Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams

2013 ◽  
Vol 99 ◽  
pp. 193-201 ◽  
Author(s):  
M.A. Eltaher ◽  
A.E. Alshorbagy ◽  
F.F. Mahmoud
Keyword(s):  
Natural Frequencies ◽  
Functionally Graded ◽  
Neutral Axis ◽  
Axis Position

scholarly journals Analysis of steel reinforced functionally graded concrete beam cross sections

2018 ◽  
Vol 195 ◽  
pp. 02031 ◽  
Author(s):  
Shota Kiryu ◽  
Ay Lie Han ◽  
Ilham Nurhuda ◽  
Buntara S. Gan
Keyword(s):  
Cross Sections ◽  
Iterative Procedure ◽  
Concrete Beam ◽  
Analytical Procedure ◽  
Functionally Graded ◽  
Neutral Axis ◽  
Mechanical Behaviors ◽  
Beam Structure ◽  
Axis Position ◽  
Concrete Materials

Owing to continuously changing strength moduli properties, functionally graded concrete (FGC) has remarkable advantages over the traditional homogeneous concrete materials regarding cement optimization. Some researchers have studied mechanical behaviors and production methodologies. Problems arise as to how to incorporate the effects of the non-homogeneity of concrete strengths in the analysis for design. For a steel Reinforced Functionally Graded Concrete (RFGC) beam structure, the associated boundary conditions at both ends have to be at the neutral axis position after the occurrence of the presumed cracks. Because the neutral axis is no longer at the mid-plane of the beam crosssection, an iterative procedure has to be implemented. The procedure is somewhat complicated since the strength of the beam cross section has to be integrated due to the non-homogeneity in concrete strengths. This paper proposes an analytical procedure that is very straightforward and simple in concept, but accurate in designing the steel reinforced functionally graded concrete beam cross-sections.

scholarly journals FREQUENCY ANALYSIS OF CRACKED FUNCTIONALLY GRADED CANTILEVER BEAM

2017 ◽  
Vol 55 (2) ◽  
pp. 229
Author(s):  
Nguyen Ngoc Huyen ◽  
Nguyen Tien Khiem
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Neutral Axis ◽  
Open Crack ◽  
Graded Material ◽  
Fgm Beam

In this paper, a functionally graded cantilever beam with an open crack is investigated on the base of Timoshenko beam theory; power law of functionally graded material (FGM) and taking into account actual position of neutral axis instead of the central one. The open and edge crack is modeled by coupled translational and rotational springs stiffness of which is calculated by the formulas conducted accordingly to fracture mechanics. Using the frequency equation obtained in the framework of the theory natural frequencies of the beam are examined along the crack parameters and material properties. This analysis demonstrates that sensitivity of natural frequencies of FGM beam to crack is strongly dependent on the material constants of FGM

scholarly journals Interfacial stresses analysis of FGM porous structures bonded with FRP plates

2018 ◽  
Vol 149 ◽  
pp. 01094
Author(s):  
A. Chedad ◽  
N. Elmeiche
Keyword(s):  
Adhesive Joint ◽  
Functionally Graded ◽  
Neutral Axis ◽  
Porous Structures ◽  
Functionally Graded Beam ◽  
Interfacial Stresses ◽  
Axis Position ◽  
Fg Beam ◽  
Compatibility Principle ◽  
Deformation Compatibility

This paper presents a method for determining the interfacial stresses in an adhesive joint between a strengthening plate and a functionally graded beam. The beam is assumed to be isotropic with a constant poisson’s ratio. The present method is based on the deformation compatibility principle taking into account the neutral axis position of the FG beam. A power law for the distribution of the mechanical characteristic with a uniform and non-uniform porosity distribution is presented. A parametric study is presented to show the effect of some parameters on the distribution of stresses in the adhesive joint between the plat and the beam.

scholarly journals Contribution to the design of bolted angle connection in the steel structures

2004 ◽  
Vol 3 (1) ◽  
pp. 1-7
Author(s):  
Dragan Velickovic
Keyword(s):  
Cross Section ◽  
Steel Structures ◽  
Neutral Axis ◽  
Bearing Plate ◽  
The Face ◽  
Axis Position ◽  
Angle Connection ◽  
Building Practice ◽  
The Given

The paper presents the equations for the determination of the neutral axis position, when it is on the face, that is, on the bearing plate, and for the highest normal tensile stress in the fastener, as well as for the determination of highest and lowest normal compressive stress occurring on the face, that is bearing plate when the neutral axis is outside the face that is, the bearing plate. Which of these three possible cases will occur depends solely on the force field occurring in the given cross-section for the dimensioning of the joint. The connection is effected by the face or bearing plate, depending on the task being solved and the bolt fasteners. The expressions for the calculation of the said connections are derived for the general case when all three forces intersecting, M, T and N, in the cross section given for their dimensioning, are other than zero or any one of them is other than zero. The paper also presents a tabular presentation of the results for all of the three possible cases of the force fields, that is, the stress fields most frequently occurring in the civil engineering building practice at these joints.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Studies on Determination of Natural Frequencies of Industrial Turbine Blades

1995 ◽  
Author(s):  
Mahesh M. Bhat ◽  
V. Ramamurti ◽  
C. Sujatha
Keyword(s):  
Steam Turbine ◽  
Dynamic Behavior ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Complex Structure ◽  
Turbine Blades ◽  
Blade Root ◽  
Steam Turbine Blade ◽  
Manufacturing Tolerances

Abstract Steam turbine blade is a very complex structure. It has geometric complexities like variation of twist, taper, width and thickness along its length. Most of the time these variations are not uniform. Apart from these geometric complexities, the blades are coupled by means of lacing wire, lacing rod or shroud. Blades are attached to a flexible disc which contributes to the dynamic behavior of the blade. Root fixity also plays an important role in this behavior. There is a considerable variation in the frequencies of blades of newly assembled turbine and frequencies after some hours of running. Again because of manufacturing tolerances there can be some variation in the blade to blade frequencies. Determination of natural frequencies of the blade is therefore a very critical job. Problems associated with typical industrial turbine bladed discs of a 235 MW steam turbine are highlighted in this paper.

Effect of the Material Types on the Fundamental Frequencies of Uniaxial Composite Conical Springs

1999 ◽  
Author(s):  
Vebil Yildirim ◽  
Erol Sancaktar ◽  
Erhan Kiral
Keyword(s):  
Transfer Matrix Method ◽  
Pitch Angle ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Helical Springs ◽  
Fundamental Frequencies ◽  
Helix Pitch ◽  
Constant Pitch ◽  
Α Helix

Abstract This paper deals with the effect of the material types (Graphite-Epoxies and Kevlar-Epoxy) on the fundamental frequencies of uniaxial constant-pitch composite conical helical springs with solid circle section and fixed-fixed ends. The transfer matrix method is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution. The free vibrational charts for each material presented in this study cover the following vibrational parameters: n (number of active turns) = 5–10, α = (helix pitch angle) = 5° and 25°, R2/R1, (minimum to maximum radii of the cylinder) = 0.1 and 0.9, and Dmax/d (maximum cylinder to wire diameters) = 5 and 15. These charts can be used for the design of uniaxial composite conical springs.

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