Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory

Microsystem Technologies - A new modeling of nano-mechanical mass sensors constructed from porous nanomaterials is presented based on generalized nonlocal strain gradient theory (NSGT). In this...     

Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

In the present study, nonlinear free and forced vibration of Euler–Bernoulli nanobeam with attached nanoparticle at the free end is investigated based on nonlocal elasticity theory. The effects of the different nonlocal parameters (γ) and mass ratios (α) as well as effects of fixed-free boundary conditions on the vibrations are determined. To obtain the equation of motion of the system, the Hamilton’s principle is employed. The stretching of neutral axis which introduces cubic nonlinearity is included into the equation for deriving nonlinear equation. And also effects of damping and forcing are included into the equations. The approximate solutions of the equations are derived by using the multiple scale method. Fundamental frequencies, frequency shift and mode shapes for the linear problem are estimated for a nonlocal Euler–Bernoulli nanobeam with an attached nanoparticle and graphically represented the frequency shift and mode shapes. Nonlinear frequencies are derived depending on amplitude and phase modulation. Frequency–response curves are drawn for different nonlocal parameters and different modes.

     

Erratum to: Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

Microsystem Technologies -     

Longitudinal vibration analysis of nanorods with multiple discontinuities based on nonlocal elasticity theory using wave approach

Microsystem Technologies - Discontinuities such as cracks and steps on the length, and the mass of attached buckyball on the tip, of nanoresonators have large effects on nanoresonators natural...     

On the use of shape functions in the cell centered finite volume formulation for plate bending analysis based on Mindlin–Reissner plate theory

This paper deals with a new formulation of the cell centered finite volume application for plate bending analysis based on Mindlin–Reissner plate theory. In this formulation shape functions are used to represent the variation of the unknown variables across the control volumes’ faces, which facilitates the calculation of stress resultants on the faces. The performance of the formulation for the computation of displacements and stress resultants for thin and thick plates is evaluated in a number of test problems. This testing reveals that the proposed approach enhances the predictive capability of the finite volume method in the analysis of thin to thick plates.     

Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory

Microsystem Technologies - In this present work the critical loading of magneto-electro-viscoelastic-hygro-thermal (MEVHT) piezoelectric nanoplates embedded in a viscoelastic foundation are...     

Nonlinear resonant behaviors of embedded thick FG double layered nanoplates via nonlocal strain gradient theory

Microsystem Technologies - This research deals with the nonlinear forced vibration behavior of embedded functionally graded double layered nanoplates with all edges simply supported via nonlocal...     

Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory

Microsystem Technologies - This paper develops a nonlocal strain gradient plate model for damping vibration analysis of visco-elastically coupled double-layered graphene sheets. For more accurate...     

Correction to: Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory

Microsystem Technologies - The original version of this article unfortunately contained a mistake. Farzad Ebrahimi was not listed among the authors.     

Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

Free longitudinal vibration analysis of a rotating rod based on the Eringen’s nonlocal elasticity is studied in this paper. Rod is supposed to rotate around a fixed axis with a constant angular velocity. To capture the effect of the rotational motion into analysis of the continuous system, a linear proportional relation is introduced between axial and angular velocities. For the first time the mentioned relation is presented based on the internal motions of the infinitesimal element. This novelty makes the rotational displacement as a dependent function of axial displacement playing a significant role through the analysis. Variational approach is adopted to derive the equations of motion for clamped–clamped and clamped-free boundary conditions. For verification of the results obtained from the Galerkin approach, comparison with technical literature is reported. Finally current results illustrate the dependency of the dynamic-vibration analysis of the presented system on the nonlocality and the rotational velocity parameter. This dependency shows the decrement of the frequency with increment in both the angular velocity and the nonlocal parameter. As a result, the mentioned parameters are key factors in the design and analysis of such systems.

     

Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving and rotating nanobeams based on nonlocal strain gradient theory

Microsystem Technologies - Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving nanobeam and rotating nanobeam based on nonlocal strain gradient theory are...     

Free vibration of laminated plates using a finite strip method based on a higher-order plate theory

The finite strip method based on the higher-order plate theory is developed for determining the natural frequencies of laminated plates. This method can accurately predict the through thickness effect of transverse shear deformation. Furthermore, only a few degress of freedom are required in the finite strip method. Some numerical results for various span-to-thickness ratios, material properties and stack sequences are presented for illustrative purposes. The present model provides a better way to obtain more accurate natural frequency results.     

微型压电层合板结构的振动特性研究

从经典薄板理论出发,基于应变梯度理论,综合考虑尺寸效应和压电效应的影响,利用哈密顿原理建立了微型压电层合板结构的动力学模型及其边界条件.在选取符合其边界条件的模态函数后,利用Ritz法分别研究四边简支和悬臂条件下的微型压电层合板的振动特性,求解了前五阶固有频率并绘制了3D模态图.分析了微尺度带来的尺寸效应对于固有频率的影响,最后研究了外加电压对于系统固有频率的影响.     

Analysis of nonlinear vibration and instability of electrostatic functionally graded micro-actuator based on nonlocal strain gradient theory considering thickness effect

Microsystem Technologies - In this work, we develop a model of an electrostatic functionally graded (FG) micro-actuator based on the nonlocal strain gradient theory (NSGT) incorporated the...     

Dynamics and vibration analysis of suspended microchannel resonators based on strain gradient theory

Microsystem Technologies - In this paper, dynamics of a suspended microchannel resonator (SMR) will be derived using the strain gradient theory. Accordingly, the size dependent governing equation...     

Nonlinear analysis of size-dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory

A nonlocal strain gradient model is developed in this research to analyse the nonlinear frequencies of functionally graded porous curved nanotubes. It is assumed that the curved nanotube is in contact with a two-parameter nonlinear elastic foundation and is also subjected to the uniform temperature rise. The non-classical theory presented for curved nanotubes contains a nonlocal parameter and a material length scale parameter which can capture the size effect. A power law distribution function is used to describe the graded properties through the thickness direction of curved nanotubes. The even dispersion pattern is used to model the porosities distribution. The high-order shear deformation theory and the von Kármán type of geometric non-linearity are utilized to obtain the nonlinear governing equations of the structure. The size-dependent equations of motion for the large amplitude vibrations of curved nanotubes are obtained by employing Hamilton’s principle. The analytical solutions are extracted for the curved nanotube with immovable hinged-hinged boundary conditions. Size-dependent frequencies of the curved nanotube exposed to thermal field are obtained using the two-step perturbation technique and Galerkin procedure. The effects of important parameters such as nonlocal and length scale parameters, temperature field, elastic foundation, porosity, power law index and geometrical parameters are studied in detail.

     

三阶剪切变形板的振动特性研究

对于中厚板或层合板而言,横向剪切变形的影响是显著的,采用三阶剪切变形理论比采用经典薄板理论和一阶剪切变形理论能更好的满足精度的要求,而且能更好地描述板的剪切变形和剪应力沿厚度方向的分布情况.本文用解析的方法研究了简支、自由和固定三种边界条件的任意组合下三阶剪切变形板的自由振动问题.首先应用哈密顿原理建立自由振动方程,再通过引入中间变量使得原来耦合的自由振动方程得到解耦和简化,基于分离变量法,利用边界条件得到基函数的表达式,利用Rayleigh-Ritz法,求得三阶剪切变形板在任意边界条件下的固有频率和振型.本文得到的结果可以为厚板在工程中的应用提供理论依据,具有较高的工程实际应用价值.     

Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory

In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton’s principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums.

     

Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory

Size-dependent Timoshenko and Euler–Bernoulli models are derived for fluid-conveying microtubes in the framework of the nonlocal strain gradient theory. The equations of motion and boundary conditions are deduced by employing the Hamilton principle. A flow-profile-modification factor, which is related to the flow velocity profile, is introduced to consider the size-dependent effects of flow. The analytical solutions of predicting the critical flow velocity of the microtubes with simply supported ends are derived. By choosing different values of the nonlocal parameter and the material length scale parameter, the critical flow velocity of the nonlocal strain gradient theory can be reduced to that of the nonlocal elasticity theory, the strain gradient theory, or the classical elasticity theory. It is shown that the critical flow velocity can be increased by increasing the flexural rigidity, decreasing the length of tube, decreasing the mass density of internal flow, or increasing the shear rigidity. The critical flow velocity can generally increase with the increasing material length scale parameter or the decreasing nonlocal parameter. The flow-profile-modification factor can decrease the critical flow velocity. The critical flow velocity predicted by classical elasticity theory is generally larger than that of nonlocal strain gradient theory when considering the size-dependent effect of flow.     

Free vibration analysis of double-viscoelastic nano-composite micro-plates reinforced by FG-SWCNTs based on the third-order shear deformation theory

Microsystem Technologies - In this paper, free vibration analysis of a double viscoelastic nano-composite plate system reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNT)...