Vibrational behavior of variable section functionally graded microbeams carrying microparticles in thermal environment

Shenas, Amin Ghorbani; Malekzadeh, P.; Mohebpour, Saeed Reza

doi:10.1016/j.tws.2016.08.010

Cited by 16 publications

(4 citation statements)

References 43 publications

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“…Linear and nonlinear vibrations of FG Timoshenko microbeams were carried out by Ansari et al [39]. Based on Timoshenko beam theory, Shenas et al [40] conducted vibration analysis of FG microbeam carrying microparticles in the thermal environment. The static bending, instability and free vibration analyses of simply supported miroplates based on Kirchhoff assumptions were studied by Wang et al [41].…”

Section: Mctmentioning

confidence: 99%

Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

Thai

et al. 2017

Computers & Structures

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This paper presents a robust numerical model, which takes into account both size-dependent and shear deformation effects, for the bending, buckling and free vibration analyses of functionally graded microplates. The size-dependent effect is captured by using the modified strain gradient elasticity theory with three length scale parameters, whilst the shear deformation effect is accounted by using the third-order shear deformation theory. The rule of mixture is employed to describe the distributions of material phrases through the plate thickness. By using Hamilton's principle, the governing equations are derived and then discretized by employing an Isogeometric Analysis (IGA) approach, where the Non-Uniform Rational B-Splines (NURBS) basis functions are adopted to meet the C 2 −continuity requirement. Physical mesh convergence and verification studies are performed to prove the accuracy and reliability of the present model. In addition, parametric studies are also carried out to investigate the size effect in conjunction with the influences of gradient index, shear deformation effect and boundary conditions on the responses of microplates.

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Section: Mctmentioning

confidence: 99%

Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

Thai

et al. 2017

Computers & Structures

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“…The classical continuum mechanics theories are unable to explain and predict the mechanical behavior of the materials in small sizes. Therefore, some of the non-classical continuum theories such as strain gradient theory, couple stress theory, nonlocal elasticity theory, and surface elasticity theory have been introduced to capture the size e ect on elastic deformation behavior of micro-structures [14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

Rahi

2018

Scientia Iranica

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In this paper, the modi ed couple stress theory is used to capture size e ect on dynamic behavior of a micro-drill subjected to an axial load and a concentrated mass, which is attached to its free end. Governing equations of lateral vibrations of the system and associated boundary conditions were derived by rst, obtaining the total kinetic and potential energy of the system and then, using Hamilton's principle. The Assumed Modes method was applied for transforming the governing partial di erential equations into a set of in nite ordinary di erential equations. Considering two terms of the equations, the rst two natural frequencies and instability rotational speeds of the micro-drill system were determined semi-analytically. Finally, numerical results of natural frequencies and the threshold of instability speeds of the system were derived with respect to di erent values of the system parameters such as rotational speed, axial load, rotor length, concentrated mass, and material length scale. The results showed that the material length scale parameter was extremely e ective on natural frequencies and the threshold of instability speeds of the micro-drill.

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“…Recently, many researchers have devoted their time and efforts to investigate the mechanical and vibrational behavior of both micro- and nano- structures (Younis and Nayfeh, 2003; Farokhi et al., 2013; Askari, 2014; Askari et al., 2014; Farokhi and Ghayesh, 2015a, 2015b; Ghayesh and Farokhi, 2015a, 2015c; Han et al., 2015; Ghorbanpour Arani et al., 2016). A few more recent research works in this area include the study of the functionally graded microbeams carrying microparticles in a thermal environment by Shenas et al. (2016), the size-dependent behavior of functionally graded microbeams using various shear deformation theories by Trinh et al.…”

Section: Introductionmentioning

confidence: 99%

Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations

Saadatnia

Argani

Esmailzadeh

2017

Journal of Vibration and Control

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The multi-frequency excitation of a microbeam, resting on a nonlinear foundation, is investigated and the governing equation of motion of the microbeam system is developed. The viscoelastic-type foundation is considered by assuming nonlinear parameters for both Pasternak and Winkler coefficients. The well-known Galerkin approach is utilized to discretize the governing equation of motion and to obtain its nonlinear ordinary differential equations. The multiple time-scales method is employed to study the multi-frequency excitation of the microbeam. Furthermore, the resonant conditions due to the external excitation as well as the combination resonances for the first two modes are investigated. The influences of different parameters, namely the Pasternak and Winkler coefficients, the position of the applied force and the geometrical factors on the frequency response of the system are examined.

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Vibrational behavior of variable section functionally graded microbeams carrying microparticles in thermal environment

Cited by 16 publications

References 43 publications

Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

Size-dependant behaviour of functionally graded microplates based on the modified strain gradient elasticity theory and isogeometric analysis

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations

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