Reflection and Transmission of Circularly Polarized Elastic Waves of Finite Amplitude

1979 ◽  
Vol 46 (4) ◽  
pp. 867-872 ◽  
Author(s):  
M. M. Carroll
Keyword(s):  
Elastic Waves ◽  
Finite Elasticity ◽  
Elliptic Functions ◽  
Finite Amplitude ◽  
Plane Boundary ◽  
Elastic Solids ◽  
Jacobian Elliptic Functions ◽  
Reflection And Transmission ◽  
The Third ◽  
Fixed Boundaries

Finite amplitude standing wave solutions, obtained previously, are specialized to the case of incompressible isotropic elastic solids with cubic or quintic shear response. This allows closed-form expressions for the motion and stress field, in terms of Jacobian elliptic functions and elliptic integrals and furnishes solutions for approximate finite elasticity theories in which terms up to sixth degree in the stress and strains are retained. The solutions for reflection from free or fixed boundaries, for resonant standing waves in a plate, and for reflection and transmission at a plane boundary are examined in the context of the third and fourth-order approximations.

Jacobian elliptic functions and a family of bivariate peak polynomials

2021 ◽  
Vol 97 ◽  
pp. 103371
Author(s):  
Shi-Mei Ma ◽  
Jun Ma ◽  
Yeong-Nan Yeh ◽  
Roberta R. Zhou
Keyword(s):  
Elliptic Functions ◽  
Jacobian Elliptic Functions

ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD

2010 ◽  
Vol 24 (08) ◽  
pp. 761-773
Author(s):  
HONG ZHAO
Keyword(s):  
Difference Equations ◽  
Elliptic Function ◽  
Analytical Study ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobian Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Periodic Wave Solutions ◽  
Trigonometric Function Solutions

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

Reflection and transmission of elastic waves through nonlocal piezoelectric plates sandwiched in two solid half-spaces

2021 ◽  
Vol 168 ◽  
pp. 108306
Author(s):  
Cancan Liu ◽  
Jiangong Yu ◽  
Xianhui Wang ◽  
Bo Zhang ◽  
Xiaoming Zhang ◽  
...  
Keyword(s):  
Elastic Waves ◽  
Reflection And Transmission ◽  
Piezoelectric Plates

Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

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