent when small-sized nanoparticles are employed as drug transport particles. The results obtained can potentially serve as the guideline to optimize regimens for the targeted therapy of atherosclerosis.

Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section

P. NAG, M. M. MOLLA, M. A. HOSSAIN

2020, 41(2):  361-382.  doi:10.1007/s10483-020-2562-8

Abstract ( 407 )   HTML ( 9)   PDF (2523KB) ( 138 )  

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The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n>1) than the other fluids (n ≤ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.