Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method

2020 ◽  
pp. 107754632094908
Author(s):  
Mehdi Mohammadimehr ◽  
Mojtaba Mehrabi ◽  
Fatemeh S Mousavinejad
Keyword(s):  
Magnetic Field ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Graphene Platelet ◽  
Graphene Platelets ◽  
Equations Of Motions

This article discusses about vibration analysis of single-/three-layered microsandwich Timoshenko beams with porous core and graphene platelet–reinforced composite face sheets under magnetic field and elastic foundation based on the modified strain gradient theory. It is assumed that the material properties of matrix and reinforcement vary in thickness directions. Hamilton’s principle based on the energy approach is used to obtain the governing equations of motions. The equations of motions are solved using a numerical differential quadrature method for various boundary conditions. The obtained results of this study are compared with other previous research studies, and there is a good agreement between them. Moreover, the effects of different parameters such as length-to-thickness ratio, magnetic field, various distributions of graphene platelets and porous beams, and volume fractions of graphene platelets are studied on the dimensionless natural frequencies. In fact, the main idea of this work is combination of structure reinforcement with magnetic field and graphene platelets on the sandwich porous beams at microscale, and the effects of these parameters are developed on the dimensionless natural frequencies of the microbeam. The results of the present study demonstrate that applying magnetic field and increasing its intensity lead to enhance the natural frequency. Also, it is showed that graphene platelet reinforcement with one percent of weight fraction has an effective effect on the increasing dimensionless natural frequencies of the microporous beam. Thus, it can be predicted that graphene platelets can be used instead of nanotubes because they do not have the problem of nanotube accumulation and they are more economical than nanotubes.

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

2021 ◽  
pp. 095440622110458
Author(s):  
Vahid Movahedfar ◽  
Mohammad M Kheirikhah ◽  
Younes Mohammadi ◽  
Farzad Ebrahimi
Keyword(s):  
Nonlinear Vibration ◽  
Material Properties ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Scale Parameters ◽  
Functionally Graded Piezoelectric ◽  
Doubly Curved

Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

NONLINEAR STRAIN GRADIENT THEORY BASED VIBRATION AND INSTABILITY OF BORON NITRIDE MICRO-TUBES CONVEYING FERROFLUID

2014 ◽  
Vol 06 (05) ◽  
pp. 1450060 ◽  
Author(s):  
ALI GHORBANPOUR ARANI ◽  
ABDOLREZA JALILVAND ◽  
REZA KOLAHCHI
Keyword(s):  
Magnetic Field ◽  
Boron Nitride ◽  
Boundary Conditions ◽  
Electric Fields ◽  
Strain Gradient ◽  
Differential Quadrature Method ◽  
Fluid Velocity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlinear Frequency

Nonlinear vibration and instability of a boron nitride micro-tube (BNMT) conveying ferrofluid under the combined magnetic and electric fields are investigated. Based on Euler–Bernoulli beam (EBB), piezoelasticity strain gradient theory and Hamilton's principle, high order equations of motion are derived for three boundary conditions namely as clamped–clamped (C–C), simply–simply (S–S) and clamped–simply (C–S). The differential quadrature method (DQM) is applied to discretize the motion equations in order to obtain the nonlinear frequency and critical fluid velocity using a direct iterative method. A detailed parametric study is conducted to elucidate the influences of the various boundary conditions, size diameter and magnetic field on vibrational characteristic of BNMT. Numerical results indicate that the effect of magnetic field appears in higher speed of ferrofluid and increases the critical velocity or enlarges the stability region. The results are in good agreement with the previous researches. The results of this study can be used to manufacture smart micro/nano electromechanical systems in advanced biomechanics applications with magnetic and electric fields as parametric controllers.

Vibration analysis of graphene sheets resting on the orthotropic elastic medium subjected to hygro-thermal and in-plane magnetic fields based on the nonlocal strain gradient theory

2017 ◽  
Vol 232 (13) ◽  
pp. 2469-2481 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Magnetic Field ◽  
Graphene Sheet ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Nonlocal Parameter ◽  
Strain Gradient Theory ◽  
Graphene Sheets ◽  
Gradient Theory ◽  
Governing Equations ◽  
Nonlocal Strain Gradient

This paper develops a nonlocal strain gradient plate model for vibration analysis of the graphene sheets under in-plane magnetic field and hygro-thermal environments. For more accurate analysis of the graphene sheets, the proposed theory contains two-scale parameters related to the nonlocal and strain gradient effects. The graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton’s principle. Galerkin’s method is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as moisture concentration rise, temperature rise, nonlocal parameter, length scale parameter, elastic foundation, and magnetic field on vibration characteristics of the graphene sheets are examined.

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

2017 ◽  
Vol 21 (1) ◽  
pp. 175-210 ◽  
Author(s):  
A Jamalpoor ◽  
M Bahreman ◽  
M Hosseini
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Free Transverse Vibration ◽  
Foundation Parameters

In this paper, an analytical process is proposed to investigate the size-dependent free vibration of orthotropic multi-viscoelastic microplate systems (OMVMPS) embedded in Kelvin–Voigt visco-Pasternak medium according to the modified strain gradient theory. Governing equations of motion in the partial form and the related boundary conditions are derived by utilizing the Kirchhoff plate theory and Hamilton’s variational principle. The two different sorts of “chain” boundary conditions like “clamped Chain” and “free chain” systems are considered for the ends of microplate system. Navier’s method, which convinces that the simply supported boundary conditions and trigonometric methods are applied to analytically investigate the size effect of the natural frequencies of OMVMPS. The numerical outcomes are offered to report the variation of OMVMPS natural frequencies with the numerous amounts of the microplate numbers, the length scale parameter, aspect ratio, visco-Pasternak foundation parameters, the thickness of microplate, and higher modes number. Several numerical outcomes of this research depict that when the number of microplates is low, there is a significant distinction between natural frequencies achieved for “clamped chain” and “free chain” systems. Also, it is demonstrated that by increasing the number of microplates, the effect of the visco-Pasternak substrate on the natural frequency of system vibration decreases.

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