• Advances in nano research
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• v.10 no.3
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• pp.235-251
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• 2021

In the current study, the free vibrational behavior of a Porous Micro (PM) beam which is integrated with Functionally Graded Piezoelectric (FGP) layers with initial curvature is considered based on the two trigonometric shear deformation theories namely SSDBT and Tan-SDBT. The structure's mechanical properties are varied through its thicknesses following the given functions. The curved microbeam is exposed to electro-mechanical preload and also is rested on a Pasternak type of elastic foundation. Hamilton's principle is used to extract the motion equations and the MCST is used to capture the size effect. Navier's solution method is selected as an analytical method to solve the motion equations for a simply supported ends case and by validating the results for a simpler state with previously published works, effects of different important parameters on the behavior of the structure are considered. It is found that although increasing the porosity reduces the natural frequency, but enhancing the volume fraction of CNTs increasing it. Also, by increasing the central angle of the curved beam the vibrations of the structure increases. Designing and manufacturing more efficient smart structures such as sensors and actuators are of the aims of this study.

• Steel and Composite Structures
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• v.21 no.1
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• pp.1-36
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• 2016

In the present study, the nonlinear magneto-electro-mechanical free vibration behavior of rectangular double-bonded sandwich microbeams based on the modified strain gradient theory (MSGT) is investigated. It is noted that the top and bottom sandwich microbeams are considered with boron nitride nanotube reinforced composite face sheets (BNNTRC-SB) with electrical properties and carbon nanotube reinforced composite face sheets (CNTRC-SB) with magnetic fields, respectively, and also the homogenous core is used for both sandwich beams. The connections of every sandwich beam with its surrounding medium and also between them have been carried out by considering Pasternak foundations. To take size effect into account, the MSGT is introduced into the classical Timoshenko beam theory (CT) to develop a size-dependent beam model containing three additional material length scale parameters. For the CNTRC and BNNTRC face sheets of sandwich microbeams, uniform distribution (UD) and functionally graded (FG) distribution patterns of CNTs or BNNTs in four cases FG-X, FG-O, FG-A, and FG-V are employed. It is assumed that the material properties of face sheets for both sandwich beams are varied in the thickness direction and estimated through the extended rule of mixture. On the basis of the Hamilton's principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized by using generalized differential quadrature method (GDQM). A detailed parametric study is presented to indicate the influences of electric and magnetic fields, slenderness ratio, thickness ratio of both sandwich microbeams, thickness ratio of every sandwich microbeam, dimensionless three material length scale parameters, Winkler spring modulus and various distribution types of face sheets on the first two natural frequencies of double-bonded sandwich microbeams. Furthermore, a comparison between the various beam models on the basis of the CT, modified couple stress theory (MCST), and MSGT is performed. It is illustrated that the thickness ratio of sandwich microbeams plays an important role in the vibrational behavior of the double-bonded sandwich microstructures. Meanwhile, it is concluded that by increasing H/lm, the values of first two natural frequencies tend to decrease for all amounts of the Winkler spring modulus.

• Advances in nano research
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• v.7 no.2
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• pp.109-123
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• 2019

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.