Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis

Shariati, Ali; Hosseini, S. Hamed S.; Ebrahimi, Farzad; Toghroli, Ali

doi:10.1007/s00366-020-00942-y

Cited by 17 publications

(3 citation statements)

References 77 publications

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“…They presented their results by using the differential cubature method and the Bolotin method and considering polyvinylidene fluoride and the Kelvin-Voigt model. Shariati et al 25 studied the analysis of dynamic parametric excitation and nonlinear vibrations of plate with considering size effects. Considering Mathiue-Hill nonlinear systems, they came to the conclusion that the damping coefficient is the factor that changes the bifurcation Point.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

Sourani,

Ghorbanpour Arani,

Hashemian

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study analyzes the nonlinear dynamic stability of carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic compressive biaxial mechanical loading. The nano/micro plate is single-layer with a uniform and rectangular cross section. Polyvinylidene fluoride (PVDF) is the material used for the nano/micro plate. Also, it is located on a nonlinear viscoelastic piezoelectric foundation made of Zinc Oxide (ZnO). Single-walled carbon nanotubes (SWCNTs) have been used to strengthen nano/micro plate. Using Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Nano/micro plate is subjected to 2D magnetic field and electric potential. Magnetic field effects are incorporated using Maxwell’s relations. An alternating and direct voltage is applied to the nano/micro plate and also smart foundation in thickness direction. Eshelby-Mori-Tanaka approach is used to estimate the effective elastic properties. Additionally, follower force and uniform thermal gradient is applied to nano/micro plate in this study. The nonlinear strain–displacement relations are based on the Von-Kármán theory. According to classical, first order, third order, sinusoidal, parabolic, hyperbolic and exponential shear deformation plate theories, a new formulation is proposed incorporating surface stress effects through the Gurtin-Murdoch elasticity theory. In order to consider small scale parameters, this research is based on modified strain gradient theory (MSGT). Using the energy method and Hamilton’s principle, the non classical governing equations are derived. For nano/micro plate, simply supported boundary conditions are considered. For the purpose of solving differential equations, an analysis based on Galerkin procedure and finally the Bolotin method will be used to obtain the dynamic instability region (DIR). It is the objective of this study to investigate the impact of such parameters as small-scale parameters, alternating and direct applied voltage, intensity of magnetic field, surface effects, thermal environment and static load factor on the DIR. This study revealed that taking into account the smart foundation reduces the area of dynamic instability region by more than 60% for a constant intensity of magnetic field. The stability responses are also more convergent with the smart foundation. Additionally, the range is moved toward higher excitation frequencies and greater system stability. Validation of answers based on reliable scientific articles is one of the final stages of this research. These results can be used to design nano/micro electromechanical systems.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

Sourani,

Ghorbanpour Arani,

Hashemian

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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show abstract

“…Keshtegar et al [9] evaluated the buckling, vibration, and bending behavior of integrating annular nanoplate with smart layers at both surfaces. Shariati et al [10] presented the nonlinear dynamic instability of the reinforced piezoelectric nanoplates. Mendes et al [11] presented the utilize of a smart element for the sake of energy harvesting from a rod assemblage under the varying normal force.…”

Section: Introductionmentioning

confidence: 99%

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

et al. 2021

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The dynamic stability response of a micro sandwich beam with leptadenia pyrotechnica rheological elastomer (LPRE) core is studied. The top and bottom layers respectively are assumed as piezoelectric reinforced with carbon nanotubes (CNTs) and porous functionally graded materials (FGM). The core and top layers are affected by magnetic and electric fields for the magnetic and piezoelectric characteristics of the layers, respectively. The Halpin-Tsai micromechanics theory for obtaining the effective material properties of the nanocomposite layer is utilized. On the basis of Kelvin-Voigt model, the structural damping of the smart micro beam is assumed. The microstructure is located on the viscoelastic model which is simulated using Visco-Pasternak platform. The size effects are assumed according to the theory of strain gradient including three-length scale constants. The various theories of first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), parabolic shear deformation beam theory (PSDBT), and exponential shear deformation beam theory (ESDBT) are utilized for driving the governing equations according to the Hamilton's principle. The motion final relations are solved by the differential quadrature method (DQM) for presenting the dynamic buckling area. The effects of different components such as volume percentage and distribution of GPLs, porosities, magnetic field of LPRE, applied voltage, FG index, structural damping, and geometric components of the micro sandwich beam on the dynamic stability reign (DIR) of the system are shown. The results with other researcher papers are compared. The results show that the DIR increases by applying a magnetic field to the LPRE layer.

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“…The low order damping behavior remarkably rise by the several VE layers -The coupling influence of geometric & material NLs significantly enhance the vibration parameters in the 1st mode -A repetitive variations in the 2nd & 3rd mode NFs & damping ratio caused by the continuous increasing in the excitation amplitude Investigate the NL vibrational behavior-The nonlinearity has low impact on bifurcation points -The parametric excitation and the external applied voltage have the same impact on dynamic stability -The amplitude response is directly reliant on foundation constant[523] …”

mentioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis

Cited by 17 publications

References 77 publications

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

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