Nonlinear shear wave interaction in soft solids.
This paper describes nonlinear shear wave experiments conducted in soft solids with transient elastography technique. The nonlinear solutions that theoretically account for plane and nonplane shear wave propagation are compared with experimental results. It is observed that the cubic nonlinearity implied in high amplitude transverse waves at f(0)=100 Hz results in the generation of odd harmonics 3f(0), 5f(0). In the case of the nonlinear interaction between two transverse waves at frequencies f(1) and f(2), the resulting harmonics are f(i)+/-2f(j)(i,j=1,2). Experimental data are compared to numerical solutions of the modified Burgers equation, allowing an estimation of the nonlinear parameter relative to shear waves. The definition of this combination of elastic moduli (up to fourth order) can be obtained using an energy development adapted to soft solid. In the more complex situation of nonplane shear waves, the quadratic nonlinearity gives rise to more usual harmonics, at sum and difference frequencies, f(i)+/-f(j). All components of the field have to be taken into account.
Jacob
Xavier
X
Laboratoire Ondes et Acoustique, ESPCI-CNRS UMR 7587-INSERM-Universite Paris VII, 10 rue Vauquelin 75231 Paris Cedex 05, France.
Catheline
Stefan
S
Gennisson
Jean-Luc
JL
Barrière
Christophe
C
Royer
Daniel
D
Fink
Mathias
M
D000162:Acoustics; D016880:Anisotropy; D001696:Biomechanical Phenomena; D004548:Elasticity; D020342:Finite Element Analysis; D006801:Humans; D016014:Linear Models; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D019047:Phantoms, Imaging; D012212:Rheology; D033081:Shear Strength; D013018:Sound Spectrography; D013718:Tensile Strength; D014783:Viscosity