Static and free vibration analyses of small - scale functionally graded beams possessing a variable length scale parameter using different beam theories

Aghazadeh, Reza
This study presents static and free vibration analyses of functionally graded (FG) micro - beams on the basis of higher order continuum mechanics used in conjunction with classical and higher order shear deformation beam theories. Unlike conventional ones, higher order elastic theories consider the size effect for the beam. Strain gradient theory (SGT) and modified couple stress theory (MCST) are the two common non-classical continuum approaches capable of capturing the size effect. Shear deformation beam theories consider the effects of shear strain across the thickness. In the base of SGT and generalized beam theories and taking the thermal effects into account, the governing equations and boundary conditions are derived using a variational formulation based on Hamilton’s principle. This new model may be reduced to the non-classical Bernoulli-Euler beam model based on the modified couple stress theory (MCST) when two of the material length scale parameters and extra terms of higher order beam theories are taken to be zero. Numerical analyses using differential quadrature method (DQM) are conducted by considering static bending and free vibration problems of a simply supported FG beam.


Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories
Aghazadeh, Reza; Ciğeroğlu, Ender; Dağ, Serkan (Elsevier BV, 2014-07-01)
This article puts forward a modified couple stress theory based approach of analysis for small-scale functionally graded beams, that possess a variable length scale parameter. Presented procedures are capable of predicting static and dynamic beam responses according to three different beam theories, namely: Euler - Bernoulli beam theory, Timoshenko beam theory and third-order shear deformation beam theory. A variational method is used in conjunction with the modified couple stress theory to derive the gover...
Nonlinear Vibrations of a Functionally Graded Material Microbeam with Geometric Nonlinearity
Uz, Canan; Ciğeroğlu, Ender (2017-02-02)
In this paper, nonlinear vibration analysis of micro scale functionally graded material (FGM) beams with geometric nonlinearity due to large deflection is studied using modified couple stress theory (MCST). MCST is a nonlocal elasticity theory which includes a material length scale parameter since the size of an atomic microstructure becomes comparable to the length of the microbeam. Equations of motion of the micro scale FGM beam are obtained by using Hamilton's principle. Nonlinear free vibrations of the ...
Pressure-velocity coupling algorithm-based pressure reconstruction from PIV for laminar flows
Gunaydinoglu, Erkan; Kurtuluş, Dilek Funda (Springer Science and Business Media LLC, 2020-01-01)
In this study, we propose a method to reconstruct pressure fields from planar particle image velocimetry measurements for laminar flows by employing semi-implicit method for pressure-linked equations algorithm to solve governing equations where measured velocities are inherently used as boundary conditions. The method starts with interpolating the measured velocity field on a staggered computational grid. The continuity equation, in the form of pressure equation for incompressible flows, is solved with this...
Static and dynamic analysis of shear deformable composite shells of revolution by semi-analytical approach
Kayran, Altan (2013-10-18)
In the present study, multi-segment numerical integration technique is applied for the static and dynamic analysis of macroscopically anisotropic shells of revolution including transverse shear deformation. Application of the multi-segment numerical integration technique is achieved through the use of finite exponential Fourier transform of the fundamental shell of revolution equations governing the static loading and free vibration of the shell of revolution. For the non-axisymmetrically loaded shells of r...
Nonlinear Vibration Analysis of Uniform and Functionally Graded Beams with Spectral Chebyshev Technique and Harmonic Balance Method
Dedekoy, Demir; Ciğeroğlu, Ender; Bediz, Bekir (2023-01-01)
In this paper, nonlinear forced vibrations of uniform and functionally graded Euler-Bernoulli beams with large deformation are studied. Spectral and temporal boundary value problems of beam vibrations do not always have closed-form analytical solutions. As a result, many approximate methods are used to obtain the solution by discretizing the spatial problem. Spectral Chebyshev technique (SCT) utilizes the Chebyshev polynomials for spatial discretization and applies Galerkin's method to obtain boundary condi...
Citation Formats
R. Aghazadeh, “Static and free vibration analyses of small - scale functionally graded beams possessing a variable length scale parameter using different beam theories,” M.S. - Master of Science, Middle East Technical University, 2013.