Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto–electro–thermo elastic nanobeams

Ansari, R.; Hasrati, E.; Gholami, R.; Sadeghi, Fatemeh

doi:10.1016/j.compositesb.2015.08.038

Cited by 87 publications

(26 citation statements)

References 64 publications

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“…After calculating the sum of the squares of Eqs. (24) and (25) and eliminating the terms associated with time, we obtain the following:…”

Section: Frequency Responses In Beam System Without Dvamentioning

confidence: 99%

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Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Wang¹,

Lu²

2017

IJAV

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This study investigated the damping effects of a dynamic vibration absorber (DVA) attached to a hinged-hinged nonlinear Euler-Bernoulli beam. The model constructed in this study was used to simulate suspended nonlinear elastic beam systems or vibrating elastic beam systems on a nonlinear Winkler-type foundation. This makes the modeling in this study applicable to suspension bridges, railway tracks, and even carbon nanotubes. The hinged-hinged beam in this study includes nonlinear stretching effects, which is why we adopted the method of multiple scales (MOMS) to analyze the frequency responses of fixed points in various modes. The use of amplitudes and vibration modes made it possible to examine the internal resonance. Our results indicate that particular elastic foundations or suspension systems can cause 1:3 internal resonance in a beam. The use of 3D maximum amplitude contour plots (3DMACPs) enabled us to obtain a comprehensive understanding of various DVA parameters, including mass, spring coefficient, and the location of DVA on the beam, and thereby combine them for optimal effect. Our results were verified using numerical calculations.

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“…After calculating the sum of the squares of Eqs. (24) and (25) and eliminating the terms associated with time, we obtain the following:…”

Section: Frequency Responses In Beam System Without Dvamentioning

confidence: 99%

“…Stability properties with and without internal resonance were presented. Ansari et al 24 investigated the forced vibration of nonlinear magneto-electro-thermo elastic (METE) nanobeams. The Galerkin technique was applied to obtain a time-varying set of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Wang¹,

Lu²

2017

IJAV

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“…Some experiments have demonstrably approved the size-dependent mechanical behaviors in microbeams [4][5][6][7] and have shown that size-dependency is an inherent property that gets important when the thickness of A C C E P T E D M A N U S C R I P T 3 beam is comparable to the internal material length scale parameter. Therefore, a variety of examinations have been performed on the estimation of mechanical characteristics of small-scale structures based upon the non-classical continuum mechanics theories [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Ansari

Gholami

Shojaei

et al. 2016

Applied Mathematical Modelling

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1 Highlights  Development of a nonlinear first-order shear deformable small-scale beam model  Presenting formulation based on the most general Mindlin's strain gradient theory  Prediction of coupled free vibration of post-buckled micro-and nano-beams with various BCS  Study of the effects of ⁄ , ⁄ , and BCs on the postbuckling path and frequency  Comparing the results predicted by CT, MCST and MSGT Abstract Presented herein is a comprehensive study on the size-dependent coupled longitudinal-transverserotational free vibration behavior of post-buckled functionally graded (FG) micro-and nano-beams based on the most general Mindlin's strain gradient theory. The current model enables us to incorporate size effects via introducing material length scale parameters and is developed in the framework of the firstorder shear deformable beam model and the von Karman geometric nonlinearity. The FG micro-and nano-beams, whose volume fraction is expressed by using a power law function, are assumed to be made of a mixture of metals and ceramics. By using Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-and nano-beams in the postbuckling domain. Afterwards, the governing equations and boundary conditions are discretized using the generalized differential quadrature (GDQ) method in conjunction with a direct approach without linearization, before solving numerically by Newton's method. The effects of length scale parameter, length-to-thickness ratio, material gradient index and boundary conditions on the postbuckling path and frequency of FG micro-and nano-beams are carefully investigated. Finally, numerical results obtained from both the modified strain gradient theory (MSGT) and modified couple stress theory (MCST) are compared.Mindlin's strain gradient elasticity; Size-dependent first-order shear deformable beam model.

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“…τ ¼ e 0 a=l is defined as scale coefficient, where e 0 is a material constant which is determined experimentally or approximated by matching the dispersion curves of plane waves with those of atomic lattice dynamics; and a and l are the internal and external characteristic length of the nanostructures, respectively. Finally, it is possible to represent the integral constitutive relations given by Equation (32) in an equivalent differential form as [7] …”

Section: Nonlocal Elasticity Theory For the Mete Materialsmentioning

confidence: 99%

“…They showed the effects of the small-scale parameter and the electric and magnetic field intensities on the transverse displacement, rotation, buckling load, and natural frequency. Also, Ansari et al [32] studied the effect of temperature field on forced vibration of MEE nanobeams based on the nonlocal third-order beam theory. Farajpour et al [10] presented largeamplitude vibration analysis of MEE nanoplates based on nonlocal plate model.…”

Section: Introductionmentioning

confidence: 99%

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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This work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic functionally graded (METE-FG) nanoplates in thermal environments based on a refined trigonometric plate theory. Temperature field has uniform, linear, and nonlinear distributions across the thickness. Nonlinear thermal loadings are considered as heat conduction (HC) and sinusoidal temperature rise (STR). A power law function is applied to govern the gradation of material properties through the nanoplate thickness. Considering coupling impacts between magneto, electro, thermo-mechanical loadings, the equations of motion, and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived. The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier's method. Moreover, the accuracy of the present formulation is examined by comparing the obtained results with published ones. Furthermore, the effects played by the magneto-electrical field, various temperature rises, nonlocality, power law index, side-tothickness ratio, and aspect ratio on the critical buckling temperature response are all investigated and reported.ARTICLE HISTORY

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Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto–electro–thermo elastic nanobeams

Cited by 87 publications

References 64 publications

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory

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