Size-dependent in vibration analysis of magnetostrictive sandwich composite micro-plate in magnetic field using modified couple stress theory

2017 ◽  
Vol 21 (2) ◽  
pp. 580-603 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
H Khani Arani ◽  
Z Khoddami Maraghi
Keyword(s):  
Magnetic Field ◽  
Couple Stress Theory ◽  
Composite Fiber ◽  
Modified Couple Stress Theory ◽  
Sandwich Composite ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Stress Theory ◽  
Fiber Angle ◽  
Modified Couple Stress

In the present study, free vibration of magnetostrictive sandwich composite micro plate with magnetostrictive core and composite face sheets are investigated. The modified couple stress theory is taken into account so as to consider the small scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of both damping and shear effects. Using energy method, Hamilton’s principle and first-order shear deformation theory, the governing equations of motion and related boundary conditions are obtained. Finally, the differential quadrature method is employed to analysis the vibration of magnetostrictive sandwich composite micro plate. In this regard, the dimensionless frequency are plotted to study the effects of small scale parameter, surrounding elastic medium, magnetic field, composite fiber angle, aspect ratio, thickness ratio, and boundary conditions. The results indicate that the magnetic field and composite fiber angle play a key role in the dimensionless frequency of magnetostrictive sandwich composite micro plate. The obtained results in this article can be used to design sensors and actuators, aerospace industry, and control of vibration response of systems.

Nonlinear free vibration and damping analysis of a microbeam with pseudoelastic shape memory alloy layer based on the modified couple stress theory

2020 ◽  
pp. 107754632093528
Author(s):  
Mohammad Javad Ashrafi ◽  
Iman Ghaffari ◽  
Mohammad Elahinia ◽  
Mohammad Reza Nematollahi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Alloy Layer ◽  
Sandwich Composite ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length

The aim of this investigation is to evaluate the size effects on the nonlinear free vibration of the sandwich composite microbeam with an extensible shape memory alloy layer in the midplane. A one-dimensional constitutive model is considered to simulate the pseudoelastic behavior of the shape memory alloy layer. The governing equation of motion is derived using the Euler–Bernoulli beam theory together with the modified couple stress theory through the Hamilton’s principle. Midplane stretching and phase transformation of the shape memory alloy which are sources of nonlinearity were considered, and a numerical solution method is presented. A damped response of the sandwich composite microbeam is observed because of the hysteresis behavior of the extensible shape memory alloy layer in the midplane. Results are appraised by comparing with the available literature. The influence of material length scale, temperature, and initial velocity on the loss factor and other pivotal vibrational behavior is evaluated. Results show that increasing the material length scale to thickness ratio has a decreasing effect on damping capacity.

scholarly journals Free Vibration Analysis of Shear Deformable Small-Scale Tubes

2020 ◽  
Vol 3 (1) ◽  
pp. 418-427
Author(s):  
Reza Aghazadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Tube Model ◽  
Stress Theory ◽  
Modified Couple Stress

This study presents an approach for investigating free vibration problem of small-scale tubes based on modified couple stress theory in conjunction with higher order shear deformation tube model. The size effect is captured through utilization of a length scale parameter involved in modified couple stress theory. A newly developed refined tube model is employed to satisfy friction-free conditions on inner and outer surfaces of micro-tubes. Hamilton’s principle is used as a variational technique for derivation of governing system of equations. For axial vibrations, an analytical procedure is conducted, while for transverse vibrations differential quadrature method is used as a numerical technique. The correctness of numerical results are verified through comparisons made with results which are available in the literature for limiting cases. The analyses reveal the effects of size and transverse shear deformation on the natural frequencies of micro-tubes.

Effects of couple stresses on the in-plane vibration of micro-rotating disks

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1246-1259
Author(s):  
Emadoddin Bagheri ◽  
Mostafa Jahangiri ◽  
Mohsen Asghari
Keyword(s):  
Free Vibration ◽  
Mechanical Behavior ◽  
Couple Stress ◽  
Scale Effects ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Rotating Disks ◽  
Stress Theory ◽  
Modified Couple Stress

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential motion of the disk particles with their corresponding boundary conditions are derived. Then, the solution for the boundary value problem is analytically presented. The effects of the angular speed of the micro-disks and the length scale parameter of the modified couple stress theory on the steady radial and tangential displacements, and on the natural frequencies are investigated. Those results are compared with the ones previously obtained from the classical continuum mechanics analysis.

Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method

2016 ◽  
Vol 231 (20) ◽  
pp. 3866-3885 ◽  
Author(s):  
M Mohammadimehr ◽  
S Shahedi ◽  
B Rousta Navi
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Longitudinal Magnetic Field ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Sandwich Beam ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Generalized Differential

In this paper, the magneto-mechanical nonlinear vibration behavior of rectangular functionally graded carbon nanotube reinforced composite (FG-CNTRC) sandwich Timoshenko beam based on modified couple stress theory (MCST) is investigated by the generalized differential quadrature method. The FG-CNTRC sandwich beam consists of two FG-CNTRC face sheets and homogenous core subjected to longitudinal magnetic field. In the FG-CNTRC face sheets, carbon nanotubes are disseminated in different patterns as uniform distribution, FG-X, FG-V, and FG-O. Based on von Kármán geometric nonlinearity, the nonlinear governing equations are derived by the Hamilton’s principle. Accuracy and convergence of this study are validated by comparing the numerical results with those found in literature. Various parameters effects are examined on the nonlinear 1st frequency of the sandwich beam. The results reveal that composition of the CNTRC face sheets and homogenous core in sandwich beam can be achieved remarkable stiffness in comparison to only CNTRC beam or only homogenous beam. For achieving the highest stiffness of FG-CNTRC sandwich beam, the value of thickness ratio is obtained about 0.34 and 0.27 in the presence and absence of Pasternak foundation, respectively. Moreover, the linear and nonlinear 1st frequencies increase with an increase in the magnetic field for all of CNT distribution types of sandwich beam and different boundary conditions whereas the frequency ratio decreases. Also the highest and lowest nonlinear 1st frequencies are corresponding to FG-A and FG-V distributions of CNT in face sheets, respectively.

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