A new approach for time-dependent response of viscoelastic graphene sheets embedded in visco-Pasternak foundation based
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A new approach for time-dependent response of viscoelastic graphene sheets embedded in visco-Pasternak foundation based on nonlocal FSDT and MHSDT theories Shahriar Dastjerdi1 · Mohammad Abbasi1
Received: 24 November 2018 / Accepted: 16 August 2019 © Springer Nature B.V. 2019
Abstract In this paper, the thermo-mechanical dynamic response of annular/circular viscoelastic graphene plates embedded in visco-Pasternak foundation has been investigated using nonlocal first and modified higher-order shear deformation theories. The modified higher-order shear deformation theory is assumed to obtain the results of thick (high ratio of thickness to size) plates too. Also, the sheet is considered in thermal environment in order to study the thermal effects on the viscoelastic analysis. The viscoelastic behavior of the plate is simulated based on the Kelvin–Voigt model and the nonlinear von Kármán strains have been considered. The dynamic governing equations have been derived using the Hamilton stationary of minimum potential energy based on the nonlocal first and modified higher-order shear theories and have been solved applying semi-analytical polynomial method solving method. The solving methodology is unique and has not been used in any other dynamic analysis before and its ability for solving the dynamic governing equations has also been confirmed. The time-dependent deflection of the sheet under uniform and non-uniform loads has been obtained. Different effects on the problem, including boundary conditions, damping coefficient of visco-Pasternak foundation, viscoelastic coefficient of the plate, small-scale effects, loading, and nonlinear effects have been discussed more precisely. Keywords Annular/circular viscoelastic graphene plate · Kelvin–Voigt model · Visco-Pasternak foundation · Nonlocal first and modified higher-order shear deformation theories · SAPM
1 Introduction There are so many number of studies have been done on the analysis of elastic structural plates and shells. However, in recent years, the viscoelastic materials have been used increasingly for plate and shell structures because of their unique applications (Wei and Tan 2004; Vogel et al. 2010; Zhou et al. 2016). Consequently, proposing an accurate solution of the
B M. Abbasi
[email protected]
1
Department of Mechanical Engineering, Shahrood branch, Islamic Azad University, Shahrood, Iran
Mech Time-Depend Mater
mathematical model of the viscoelastic structural components is necessary. Due to this fact, when the structure is made of viscoelastic material, the problem becomes much more complicated. In recent years, as an efficient and simple higher theory the nonlocal theory has been used widely. With investigating the former articles, it is found that the analytical bending and vibration of viscoelastic plates had been done according to classical plate theory and the governing equations derived by the Laplace transform (Mase 1961; Sarkar 1964; Nagaya 1978), the Fourier transform (Srinivas and Rao 1971), the superposition principle (Deleeuw 1
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