Geometrically Non-Linear Free and Forced Vibration of Clamped-Clamped Functionally Graded Beam with Discontinuities.

Chajdi, Mohcine; Bekkaye, Merrimi El; Khalid, El Bikri

doi:10.1016/j.proeng.2017.09.117

Cited by 9 publications

(6 citation statements)

References 7 publications

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“…Forced vibration analysis of FGM beams under classical boundary conditions were reported in the literature. [27][28][29][30][31][32] Considering Euler-Bernoulli beam theory (EBT) and von Ka´rma´n non-linearity, forced vibration behavior of FGM beams had been reported by Shooshtari and Rafiee 27 for clamped beam-ends and by Hosseini et al 28 for both hinged-hinged and clampedhinged beams. Based on TBT and von Ka´rma´n nonlinearity, Ansari et al 29 investigated the non-linear forced vibration behavior of functionally graded (FG) composite beams reinforced by single-walled carbon nanotubes for clamped and simply supported boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Using a meshfree boundary-domain integral method, Yang et al 31 investigated the forced vibration behavior of FG cantilever beam for harmonic and transient loadings. Mohcine et al 32 presented a study on geometrically non-linear forced vibration behavior of cracked FGM beam with porosities for clamped boundary condition subjected to harmonic concentrated force. Forced vibration behavior of FGM beams resting on elastic foundation are reported in Kanani et al 33 and Calim.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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Geometrically non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam under harmonic excitation and supported on three-parameter non-linear elastic foundation is presented. The beam is immovably clamped and is considered to be under static thermal loading due to uniform temperature rise. Reddy's third-order shear-deformable beam theory in conjunction with von Kármán geometric non-linearity is considered to derive the governing equations employing Hamilton's principle, and Ritz method is followed for approximating the displacement and rotation fields. A numerical algorithm based on iterative substitution method and Broyden's method is proposed to predict the stable regions of frequency-response behavior. The frequency-response curves are presented in normalized plane for variations of load-amplitude, elastic foundation parameters, temperature rise, gradation index and functionally graded material composition, and their effects are discussed in detail. It is found that the load-amplitude, elastic foundation parameters, thermal loading and some of the functionally graded material compositions significantly affect the frequency response; whereas, the effect of gradation index is found to be relatively small. A comparative frequency-response curve between Voigt model and Mori-Tanaka scheme of functionally graded material modeling is presented, and it shows negligible difference between these two models. The present problem under thermal environment is studied for the first time through this work, and the proposed model and the numerical algorithm provide a simplified approach to study the non-linear frequency-response behavior.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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“…Some studies consider beams with delaminations [13, 14]. Studies on beams containing porosities are also available [15, 16]. Papers on the modal analysis of a beam coated with functionally graded material are scarce.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis of an aluminum beam coated with damaged and porous functionally graded material

Erdurcan

Cunedioĝlu

2021

Materialwissenschaft Werkst

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In this paper modal analysis is performed on a symmetric aluminum beam which is coated with functionally graded material containing porosities. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with classical lamination theory. To achieve a truthful modeling the gradually changing mechanical properties of the coating are modeled as 25 layers of material, while each individual layer is isotropic and homogeneous. MATLAB is used to write a finite element code and Timoshenko beam elements are used to include shear deformation effects. To show the influences of crack location, crack depth, porosity and the polynomial function index on the natural beam frequencies a parametric study is conducted. Multiple boundary conditions were also considered and it was found that the natural frequency values were significantly affected by the studied parameters.

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“…Mohcine ve ark. [5] porositeli bir FDM kirişe çatlak da ekleyerek simetrik olmayan bir kirişin dinamik karakteristiklerini belirlemişlerdir. Bouakkaz ve ark.…”

Section: Introductionunclassified

Porosi̇teli̇ FDM İle Kapli Alümi̇nyum Ki̇ri̇şi̇n Serbest Ti̇treşi̇mi̇ni̇n İncelenmesi̇

Erdurcan¹,

Cunedioĝlu²

2020

Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi

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Bu çalışmada çekirdek tabakası alüminyum ve yüzeyleri porosite ihtiva eden fonksiyonel derecelendirilmiş malzeme (FDM) ile kaplı simetrik yapıda ankastre sandviç bir kirişin serbest titreşim analizi incelenmiştir. Fonksiyonel derecelendirilmiş malzemenin elastisite modülü ve yoğunluğu kirişin tabaka kalınlığı boyunca bir polinom fonksiyonla değiştiği kabul edilmiştir. FDM'yi gerçeğe yakın bir şekilde temsil etmek için kaplama kalınlığının 25 tabakadan oluştuğu ve her bir tabaka kendi içinde homojen izotrop olarak modellenmiştir. Bu yapılara ait efektif yoğunluk ve elastisite modülü tabakalı kompozit kiriş teorisi kullanılarak belirlenmiştir. Çalışmada birinci mertebe kayma deformasyonu içeren Timoshenko kiriş teorisi kullanılarak problemin çözümü sonlu elemanlar metoduyla gerçekleştirilmiştir. Kirişin doğal frekanslarının hesaplanması için MATLAB'ta sonlu elemanlar kodu yazılmıştır. Çalışmada porosite hacim oranının (a), çekirdek tabaka kalınlığının FDM kalınlık oranına (h/H), kiriş açıklığının yüksekliğine oranının (L/H) ve FDM'nin mekanik özelliklerini belirleyen polinom parametresinin (n) doğal frekansların üzerindeki etkisi incelenmiştir. İncelenen parametrelerin kirişin doğal frekanslarını önemli ölçüde etkilediği gözlemlenmiştir.

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Geometrically Non-Linear Free and Forced Vibration of Clamped-Clamped Functionally Graded Beam with Discontinuities.

Cited by 9 publications

References 7 publications

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Modal analysis of an aluminum beam coated with damaged and porous functionally graded material

Porosi̇teli̇ FDM İle Kapli Alümi̇nyum Ki̇ri̇şi̇n Serbest Ti̇treşi̇mi̇ni̇n İncelenmesi̇

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