Nonlinear resonance responses of size-dependent functionally graded cylindrical microshells with thermal effect and elastic medium

The nonlinear resonance responses of functionally graded (FG) cylindrical microshells with the elastic medium is investigated by considering thermal and scale effects. First, using the modified couple stress theory, the nonlinear dynamics model for FG microshell are established. Then the reduced nonlinear differential equations are derived by Galerkin’s method and static condensation. Finally, subharmonic, superharmonic and primary resonances of FG cylindrical microshells are analyzed by a perturbation method. In addition, the bifurcation characteristics of the nonlinear dynamic responses are investigated by some numerical examples. The effects of key parameters (modal damping, excitation frequency, foundation medium, scale parameter and thermal effect) on the nonlinear resonance responses are also discussed by numerical simulation.

     

Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform micro-tube

In this paper, to improve the vibrational response of microstructures, the impact of the nonlinear modal analysis of axially functionally graded (AFG) truncated conical micro-scale tube including the thermal loading for the different type of cross sections such as uniform section, linear tapered section, convex section, the exponential section are studied that are applicable for various application, for example, the micro-thermal fins, macro-/micro-fluid-flow diffuser, fluid-flow nozzle, fluid-flow throat, micro-sensor, etc. The nonlinear equations are obtained applying Hamilton’s principles based on the modified couple stress to determine the size effect and Euler–Bernoulli beam theory considering the von-Kármán’s nonlinear strain. The material combination varies along the tube’s length, denouncing the AFG tube made by metal and ceramic phases. The nonlinear equations are solved by applying a couple of homotopy perturbation methods (HPM) to calculating the nonlinear results and the generalized differential quadrature method (GDQM) to providing the initial conditions. The linear and nonlinear results presented the effect of various cross sections and other parameters on the micro-tube frequency that are valuable to design and manufacture the micro-electro-mechanical systems (MEMS).

     

Size dependency in nonlinear instability of smart magneto-electro-elastic cylindrical composite nanopanels based upon nonlocal strain gradient elasticity

In the present article, a new size-dependent panel model is established incorporating the both hardening-stiffness and softening-stiffness small scale effects jointly with electrostatics and magnetostatics to study analytically the buckling and postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanopanels under combination of axial compression, external electric and magnetic potentials. To this end, the nonlocal strain gradient elasticity theory in conjunction with the Maxwell equations is applied to the classical panel theory to develop a more comprehensive size-dependent panel model including simultaneously the both nonlocality and strain gradient size dependency. With the aid of the virtual work’s principle, the size-dependent differential equations of the problem are derived. The attained non-classical governing differential equations are solved analytically by means an improved perturbation technique within the framework of the boundary layer theory of shell buckling. Explicit analytical expressions associated with the nonlinear axial stability equilibrium paths of the electromagnetic actuated smart MEE composite nanopanels including nonlocality and strain gradient micro-size dependency are proposed. It is displayed that the nonlocal size effect leads to reduce the buckling stiffness, while the strain gradient size dependency causes to enhance it. Moreover, it is found that by applying a negative electric field as well as positive magnetic field, the influences of the nonlocal and strain gradient size effects on the critical buckling load of an axially loaded MEE composite nanopanel are more significant.

     

Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams

In this paper, free and forced vibration analysis of viscoelastic microcomposite beam reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) is studied using the modified couple stress theory (MCST). The material properties of micro composite beam by generalized rule of mixtures carbon nanotubes are estimated. In addition, these properties are stated as uniform, and functionally graded (FG) distributions in the thickness direction. Energy method and Hamilton’s principle are employed to establish the governing equations of motion for the vibration of viscoelastic damped micro composite beam reinforced by SWCNTs based on the Kelvin–Voigt model. The influences of material length scale parameter, structural damping coefficient and different distributions of SWCNTs on non-dimensional complex natural frequency and amplitude vibration of the viscoelastic micro composite beam are investigated. The results reveal that the lowest vibration amplitude of FG microcomposite beam by the FG-X and the highest occurs by FG-◊. Moreover, in the presence of external periodic load and the absence of structural damping coefficient, the vibration amplitude increases and FG microcomposite beam becomes unstable, even though the amplitude of vibration decreases with increasing structural damping coefficient. It is shown that the natural frequency of SWCNT reinforced composite is more than the frequency of multi-walled carbon nanotubes because SWCNT have more stiffness. In addition, the results illustrate that the experimental data by Lei et al. agree well with those predicted by the MCST in the present work.

     

Terfenol-D/SAW谐振器/Terfenol-D复合磁传感器

设计了一种由超磁致伸缩材料Terfenol-D和SAW谐振器构成的复合磁传感器,在磁场作用下,Terfenol-D沿长度方向伸缩,并将应力应变传递至SAW谐振器,使其产生应变,造成谐振频率改变,通过测量SAW谐振器谐振频率的变化来测量磁场强度.分析了该磁传感器的传感原理,建立了该复合磁传感器的静态模型,对弹性敏感元件进行了受力分析,根据压磁方程和受力平衡得到该磁传感器的静态特性.实验结果表明:该复合磁传感器灵敏度可达341.6Hz/Oe,较Terfenol-D/SAW谐振器结构灵敏度提高了3倍;测量谐振频率的分辨率为1Hz,SAW谐振器频率稳定度为0.1×10-6时,该磁传感器对磁场的分辨率为10-6T.     

On the interdependency of primary and initial secondary equilibrium paths in sensitivity analysis of elastic structures

The scientific motivation for this paper is lack of clarity about the interdependency of primary and initial secondary equilibrium paths in the frame of sensitivity analysis of elastic structures. The investigation of this interdependency comprises of the following four cases: (1) nonlinear primary path, nonlinear stability problem, (2) linear primary path, nonlinear stability problem, (3) nonlinear primary path, linear stability problem, and (4) linear primary path, linear stability problem. The consistently linearized eigenproblem is used for differentiation of two classes of nonlinear stability problems with markedly different characteristics of both the prebuckling and the postbuckling behavior. For one of them, e.g. zero-stiffness postbuckling is impossible. For the other one, which is restricted to a prebuckling regime with axial deformations only, sensitivity analysis of the initial postbuckling behavior either exhibits its continuous improvement or its continuous deterioration, depending on whether the bifurcation point diverges from or converges to the snap-through point. In other words, a monotonic variation of the design parameter cannot result in a non-monotonic change of the initial postbuckling behavior. The practical motivation for this work is to explore the mechanical reasons for qualitatively different modes of transition from imperfection sensitivity to insensitivity in the course of sensitivity analysis for the purpose of improving the postbuckling behavior of structures by means of minor design changes. Results from a numerical investigation corroborate the theoretical findings.     

Nonlinear torsional buckling and postbuckling analysis of cylindrical silicon nanoshells incorporating surface free energy effects

In the present study, a size-dependent shell model is developed which can afford to describe the nonlinear torsional buckling and postbuckling characteristics of cylindrical nanoshells in the presence of surface stress effects. To accomplish this purpose, the Gurtin–Murdoch theory of elasticity together with the von Karman geometric nonlinearity is implemented into the first-order shear deformation shell theory. A linear variation through the thickness is considered for the normal stress component of the bulk to satisfy the balance conditions on the free surfaces of the nanoshell. By means of the virtual work principle, the non-classical governing differential equations are constructed in which the transverse displacement and Airy stress function are considered as independent variables. Thereafter, a boundary layer theory is employed including the effect of surface stress in conjunction with the nonlinear prebuckling deformations and the large postbuckling deflections. Subsequently, an efficient solution methodology based on an improved perturbation technique is put to use to obtain the size-dependent critical torsional buckling loads and the associated postbuckling equilibrium paths. It is observed that the torsional load exhibits a significant increase after reaching the minimum postbuckling load. Also, it is revealed that the effect of surface stress becomes negligible at high values of the deflection.

     

An efficient size-dependent shear deformable shell model and molecular dynamics simulation for axial instability analysis of silicon nanoshells

Understanding the size-dependent behavior of structures at nanoscale is essential in order to have an effective design of nanosystems. In the current investigation, the surface elasticity theory is extended to study the nonlinear buckling and postbuckling response of axially loaded silicon cylindrical naoshells. Thereby, an efficient size-dependent shear deformable shell model is developed including the size effect of surface free energy. A boundary layer theory of shell buckling in conjunction with a perturbation-based solution methodology is employed to predict the size dependency in the buckling loads and postbuckling behavior of silicon nanoshells having various thicknesses. After that, on the basis of the Tersoff empirical potential, a molecular dynamics (MD) simulation is performed for a silicon cylindrical nanoshell with thickness of four times of silicon lattice constant, the critical buckling load and critical shortening of which are extracted and compared with those of the developed non-classical shell model. It is demonstrated that by taking the effects of surface free energy into account, a very good agreement is achieved between the results of the developed size-dependent continuum shell model and those of MD simulation.     

用微分求积法分析轴向移动粘弹性梁的非平面非线性振动

用微分求积法分析了轴向移动粘弹性梁非平面非线性振动的动力学行为.轴向移动粘弹性梁非平面非线性振动的数学模型是一非常复杂的非线性偏微分方程组.首先用微分求积法对其控制方程组进行空间离散,得到非线性常微分方程组,然后求解常微分方程组得到数值结果.在数值结果的基础上结合非线性动力学理论,利用分叉图、时间历程图、相图对其非线性动力学特性进行了分析.     

Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed

Qualitative aspects of parametric excitation due to the non-constant traveling velocity of a viscoelastic string are investigated. The problem considered is an initially stressed viscoelastic string subjected to steady-state and harmonic variation of axially traveling motion. The string material is considered as a Violet element in series with a spring (three-parameter model). The partial differential equation of motion is derived first, and then is reduced to be a set of third-order nonlinear ordinary differential equations by applying Galerkin's method. Finally, the effects of elastic and viscoelastic parameters, constant and non-uniform transport speed, wave propagation speed ratio, and nonlinear terms on the transient amplitudes are investigated numerically.     

Optimization of nonhomogeneous facesheets in composite sandwich plates

The optimal design of composite sandwich plates in which the facesheets are composed of a carbon fiber/epoxy net is considered. The objective of the work is to obtain minimum mass designs while maintaining constraints on the first natural frequency and selected facesheet stress components. The facesheets are assumed to be composed of an orthotropic net of unidirectional composite fiber strips and the optimal design (the least mass design) is achieved by changing the strip widths and the spacings between them. It is demonstrated that varying the spatial fiber strip distribution can lead to significant structural advantages; in the example presented, a 32% facesheet mass reduction is achieved.     

粘弹性传动带非线性振动实验研究

利用实验方法研究粘弹性传动带的非线性振动.实验装置中的粘弹性传动带是同步带,通过伺服电机进行驱动,当电动机转速在某一恒定值上下变动时,带中的张紧力也会呈现周期性变化.通过改变传动带中张紧力的频率和幅值,得到了粘弹性传动带的频率响应曲线和周期运动、倍周期运动以及混沌运动的波形图和相图.     

Optimum design and evaluation of stiffened panels with practical loading

Optimum design of a blade-stiffened panel of composite/honeycomb sandwich construction and a metal T-stiffened panel is considered using the buckling and strength constraint program VICONOPT. Both panels have practical loadings which produce a nonlinear out-of-plane bending moment, calculated using beam-column expressions. Large deflection finite element analysis of the optima shows that modifications to these expressions are necessary when the panels are shear loaded. The use of integrally machined stiffeners, as opposed to a conventional, built-up panel designed using PANDA2, is shown to permit 20% mass saving when the latter has no postbuckling strength and 3% saving when postbuckling strength is allowed for.     

磁致/压电/磁致层合材料磁电响应分析

对沿长度方向振动(LT模式)的磁致/压电/磁致(MPM)层合材料的磁电响应进行了理论分析,其中磁致层沿长度方向磁化,压电层沿厚度方向极化.从压电效应和压磁效应本构方程出发,结合材料的机械运动学方程和电路状态方程,重新推导了LT模式下MPM结构的等效电路,完善了文献中的方法,得到了复合材料的磁电电压系数、开路电流、材料内阻、可供电功率与压电、磁致材料各物理参数以及体积参数之间的关系式.以Terfenol-D/PZT/Terfenol-D层合材料为例,对材料磁电响应进行了数值计算,将计算结果与相关实验结果进行了比较.利用磁电响应仿真结果,对磁电层合材料用于磁敏传感器以及自供电换能器进行了讨论.     

RETRACTED ARTICLE: Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM

In this research, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid nano-composite reinforced disk in the thermal environment and subject to a harmonic external load. Using Hamilton’s principle and the von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disk subject to harmonic excitation. The fundamental and golden results of this paper could be that in the lower value of the external harmonic force, different FG patterns do not have any effects on the motion response of the structure. But, for the higher value of external harmonic force and all FG patterns, the chaos motion could be seen and for the FG-X pattern, the chaosity is more significant than other patterns of the FG. As a practical designing tip, it is recommended to choose plates with lower thickness relative to the outer radius to achieve better vibration performance.

     

轴向拉力对变速运动黏弹性梁参激振动稳定性的影响

研究了变速轴向运动黏弹性梁参激振动受拉力扰动时在主参数共振和组合参数共振范围内的稳定性.轴向运动梁的黏弹性本构关系引入了物质时间导数.当参激频率接近某一阶固有频率2倍时将发生主参数共振；当参激频率接近某两阶固有频率之和时将发生组合参数共振.运用多尺度法,直接求解轴向运动梁的控制方程,导出了稳定性边界方程.最后,通过数值...     

用微分求积法分析轴向加速粘弹性梁的非线性动力学行为

用微分求积数值方法求解了轴向加速粘弹性梁的横向振动控制方程,其方程是一复杂的非线性偏微分方程.并在数值结果的基础上利用分叉图分析了轴向定常加速度以及轴向加速度变化幅值对轴向加速粘弹性梁的非线性动力学行为的影响.     

Optimum design of stiffened cylindrical shells with natural frequency constraints

The design optimization of axially loaded, simply supported stiffened cylindrical shells for minimum mass is considered. The design variables are thickness of shell wall, thicknesses and depths of rings and stringers, number/spacing of rings and stringers. Natural frequency, local and overall buckling strengths and direct stress constraints are considered in the design problems. Three different combinations of stiffeners are considered. In each case, the independent effects of behaviour constraints are also studied. The optimum designs are achieved with one of the standard nonlinear constrained optimization techniques (Davidon-Fletcher-Powell method with interior penalty function formulation) and few optimal solutions are checked for the satisfaction of Kuhn-Tucker conditions.     

Nonlinear and postbuckling analyses of curved composite panels subjected to combined temperature change and edge shear

The results of a detailed study of the nonlinear and postbuckling responses of curved unstiffened composite panels with central circular cutouts are presented. The panels are subjected to uniform temperature change and an applied in-plane edge shear loading. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. Numerical results are presented for cylindrical panels with central circular cutouts and are subjected to uniform temperature change and an applied in-plane edge shear loading. The results show the effects of variations in the panel curvature, hole diameter, laminate stacking sequence and fiber orientation, on the nonlinear and postbuckling panel responses, and their sensitivity to changes in the various panel, layer and micromechanical parameters.     

Chaotic oscillations of viscoelastic microtubes conveying pulsatile fluid

As the first endeavour, the influence of a pulsatile flow on the large-amplitude bifurcation behaviour of viscoelastic microtubes subject to longitudinal pretention is studied with special consideration to chaos. The viscoelastic microtube is surrounded by a nonlinear spring bed. A modified size-dependent nonlinear tube model is developed based on a combination of the couple stress theory and the Euler–Bernoulli theory. Hamilton’s principle, as an equation derivation technique, and Galerkin’s procedure, as a discretisation technique, are used. Finally, the discretised differential equations of the pulsatile fluid-conveying viscoelastic microscale tube are solved using a time-integration approach. It is investigated that how the bifurcation response for both motions along the axial and transverse axes is highly dependent of the mean value and the amplitude of the speed of the pulsatile flow.