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Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

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Applied Mathematics and Mechanics(English Edition) 2024年第6期45卷 1015-1032页

作者： Songye JIN Bo ZHANG Wuyuan ZHANG Yuxing WANG huoming shen Jing WANG Juan LIU School of Mechanics and Aerospace Engineering Southwest Jiaotong UniversityChengdu 610031China School of Mechanical Engineering Southwest Jiaotong UniversityChengdu 610031China School of Mechanical and Electrical Engineering Southwest Petroleum UniversityChengdu 610500China

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

关键词： thermomechanical vibration rotating pre-twisted functionally graded(FG)microbeam refined shear deformation theory(RSDT) modified couple stress theory(MCST) modal assurance criterion(MAC)

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Wave propagation responses of porous bi-directional functionally graded magneto-electro-elastic nanoshells via nonlocal strain gradient theory

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应用数学和力学:英文版 2023年第10期44卷 1821-1840页

作者： Xinte WANG Juan LIU Biao HU Bo ZHANG huoming shen School of Mechanics and Aerospace Engineering Southwest Jiaotong UniversityChengdu 610031China School of Civil Engineering Guizhou University of Engineering ScienceBijie 551700Guizhou ProvinceChina

This study examines the wave propagation characteristics for a bi-directional functional grading of barium titanate(BaTiO_(3)) and cobalt ferrite(CoFe_(2)O_(4)) porous nanoshells,the porosity distribution of which is simulated by the honeycomb-shaped symmetrical and asymmetrical distribution functions.The nonlocal strain gradient theory(NSGT) and first-order shear deformation theory are used to determine the size effect and shear deformation,respectively.Nonlocal governing equations are derived for the nanoshells by Hamilton's principle.The resulting dimensionless differential equations are solved by means of an analytical solution of the combined exponential function after dimensionless treatment.Finally,extensive parametric surveys are conducted to investigate the influence of diverse parameters,such as dimensionless scale parameters,radiusto-thickness ratios,bi-directional functionally graded(FG) indices,porosity coefficients,and dimensionless electromagnetic potentials on the wave propagation characteristics.Based on the analysis results,the effect of the dimensionless scale parameters on the dispersion relationship is found to be related to the ratio of the scale parameters.The wave propagation characteristics of nanoshells in the presence of a magnetoelectric field depend on the bi-directional FG indices.

关键词： bi-directional functionally graded(FG) wave propagation dimensionless magneto-electro-elastic(MEE)nanoshell nonlocal strain gradient theory(NSGT) porosity

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Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

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Applied Mathematics and Mechanics(English Edition) 2023年第1期44卷 35-52页

作者： Zhaonian LI Juan LIU Biao HU Yuxing WANG huoming shen Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace EngineeringSouthwest Jiaotong UniversityChengdu 610031China

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric(FGP) nanoplates deposited in a viscoelastic foundation.It is assumed that(i) the material parameters of the nanoplates obey a power-law variation in thickness and(ii) the uniform porosity exists in the nanoplates.The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory.The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory(NSGT).The motion equations are calculated in accordance with Hamilton’s principle.Finally,the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution.The results indicate that the nonlocal parameters(NLPs) and length scale parameters(LSPs) have exactly the opposite effects on the wave frequency.In addition,it is found that the effect of porosity volume fractions(PVFs) on the wave frequency depends on the gradient indices and damping coefficients.When these two values are small,the wave frequency increases with the volume fraction.By contrast,at larger gradient index and damping coefficient values,the wave frequency decreases as the volume fraction increases.

关键词： scale effect functionally graded material(FGM) dispersion characteristic piezoelectric nanoplate viscoelastic foundation

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Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

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Applied Mathematics and Mechanics(English Edition) 2022年第9期43卷 1339-1354页

作者： Biao HU Juan LIU Yuxing WANG Bo ZHANG Jing WANG huoming shen Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace EngineeringSouthwest Jiaotong UniversityChengdu 610031China School of Mechanical and Electrical Engineering Southwest Petroleum UniversityChengdu 610500China

In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.

关键词： surface effect(SE) scale parameters orthotropic foundation functional gradient graphene piezoelectric sandwich nanoplate

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Wave Propagation in Graphene Platelet-Reinforced Piezoelectric Sandwich Composite Nanoplates with Nonlocal Strain Gradient Effects

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Acta Mechanica Solida Sinica 2021年第4期34卷 494-505页

作者： Biao Hu Juan Liu Bo Zhang huoming shen Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengdu610031China School of Mechanics and Engineering Southwest Jiaotong UniversityChengdu610031China

This research develops an analytical approach to explore the wave propagation problem of piezoelectric sandwich nanoplates.The core of the sandwich nanoplates is a nanocomposite layer reinforced with graphene platelets,which is integrated by two piezoelectric layers exposed to electric field.The material properties of nanocomposite layer are obtained by the Halpin–Tsai model and the rule of mixtures.The Euler–Lagrange equations of nanoplates are derived from Hamilton’s principle.By using the nonlocal strain gradient theory,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of propagation angle,small-scale and external loads on wave frequency.The results reveal that the frequency changes periodically with the propagation angle and can be reduced by increasing voltage,temperature and the thickness of graphene platelets.

关键词： Wave propagation Nonlocal strain gradient theory Piezoelectric sandwich nanoplates Graphene platelets

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Deep postbuckling and nonlinear bending behaviors of nanobeams with nonlocal and strain gradient effects

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Applied Mathematics and Mechanics(English Edition) 2019年第4期40卷 515-548页

作者： Bo ZHANG huoming shen Juan LIU Yuxing WANG Yingrong ZHANG School of Mechanics and Engineering Southwest Jiaotong University Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province

In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.

关键词： nanobeam nonlocal strain gradient theory two-step perturbation method,deep postbuckling

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Wave propagation in graphene reinforced piezoelectric sandwich nanoplates via high-order nonlocal strain gradient theory

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Acta Mechanica Sinica 2021年第9期37卷 1446-1456,I0003页

作者： Biao Hu Juan Liu Yuxing Wang Bo Zhang huoming shen Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and EngineeringSouthwest Jiao Tong UniversityChengdu610031China

Αn analytical method is developed to explore the wave propagation characteristics of piezoelectric sandwich nanoplates in the present work.The sandwich nanoplates are composed of a graphene reinforced composite core layer with two piezoelectric surface layers exposed to electric field.The material properties of the nanocomposite layer are given by the Halpin–Tsai model and mixture’s rule.The Euler–Lagrange equation of the nanoplates is obtained by Hamilton's principle and first-order shear deformation theory.Then,combining the high-order nonlocal strain gradient theory with the hygrothermal constitutive relationship of composite nanoplates,the nonlocal governing equations are presented.Finally,numerical studies are conducted to demonstrate the influences of scale parameters,applied external voltage,temperature variation,moisture variation,graphene size,and weight fraction on wave frequency.The results reveal that low-order and high-order nonlocal parameters and length scale parameters have different effects on wave frequency.The wave frequency can be reduced by increasing temperature and the thickness of graphene.This could facilitate the investigation of the dynamic properties of graphene nanocomposite structures.

关键词： Wave propagation High-order nonlocal strain gradient theory Piezoelectric sandwich nanoplates Graphene platelets Hygrothermal environment

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

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Applied Mathematics and Mechanics(English Edition) 2020年第2期41卷 261-278页

作者： Jing WANG Yilin ZHU Bo ZHANG huoming shen Juan LIU School of Mechanical and Electrical Engineering Southwest Petroleum UniversityChengdu 610500China School of Civil Engineering and Architecture Southwest Petroleum UniversityChengdu 610500China School of Mechanics and Engineering Southwest Jiaotong UniversityChengdu 611756China Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province Chengdu 611756China

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.

关键词： scale effect axially moving nanobeam internal resonance critical amplitude

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Nonlinear Bending Analysis of Functionally Graded CNT-Reinforced Shallow Arches Placed on Elastic Foundations

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Acta Mechanica Solida Sinica 2020年第2期33卷 164-186页

作者： Yuanyuan Zhang Bo Zhang huoming shen Yuxing Wang Xin Zhang Juan Liu School of Mechanics and Engineering Southwest Jiaotong UniversityChengdu 611756China Department of Mechanical Engineering Northwestern UniversityEvanstonIL 60208USA

This research explores the nonlinear bending behaviors of functionally graded carbon nanotube-reinforced(FG-CNTR)shallow arches with unmovable simply supported ends and clarnped-clamped ends;these arches are subjected to a uniform radial pressure and rest on a nonlinear elastic foundation.The temperature-dependent material properties of the arches are considered.Within the framework of Reddy shear deformation theory possessing von Karman nonlinearity,the motion equations and boundary conditions for the FG-CNTR arches are determined by the Euler-Lagrange variational principle.Then,a two-step perturbation technique is adopted to determine the load-deflection relationship analytically.To verify the validity of the developed model and related perturbation solutions,a numerical investigation is conducted for shallow arches with five distribution patterns of carbon nanotube(CNT)reinforcements uniaxially aligned in the axial direction.Finally,the influences of various factors,including the elastic foundation,layout type,and volume fraction of CNTs and geometric factors,on the nonlinear behaviors of FG-CNTR shallow arches are examined.The obtained results show that the load deflection curves exhibit less snap-through instability as the CNT volume fraction increases.The transverse shear stress versus the thickness of FG-CNTR shallow arches is markedly affected by the layout type and content of reinforcements.

关键词： Nonlinear bending.Carbon nanotube-reinforced composites Shallow arches Two-step perturbation technique

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多孔功能梯度压电纳米壳中波传播特性

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应用数学和力学 2024年第2期45卷 197-207页

作者：王鑫特刘娟胡彪张波沈火明西南交通大学力学与航空航天学院成都611756

基于非局部应变梯度理论,探究了含孔隙的功能梯度压电陶瓷纳米壳中波传播特性.利用Hamilton原理和一阶剪切理论推导了控制方程.结合非局部应变梯度理论和谐波解得到了尺度依赖的特征方程.数值讨论了尺度参数、波数、梯度指数、壳厚、孔... 详细信息

基于非局部应变梯度理论,探究了含孔隙的功能梯度压电陶瓷纳米壳中波传播特性.利用Hamilton原理和一阶剪切理论推导了控制方程.结合非局部应变梯度理论和谐波解得到了尺度依赖的特征方程.数值讨论了尺度参数、波数、梯度指数、壳厚、孔隙率及电压对波传播特性的影响.研究表明:非局部参数和应变梯度参数对波传播频率的影响与波数密切相关,在一定范围内波数越大,尺度参数对频率的影响越大;另外,孔隙和梯度指数对频率具有耦合作用.

关键词：压电纳米壳波动特性非局部应变梯度理论功能梯度

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