A nonlocal strain gradient model for nonlinear dynamic behavior of bi-directional functionally graded porous nanoplates on elastic foundations

2020 ◽  
pp. 1-20
Author(s):  
M. Esmaeilzadeh ◽  
M. E. Golmakani ◽  
M. Sadeghian
Keyword(s):  
Dynamic Behavior ◽  
Strain Gradient ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Elastic Foundations ◽  
Gradient Model ◽  
Nonlinear Dynamic Behavior ◽  
Strain Gradient Model ◽  
Nonlocal Strain Gradient

Modelling flexural wave propagation by the nonlocal strain gradient elasticity with fractional derivatives

2021 ◽  
pp. 108128652199120
Author(s):  
Yishuang Huang ◽  
Peijun Wei ◽  
Yuqian Xu ◽  
Yueqiu Li
Keyword(s):  
Fractional Order ◽  
Strain Gradient ◽  
Present Model ◽  
Gradient Elasticity ◽  
Flexural Wave ◽  
Strain Gradient Elasticity ◽  
Gradient Model ◽  
Flexural Wave Propagation ◽  
Strain Gradient Model ◽  
Nonlocal Strain Gradient

The flexural wave propagation in a microbeam is studied based upon the nonlocal strain gradient model with the spatial and time fractional order differentials in the present work. To capture the dispersive behaviour induced by the inherent nanoscale heterogeneity, the stress gradient elasticity and the strain gradient elasticity are often used to model the mechanical behaviour. The present model incorporates the two models and introduces the fractional order derivatives which can be understood as a generalization of integral order nonlocal strain gradient model. The Laplacian operator in the constitutive equation is replaced with the symmetric Caputo fractional differential in the present model. To illustrate the flexibility of the present model, the flexural wave propagation in a microbeam is studied. The fractional order in the present model as a new material parameter can be adjusted appropriately to describe the dispersive properties of the flexural waves. The numerical results based on the new nonlocal strain gradient elasticity with fractional order derivatives are provided for both Euler–Bernoulli beam and Timoshenko beam. The comparisons with the integer order nonlocal strain gradient model and the molecular dynamic simulation are performed to validate the flexibility of the fractional order nonlocal strain gradient model.

Dynamic Behavior of Nanobeam Using Strain Gradient Model

2020 ◽  
pp. 239-252
Author(s):  
Subrat Kumar Jena ◽  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty
Keyword(s):  
Dynamic Behavior ◽  
Strain Gradient ◽  
Gradient Model ◽  
Strain Gradient Model

Nonlinear dynamic behavior of a long temperature-dependent FGM hollow cylinder subjected to thermal shocking

2014 ◽  
Vol 21 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Hong-Liang Dai ◽  
Yan-Ni Rao
Keyword(s):  
Dynamic Behavior ◽  
Hollow Cylinder ◽  
Governing Equation ◽  
Nonlinear Dynamic ◽  
Transfer Problem ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Behavior ◽  
Graded Material ◽  
Thermoelastic Characteristics

AbstractIn this paper, the nonlinear dynamic behavior of a long hollow cylinder consisting of temperature-dependent functionally graded material (FGM) subjected to thermal shocking is investigated. Material parameters of the FGM hollow cylinder, except the Poisson’s ratio, are assumed to be graded continuously through the thickness according to the power law expressions, and they are assumed to be temperature dependent. The governing equation of the motion of the FGM hollow cylinder is obtained based on the plane-stain theory and together with the governing equation of the transient heat transfer problem is solved by the finite difference method, Newmark method, and iterative method. Numerical examples are carried out in which the Si3N4-SUS304 FGM hollow cylinders are considered, and some valuable dynamic thermoelastic characteristics of the FGM hollow cylinder subjected to symmetric or asymmetric thermal shocking are revealed.

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