Analytical approach to determine the impact of line source on SH-wave propagation in an anisotropic poro-viscoelastic layered structure in the context of Eringen's nonlocal elasticity theory

2021 ◽  
Vol 151 ◽  
pp. 106987
Author(s):  
Shishir Gupta ◽  
Rachaita Dutta ◽  
Soumik Das
Keyword(s):  
Wave Propagation ◽  
Elasticity Theory ◽  
Layered Structure ◽  
Line Source ◽  
Nonlocal Elasticity ◽  
Analytical Approach ◽  
Nonlocal Elasticity Theory ◽  
Sh Wave ◽  
The Impact

TORSIONAL WAVE PROPAGATION AND VIBRATION OF CIRCULAR NANOSTRUCTURES BASED ON NONLOCAL ELASTICITY THEORY

2014 ◽  
Vol 06 (02) ◽  
pp. 1450011 ◽  
Author(s):  
Z. M. ISLAM ◽  
P. JIA ◽  
C. W. LIM
Keyword(s):  
Wave Propagation ◽  
Elasticity Theory ◽  
Constitutive Relation ◽  
Nonlocal Elasticity ◽  
Numerical Solutions ◽  
Nonlocal Elasticity Theory ◽  
Torsional Wave ◽  
Nonlocal Model ◽  
Boundary Characteristics ◽  
Propagation Properties

The presence of size effects represented by a small nanoscale on torsional wave propagation properties of circular nanostructure, such as nanoshafts, nanorods and nanotubes, is investigated. Based on the nonlocal elasticity theory, the dynamic equation of motion for the structure is formulated. By using the derived equation, simple analytical solutions for the relation between wavenumber and frequency via the differential nonlocal constitutive relation and the numerical solutions for a discrete nonlocal model via the integral nonlocal constitutive relation have been obtained. This results not only show that the dispersion characteristics of circular nanostructures are greatly affected by the small nanoscale and the classical theory overestimates the stiffness of nanostructures, but also highlights the significance of the integral nonlocal model which is able to capture some boundary characteristics that do not appear in the differential nonlocal model.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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