Thermal effect on dynamics of thin and thick composite laminated microbeams by modified couple stress theory for different boundary conditions

2016 ◽  
Vol 122 (12) ◽  
Author(s):  
Majid Ghadiri ◽  
Asghar Zajkani ◽  
Mohammad Reza Akbarizadeh
Keyword(s):  
Boundary Conditions ◽  
Thermal Effect ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Different Boundary Conditions ◽  
Modified Couple Stress

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

A modified couple stress theory for buckling analysis of higher order inhomogeneous microbeams with porosities

2018 ◽  
Vol 233 (8) ◽  
pp. 2855-2866 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Fateme Mahmoodi
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Modified Couple Stress

In this paper, buckling behavior of a higher order functionally graded microbeam with porosities is investigated based on the modified couple stress theory and the exact position of the neutral axis. Porosities are evenly and unevenly distributed inside the functionally graded microbeam. Material properties of the functionally graded microbeam are assumed to vary in the thickness direction through a modified form of power-law distribution in which the volume fraction of porosities is considered. The governing equations are derived by using Hamilton's principle and an analytical method is employed to solve these equations for various boundary conditions. The present formulation and numerical results demonstrate a good agreement with some available cases in the literature. Influences of several important parameters such as power-law exponent, porosity distributions, porosity volume fraction, slenderness ratio, and various boundary conditions on buckling loads of porous functionally graded microbeams are investigated and discussed in detail.

Thermal Effect on Static Bending, Vibration and Buckling of Reddy Beam Based on Modified Couple Stress Theory

2013 ◽  
Vol 332 ◽  
pp. 331-338 ◽  
Author(s):  
Ali Reza Daneshmehr ◽  
Mostafa Mohammad Abadi ◽  
Amir Rajabpoor
Keyword(s):  
Thermal Effect ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Length Scale ◽  
Bending Vibration ◽  
Stress Theory ◽  
Micro Scale ◽  
Modified Couple Stress

A microstructure-dependent Reddy beam theory (RBT) which contain only one material length scale parameter and can capture the size effect in micro-scale material unlike the classical theory is developed .using the variational principle energy the governing equation of motion is derived based on modified couple stress theory for the simply supported beam. the equations obtained are solved by Fourier series and the influence of the length scale parameter and thermal effect on static bending, vibration and buckling analysis of micro-scale Reddy beam is investigated.

Dynamics of a micro scale Timoshenko beam subjected to a moving micro particle based on the modified couple stress theory

2016 ◽  
Vol 24 (3) ◽  
pp. 527-548 ◽  
Author(s):  
RA Jafari-Talookolaei ◽  
M Abedi ◽  
M Şimşek ◽  
M Attar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Micro Scale ◽  
Pasternak Elastic Foundation ◽  
Modified Couple Stress

In this study, the free and forced vibration analysis of a micro scale Timoshenko beam resting on a Pasternak elastic foundation and subjected to a moving micro particle is presented. Based on the modified couple stress theory and employing Hamilton’s principle, the governing equations along with the boundary conditions are derived. A semi-analytical solution is obtained for the free vibration of the problem by expressing the dynamic lateral displacement and cross-section rotation in terms of the series of Legendre polynomials and extremizing the objective functional of the problem with respect to the unknown displacements and Lagrange multipliers. Correspondingly, the computed eigenvalue information of the system is utilized in the modal expansion technique to obtain the transient dynamic response. For comparison purposes, the free vibration frequencies of the micro beam and the dynamic deflections using the classical Timoshenko beam theory are compared with previously published studies and very good agreements have been observed. Furthermore, more numerical examples for natural frequencies and dynamic deflection of the beam are presented and the effects of some parameters, such as the material length scale parameter, the velocity of micro particle, the Pasternak elastic foundation parameters, shear deformation effects and boundary conditions are examined.

Large Amplitude Free Vibration Analysis of Nanobeams Based on Modified Couple Stress Theory

2021 ◽  
pp. 2150129
Author(s):  
Ehsan Raeisi Estabragh ◽  
Gholam Hossein Baradaran
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, the large amplitude free vibration of nanobeams based on the modified couple stress theory was developed by using Total Lagrangian finite element formulation. In this study, Timoshenko beam theory has been used in free vibration analysis of nanobeams. Minimal kinematic assumptions have been used to model nanobeams. With this model, free vibration of nanobeams with small to large amplitude and with arbitrary boundary conditions can be analyzed. The numerical results obtained for free vibration based on the modified couple stress theory with small amplitude and the results obtained for free vibration with large amplitude without considering the modified couple stress theory are in good agreement with the similar results reported in previous research. Effects of the dimensionless length scale parameter, slenderness ratio, vibration amplitude and different boundary conditions on the nonlinear frequency ratio of nanobeams have been investigated. The results show the importance of considering nonlinear and size effects in the free vibration analysis of nanobeams with large amplitude.

Vibration of size-dependent functionally graded sandwich microbeams with different boundary conditions based on the modified couple stress theory

2017 ◽  
Vol 22 (2) ◽  
pp. 220-247 ◽  
Author(s):  
Nuttawit Wattanasakulpong ◽  
Arisara Chaikittiratana ◽  
Sacharuck Pornpeerakeat
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Slenderness Ratio ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

This paper investigates flexural vibration of functionally graded sandwich microbeams supported by different axially immovable boundary conditions. The governing equations of free vibration problem are based on Timoshenko beam theory and the modified couple stress theory which are taking into account the important effects of shear deformation, rotary inertia and material length scale parameter. To solve the governing equations presented in the forms of coupled differential equations for vibration analysis of the beams with various boundary conditions, an effective tool, namely Chebyshev collocation method, is employed to find out accurate solutions with many important parametric studies. The effects of material volume fraction index, layer thickness ratio, slenderness ratio, boundary condition, temperature rise, etc. on natural frequencies of the beams are taken into account and discussed in details. The numerical results of the beams in ambient temperature and high thermal environment are presented in several tables and figures that can serve as benchmarks for further investigations in the field of FG sandwich microbeam analysis.

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