Vibrations of fluid conveying microbeams under non-ideal boundary conditions

Atcı, Duygu; Bağdatlı, Süleyman Murat

doi:10.1007/s00542-016-3255-y

Cited by 15 publications

(6 citation statements)

References 42 publications

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“…Since the homogeneous equation has non-simple solutions, the nonhomogeneous equation can only accept TECHNICAL JOURNAL 12, 1(2018), [18][19][20][21][22][23][24][25][26] solutions with a solvability condition. Hence, the following conditions must be met for secularity-forming terms, From here, the simplest form of our equations is obtained as follows, The K expressions in the equations defined as follows, 1 1 1 1 1 1 1 1 0 1 1 0 0 11 1 1 1 1 1 0 1 1 0 0 1 1 1 2 1 1 2 1 0 1 2 1 0 0 12 1 1 1 1 1 0 1 1 0 0 1 3 2 1 2 0 13 1 1 1 0 21 1 1 2 2 2 0 2 2 0 0 1 3 2 1 2 0 22 1 1 2 2 2 0 2 2 0 0 1 1 1 2 2 2 2 3 2 2 2 2 22 2 0 0 0 1 1 2…”

Section: The Case Where the Fundamental Parametric Resonance And The mentioning

confidence: 99%

“…They show that the size effects are quite large when the thickness of the microplates is close to the material length parameter. Atcı and Bağdatlı studied the effects of non-ideal boundary conditions on the free vibrations of fluid conveying clamped microbeams [21]. They also investigated non-ideal boundary conditions for nonlinear fluid conveying microbeams [22].…”

Section: Introductionmentioning

confidence: 99%

“…Atcı and Bağdatlı studied the effects of non-ideal boundary conditions on the free vibrations of fluid conveying clamped microbeams [21]. They also investigated non-ideal boundary conditions for nonlinear fluid conveying microbeams [22]. Dai et al [23] studied nonlinear dynamic responses of microcantilevers containing internal fluid flow.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam

Kural

2018

Teh. glas. (Online)

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Microbeams are widely used in micro-electro-mechanical systems (MEMS). These systems are alternatives to piezo-resistive sensors because of their high sensitivity and low power consumption. Unlike with the classical theory of continuous media, in order to see the effects of the system being micro-sized, the effect of micro-structure was added to the system based on the modified couple stress theory (MCST) for fluid conveying microbeam. By using Hamilton’s principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Microbeam was investigated under electrical field and resting on an elastic foundation. It is assumed that the fluid velocity changes harmonically around a constant velocity and that the electrical field force changes harmonically with time. Approximate solutions of the system were achieved by using the multiple time scale method. 3:1 and 2:1 internal resonance cases were investigated. Detuning parameter-amplitude variation graphs were obtained, and stability areas were shown.

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Section: The Case Where the Fundamental Parametric Resonance And The mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam

Kural

2018

Teh. glas. (Online)

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“…Bu çalışmada ideal olmayan sınır şartlarını ifade eden bir matematiksel model geliştirilmiş ve perturbasyon yöntemlerinden olan çok ölçekli metot ile nonlineer hareket denklemleri çözülmüştür. Sonuçlar, frekans-cevap eğrileri şeklinde sunulmuş ve ideal olmayan sınır şartlarının etkileri gösterilmiştir [14][15][16].…”

Section: Introductionunclassified

İdeal Olmayan Sınır Şartları Altındaki Akışkan Taşıyan Mikrokirişlerde Temel Parametrik Rezonans

Atcı¹,

Bağdatlı²

2018

El-Cezeri Fen Ve Mühendislik Dergisi

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Bu çalışmada, ideal olmayan ankastre ve ideal olmayan basit sınır şartlarının etkisi altındaki mikrokirişlerin temel parametrik rezonans davranışları incelenmiştir. Mikrokirişler, yuvarlak kesitli olup içerisinde zamana göre değişen hıza sahip akışkan taşımaktadır. Akışkan hızı değişim frekansının kirişin doğal frekansının iki katına yakın olduğu durumlarda temel parametrik rezonans durumu ortaya çıkmaktadır. Mikrokiriş-akışkan sisteminin hareket denklemleri Hamilton Prensibi uygulanarak elde edilmiştir. Perturbasyon yöntemlerinden olan Çok Ölçekli Metot, elde edilen hareket denklemlerine uygulanmıştır. Ağırlık faktörünün (k) tanımlanması ile ideal olmayan sınır şartları için yeni bir matematiksel model geliştirilmiş ve çözüme uygulanmıştır. İdeal ve ideal olmayan sınır şartları için elde edilen sonuçlar karşılaştırılmıştır. Frekans-cevap eğrileri çizdirilerek, ideal olamayan ankastre sınır şartının frekans değerlerini düşürdüğü, ideal olmayan basit mesnet şartının ise frekans değerlerini arttırdığı görülmüştür.

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“…They can also observe that the stresses and deflections carried out by the proposed model are smaller than those based on Timoshenko and Euler-Bernoulli beam assumptions. These studies were pursued in [19][20][21][22][23] who studied the effect of size parameter on the beam model considering MCST. Kocatürk and Akbaş [24] presented responses of the free end of a cantilever micro beam under the effect of an impact force considering the MCST.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Size Effect in Euler-Bernoulli Nanobeam Using the Modified Couple Stress Theory

Toğun¹,

Bağdatlı²

2017

Celal Bayar Üniversitesi Fen Bilimleri Dergisi

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This paper presents the implementation of non-classical continuum theory for simply supported nanobeam. Hamilton's principle and modified couple stress methods are employed for obtaining differential equation of motion of nanobeam in cooperation with suitable boundary conditions. An approximate solution of the presented system is developed considering the method of multiple scales which is one of the perturbation techniques. The effect of material length scale parameter ζ and the Poisson's ratio υ on the natural frequencies are determined and represented in table form and graphically. Besides, dimensionless natural of frequency of nanobeam are investigated by taking into account various system parameters. The results of the system show that the size influence is very crucial for extremely thin beams with a height of nanoscale dimension. Besides, the outcome of the system shows that the beam modeled considering non-classical continuum theory is stiffer than those of classical one.

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Vibrations of fluid conveying microbeams under non-ideal boundary conditions

Cited by 15 publications

References 42 publications

Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam

Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam

İdeal Olmayan Sınır Şartları Altındaki Akışkan Taşıyan Mikrokirişlerde Temel Parametrik Rezonans

Investigation of the Size Effect in Euler-Bernoulli Nanobeam Using the Modified Couple Stress Theory

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