Size-Dependent Strain Gradient-Based Thermoelastic Damping in Micro-Beams Utilizing a Generalized Thermoelasticity Theory

2019 ◽  
Vol 11 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Vahid Borjalilou ◽  
Mohsen Asghari
Keyword(s):  
Heat Conduction ◽  
Strain Gradient ◽  
Scale Effects ◽  
Generalized Thermoelasticity ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Phase Lag ◽  
Thermoelastic Damping ◽  
Coupled Equations

The small-scale effects on the thermoelastic damping (TED) in Euler–Bernoulli micro-beams is investigated in this study. To this purpose, by utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model, the coupled equations of motion and heat conduction are derived. By solving these equations simultaneously and using the Galerkin method, the real and imaginary parts of the frequency and the amount of TED in thin micro-beams are obtained. The results predicted by SGT are compared with those given by the modified couple stress theory (MCST) and the classical continuum theory. In addition, TED is calculated on the basis of energy dissipation approach which shows that the difference between the obtained results and those evaluated based on the frequency approach is negligible. Some numerical results are also presented in order to study the effects of different parameters of the micro-beams as well as the type of the boundary conditions on TED and the critical thickness; these parameters include the micro-beam height, its aspect ratio and type of the material.

Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect

2020 ◽  
Vol 26 (11-12) ◽  
pp. 1042-1053 ◽  
Author(s):  
Vahid Borjalilou ◽  
Mohsen Asghari ◽  
Ehsan Taati
Keyword(s):  
Heat Conduction ◽  
Continuum Mechanics ◽  
Scale Effects ◽  
Small Scale ◽  
Phase Lag ◽  
Dual Phase ◽  
Complex Frequency ◽  
Thermoelastic Damping ◽  
Coupled Equations ◽  
The Continuum

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To clarify the influence of nonlocality and dual-phase-lagging on the amount of thermoelastic damping, numerical results are compared with the ones predicted in the framework of classical continuum and heat conduction theories. Findings reveal that the size effect on both the continuum mechanics and heat conduction modeling of nanobeams is not negligible. A number of parametric studies are also conducted to indicate the effect of beam dimensions, boundary conditions and type of material on the value of thermoelastic damping.

Mechanical Behavior of Functionally Graded Nano-Cylinders Under Radial Pressure Based on Strain Gradient Theory

2018 ◽  
Vol 35 (4) ◽  
pp. 441-454 ◽  
Author(s):  
M. Shishesaz ◽  
M. Hosseini
Keyword(s):  
Mechanical Behavior ◽  
Strain Gradient ◽  
Material Properties ◽  
Scale Effects ◽  
Radial Pressure ◽  
Functionally Graded ◽  
High Order ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory

ABSTRACTIn this paper, the mechanical behavior of a functionally graded nano-cylinder under a radial pressure is investigated. Strain gradient theory is used to include the small scale effects in this analysis. The variations in material properties along the thickness direction are included based on three different models. Due to slight variations in engineering materials, the Poisson’s ratio is assumed to be constant. The governing equation and its corresponding boundary conditions are obtained using Hamilton’s principle. Due to the complexity of the governed system of differential equations, numerical methods are employed to achieve a solution. The analysis is general and can be reduced to classical elasticity if the material length scale parameters are taken to be zero. The effect of material indexn, variations in material properties and the applied internal and external pressures on the total and high-order stresses, are well examined. For the cases in which the applied external pressure at the inside (or outside) radius is zero, due to small effects in nano-cylinder, some components of the high-order radial stresses do not vanish at the boundaries. Based on the results, the material inhomogeneity indexn, as well as the selected model through which the mechanical properties may vary along the thickness, have significant effects on the radial and circumferential stresses.

Small-Scale Effects on the Buckling of Skew Nanoplates Based on Non-Local Elasticity and Second-Order Strain Gradient Theory

2017 ◽  
Vol 34 (4) ◽  
pp. 443-452 ◽  
Author(s):  
B. Shahriari ◽  
S. Shirvani
Keyword(s):  
Strain Gradient ◽  
Scale Effects ◽  
Buckling Load ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Gradient Theory ◽  
Vast Number ◽  
Non Local ◽  
The Galerkin Method

AbstractIn recent years, nanostructures have been used in a vast number of applications, making the study of the mechanical behaviour of such structures important. In this paper, two different constitutive equations including first-order strain gradient and simplified differential non-local are employed to model the buckling behaviour of skew nanoplates. The Galerkin method is used for solving the equations in order to obtain buckling load. Using this method, the influence of different parameters consisting of non-classical properties, boundary conditions, and geometrical parameters such as length and angle on the buckling load, are studied. The results showed that small-scale effects are very important in skew graphene sheets and their inclusion results in smaller buckling loads.

Nonlinear Pull-In Instability of Strain Gradient Microplates Made of Functionally Graded Materials

2019 ◽  
Vol 19 (02) ◽  
pp. 1950007 ◽  
Author(s):  
R. Gholami ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Functionally Graded Materials ◽  
Strain Gradient ◽  
Scale Effects ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
First Order ◽  
Size Dependent

In this paper, the size-dependent nonlinear pull-in behavior of rectangular microplates made from functionally graded materials (FGMs) subjected to electrostatic actuation is numerically studied using a novel approach. The small scale effects are taken into account according to Mindlin’s first-order strain gradient theory (SGT). The plate model is formulated based on the first-order shear deformation theory (FSDT) using the virtual work principle. The size-dependent relations are derived in general form, which can be reduced to those based on different elasticity theories, including the modified strain gradient, modified couple stress and classical theories (MSGT, MCST and CT). The solution of the problem is arrived at by employing an efficient matrix-based method called the variational differential quadrature (VDQ). First, the quadratic form of the energy functional including the size effects is obtained. Then, it is discretized by the VDQ method using a set of matrix differential and integral operators. Finally, the achieved discretized nonlinear equations are solved by the pseudo arc-length continuation method. In the numerical results, the effects of material length scale parameters, side length-to-thickness ratio and FGM’s material gradient index on the nonlinear pull-in instability of microplates with different boundary conditions are investigated. A comparison is also made between the predictions by the MSGT, MCST and CT.

Flexural Vibration Characteristics of Micro-Rotors Based on the Strain Gradient Theory

2015 ◽  
Vol 07 (05) ◽  
pp. 1550075 ◽  
Author(s):  
Mohsen Asghari ◽  
Mehdi Hashemi
Keyword(s):  
Strain Gradient ◽  
Natural Frequencies ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Complex Form ◽  
Flexural Vibration ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Rotating Shaft

In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation. Parametric studies on the results for different responses illustrate that the values of higher-order material constants may have significant effects on the natural frequencies of the system.

Bifurcation and chaos of axially moving nanobeams considering two scale effects based on non-local strain gradient theory

2021 ◽  
pp. 2140010
Author(s):  
Jing Wang ◽  
Huoming Shen ◽  
Bo Zhang ◽  
Jianqiang Sun ◽  
Yuanyuan Zhang
Keyword(s):  
Strain Gradient ◽  
Scale Effects ◽  
Period Doubling ◽  
Local Strain ◽  
Strain Gradient Theory ◽  
Discrete Equation ◽  
Gradient Theory ◽  
Scale Parameters ◽  
Non Local ◽  
Axially Moving

The nonlinear vibration of axially moving nanobeams at the microscale exhibits remarkable scale effects. A model of an axially moving nanobeam is established based on non-local strain gradient theory and considering two scale effects. The discrete equation of a non-autonomous planar system is obtained using the Galerkin method. The response characteristics of the system are determined using phase diagrams and Poincaré sections, and the effects of the scale parameters on the form of the motion are analyzed. The results show that as the non-local parameter and the material characteristic length parameter vary, the system undergoes multiple forms of motion, including periodic, period-doubling and chaotic motions. Two routes to chaos — period-doubling bifurcation and intermittent chaos — are identified in the variation ranges of the two scale parameters.

Stress Analysis of a Functionally Graded Micro/ Nanorotating Disk with Variable Thickness Based on the Strain Gradient Theory

2016 ◽  
Vol 08 (02) ◽  
pp. 1650020 ◽  
Author(s):  
M. Baghani ◽  
N. Heydarzadeh ◽  
M. M. Roozbahani
Keyword(s):  
Variable Thickness ◽  
Strain Gradient ◽  
Mechanical Response ◽  
Rotating Disk ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
Remarkable Effect

In this paper, mechanical response of a micro/nanorotating disk made of functionally graded materials (FGMs) with variable thickness is investigated. Through utilizing variational method and considering the strain gradient theory, the governing equations and the boundary conditions are derived. In order to verify the developed formulation, in special limiting cases, the results are compared with those available in the literature. These comparisons show an excellent correspondence. Employing numerical techniques, some numerical results are presented to investigate the effect of variations of properties and thickness on the response of the small scale rotating disk. It is found that the non-homogeneity constants have a remarkable effect on the stress distribution in the FG rotating disk. Furthermore, the amount of stress could be reduced in the rotating disk through fabricating it with variable thickness.

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