Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support

Kumar, Yogesh; Gupta, Ankit

doi:10.1007/s00419-021-02092-z

Cited by 17 publications

(17 citation statements)

References 58 publications

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“…All the above-mentioned studies reported a significant influence of the porosities on the structural responses of FGM structures. Further, the effects of porosity distributions on the structural behavior of FGM nanobeams are presented in [29,30], using non-local elasticity theory. Madan et al [31] studied the elastic speed analysis of rotating porous FGM disks having uniform and various nonuniform porosity distributions.…”

Section: Introductionmentioning

confidence: 99%

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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Section: Introductionmentioning

confidence: 99%

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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“…Furthermore, this work is carried out using the FE approach owing to its simplicity in incorporating multi-field interactions and efficiency in capturing the complex structural responses accurately. 58–61 It is believed that the outcomes of this work will lead to novel designs of light-weight smart structures for integrated structural health monitoring and management applications.…”

Section: Introductionmentioning

confidence: 99%

Integrated effects of auxeticity and pyro-coupling on the nonlinear static behaviour of magneto-electro-elastic sandwich plates subjected to multi-field interactive loads

Mahesh

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work presents a detailed investigation of the effect of auxeticity synergised with the pyro-coupling behaviour of multiphase magneto-electro-elastic (M-MEE) composites using a finite element (FE) framework. The nonlinear deflection and bending problems of sandwich plates with auxetic core and M-MEE skins subjected to multi-physics load (electric, magnetic and thermal) are probed. The plate kinematics is governed by Reddy’s higher-order shear deformation theory (HSDT). The nonlinear relation between the strains and displacements is established through von-Karman’s nonlinear relations. The temperature profiles are considered linearly and nonlinearly varying across the thickness of the plate. Various parametric studies presented in this article highlight the influence of the auxetic cell inclination angle, rib-length ratio, rib thickness, the plate-to-core ratio etc., associated with the pyro-coupling on the nonlinear deflection and bending of sandwich plates. The results reveal that the plate deflection, bending behaviour and degree of pyro-coupling significantly depend on the auxetic unit cell dimensions and magnitude of electro-magnetic loads. The significant influence of temperature profiles on the pyro-coupling are witnessed at lower auxetic cell angle. The nonlinear deflections of the sandwich plate and hence the potentials developed tend to improve with the lower values of plate-to-core ratio and rib thickness. The prominent outcomes of this work related to integrated effects of auxeticity and pyro-coupling are not yet reported in the open literature and are deemed to be utilised as a future reference.

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“…34–36 Additionally, up to now, many studies have been carried out to investigate the static and dynamic behaviors of micro/nano structures based on the higher-order theories. 37–46…”

Section: Introductionmentioning

confidence: 99%

“…[34][35][36] Additionally, up to now, many studies have been carried out to investigate the static and dynamic behaviors of micro/nano structures based on the higher-order theories. [37][38][39][40][41][42][43][44][45][46] It is known that thermoelastic analysis for microstructures under non-uniform temperature field is vital. 47 The classical thermoelasticity proposed by Biot assumes that the speed for heat transfer is infinite due to the inherent nature of the parabolic heat conduction model.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories

Peng

2022

The Journal of Strain Analysis for Engineering Design

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Ultra-slow relaxation process of polymers has the memory-dependent feature, integer-order thermoviscoelastic models may fail to describe the dynamic behaviors of viscoelastic structures accurately. Additionally, it is noticed that the small-scale effect of elastic deformation and heat conduction in a non-isothermal temperature environment is becoming significant due to the development of micro-devices. To better capture the memory-dependent effect and the small-scale effect of viscoelastic micro-structures in heat transfer environment, as a first attempt, present work focuses on developing a refined fractional Kelvin-Voigt thermoviscoelastic model by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). Then, the model is applied to investigating the transient response of a polymer microbeam subjected to a harmonic thermal loading. The governing equations involving the modified parameters are formulated and then solved by Laplace transform method. Some parametric results are demonstrated to display the impacts of the nonlocal thermal parameter, the material length-scale parameter and the fractional-order parameter on the considered physical quantities. The results show that the small-scale effect and the memory-dependent effects strongly depend on the polymer micro-structure characteristics in thermal environment.

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Size-dependent stochastic vibration response of compositionally graded nanoplates with system randomness using nonlocal continuum model with partial support

Cited by 17 publications

References 58 publications

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

Integrated effects of auxeticity and pyro-coupling on the nonlinear static behaviour of magneto-electro-elastic sandwich plates subjected to multi-field interactive loads

Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories

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