Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam

2017 ◽  
Vol 24 (18) ◽  
pp. 4211-4225 ◽  
Author(s):  
Seyed Sajad Mirjavadi ◽  
Behzad Mohasel Afshari ◽  
Navvab Shafiei ◽  
Samira Rabby ◽  
Mohammad Kazemi
Keyword(s):  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Beam Theory ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Two Dimensional ◽  
Stress Theory ◽  
Micro Scale ◽  
Generalized Differential

This work is aimed to present analysis on the thermal vibrational behavior of two-dimensional functionally graded porous microbeams based on Timoshenko beam theory. According to the power law function, the material composition and so the material properties are varying along thickness and axis of the microbeam. The governing equations are derived on the basis of the couple stress theory and the generalized differential quadrature method is used to solve the equations. The temperature gradient is considered to be uniform and nonuniform across the thickness of the microbeam. The results are presented to show the effect of temperature change, porosity, functionally graded and axially functionally graded power indexes and also micro-scale parameter on the vibration of the microbeam.

scholarly journals Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

Vibration ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 201-221 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Ali Farajpour ◽  
Hamed Farokhi
Keyword(s):  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Timoshenko Beam Theory ◽  
Cross Sectional ◽  
Stress Theory ◽  
Size Dependent ◽  
Modified Couple Stress

A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated.

Static Torsion of Bi-Directional Functionally Graded Microtube Based on the Couple Stress Theory Under Magnetic Field

2020 ◽  
Vol 12 (02) ◽  
pp. 2050021
Author(s):  
Abbas Barati ◽  
Mohsen Mahdavi Adeli ◽  
Amin Hadi
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Axial Magnetic Field ◽  
Couple Stress Theory ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Small Scale ◽  
Stress Theory ◽  
Generalized Differential ◽  
Static Torsion

This paper presents is a solution for static torsion in a microtube made of bi-directional functionally graded materials (BDFGMs). The material properties are assumed to vary according to the arbitrary function along radius and length of microtube. As for the torque effect of the axial magnetic field, the well-known Maxwell’s relation is used. Couple stress theory is employed to study the influence of small-scale on static torsion of microtube. The Navier equation and boundary conditions of the size-dependent BDFG microtube were derived by the minimum potential energy. These equations were solved by employing the generalized differential quadrature method (GDQM). Comparison between the results of this work with the analytical method for static torsion of microtube made of one direction FG material reveals the accuracy of this study. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants on the static torsion of the bi-directional functionally graded microtube.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Roshan Lal ◽  
Chinika Dangi
Keyword(s):  
Thermal Environment ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Energy Principle

Abstract In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

Free Vibration of Edge Cracked Functionally Graded Microscale Beams Based on the Modified Couple Stress Theory

2017 ◽  
Vol 17 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Cracked Beam ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler–Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange’s equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

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