Modelling the flexural waves in a nanoplate based on the fractional order nonlocal strain gradient elasticity and thermoelasticity

2021 ◽  
Vol 266 ◽  
pp. 113793
Author(s):  
Yishuang Huang ◽  
Peijun Wei
Keyword(s):  
Fractional Order ◽  
Strain Gradient ◽  
Gradient Elasticity ◽  
Strain Gradient Elasticity ◽  
Flexural Waves ◽  
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.

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