Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach

2015 ◽  
Vol 230 (9) ◽  
pp. 1486-1497 ◽  
Author(s):  
Brajesh Panigrahi ◽  
Goutam Pohit
Keyword(s):  
Beam Theory ◽  
Nonlinear Problems ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Surface Approach ◽  
Present Solution ◽  
Graded Material ◽  
Surface Location ◽  
First Time

The present work accounts Timoshenko beam theory followed by Ritz approximation and an iterative technique to deal nonlinear free vibration problems of cracked Functionally Graded Material (FGM) beams based on neutral surface location. Using neutral surface as a reference rather than the midsurface reduces the complexity of nonlinear problems. It is assumed that crack always remains open. Analysis is carried out for clamped-clamped and clamped-free boundary conditions. Nonlinear frequencies and mode shapes corresponding to first three mode of vibration are obtained for the first time for different crack parameters, amplitudes of vibration and material indexes. The accuracy of the present solution is verified by comparing some of the obtained results with existing solutions. It can be concluded that present results are not only accurate but the methodology is very simple and easy to perform.

Free vibration analysis of functionally graded beams using an exact plane elasticity approach

2014 ◽  
Vol 228 (14) ◽  
pp. 2488-2494 ◽  
Author(s):  
K Celebi ◽  
N Tutuncu
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Future Research ◽  
Graded Material ◽  
Beam Thickness ◽  
Plane Elasticity Theory

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory

2017 ◽  
Vol 24 (17) ◽  
pp. 3809-3818 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati ◽  
Parisa Haghi
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Wave Number ◽  
Graded Material ◽  
Fg Nanobeam

The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

2019 ◽  
Vol 233 (10) ◽  
pp. 2140-2159 ◽  
Author(s):  
Ehsan Arshid ◽  
Ali Kiani ◽  
Saeed Amir
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Sensors And Actuators

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

scholarly journals Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method

2017 ◽  
Vol 39 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc ◽  
Nguyen Tien Khiem
Keyword(s):  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Functionally Graded Beam ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Fgm Beam

Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.

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

A new first shear deformation beam theory based on neutral surface position for functionally graded beams

2013 ◽  
Vol 15 (5) ◽  
pp. 467-479 ◽  
Author(s):  
Mohammed Bouremana ◽  
Mohammed Sid Ahmed Houari ◽  
Abdelouahed Tounsi ◽  
Abdelhakim Kaci ◽  
El Abbas Adda Bedia
Keyword(s):  
Shear Deformation ◽  
Beam Theory ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Neutral Surface Position

scholarly journals Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

2018 ◽  
Vol 34 ◽  
pp. 01033 ◽  
Author(s):  
Abdolreza Toudehdehghan ◽  
Md. Mujibur Rahman ◽  
Faris Tarlochan
Keyword(s):  
Thermal Analysis ◽  
Mechanical Load ◽  
Beam Theory ◽  
Metal Substrate ◽  
Functionally Graded ◽  
Static Behavior ◽  
Mechanical Loads ◽  
Graded Material ◽  
Coated Layer ◽  
Principle Of Virtual Displacements

The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT). The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model). The second model was consisting of Functionally Graded Material (FGM) as a coated layer and metal substrate (FGC model). From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials.

Influence of neutral surface position on dynamic characteristics of in-homogeneous piezo-magnetically actuated nanoscale plates

2017 ◽  
Vol 232 (17) ◽  
pp. 3125-3143 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Electric Voltage ◽  
Graded Materials ◽  
Various Boundary Conditions ◽  
Exact Position ◽  
First Time

Based on exact position of neutral surface, vibrational behavior of smart nanoplates made of magneto-electro-elastic functionally graded materials is examined by implementing a Galerkin method for the first time. Magneto-electro-elastic properties of nanoplate vary in transverse direction via power-law model. The nonlocal governing equations of functionally graded plate under magneto-electrical field are formulated through Hamilton’s principle and nonlocal elasticity theory based on a four-variable refined plate theory, which avoids the use of shear correction factors by capturing shear deformation influences. Importance of various parameters including magnetic potential, electric voltage, various boundary conditions, nonlocality, material distribution, and plate thickness on natural frequencies of the magneto-electro-elastic functionally graded nanoplate are explored. It is elucidated that these parameters play significant roles on the dynamic behavior of magneto-electro-elastic functionally graded nanoplates.

BUCKLING AND WRINKLING OF A FUNCTIONALLY GRADED MATERIAL (FGM) THIN FILM

2012 ◽  
Vol 04 (02) ◽  
pp. 1250012 ◽  
Author(s):  
MASOUD NOROOZI ◽  
LIYING JIANG
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Winkler Foundation ◽  
Bending Rigidity ◽  
Free Standing ◽  
Buckling Mode ◽  
Graded Material

The instability of a functionally graded material (FGM) strip as a free standing film or a substrate-bound film is studied in this work, in which the stiffness of the film is assumed to change exponentially along the length. The buckling load and the buckling mode shapes for the free standing FGM film are determined analytically. For the substrate-bound film, the substrate is modeled as a Winkler foundation and the wrinkling load and wrinkling pattern are determined numerically by using a finite difference method and a series solution. In contrast with the wrinkling of homogenous thin films in which the wrinkles propagate in the entire domain, the wrinkles of the FGM films accumulate around the location with the least bending rigidity. The results of this work show that the sensitivity of the wrinkle accumulation around the weak locations of the system with lower stiffness is very high. This work is expected to provide a better understanding for localization of wrinkles around a region of substrate-bounded thin films in thin film technology.

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