Wave Propagation in Nonlinear-elastic Isotropic Media : Two-Dimensional Case
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Wave propagation in the nonlinear-elastic isotropic media was analyzed in a two-dimensional case. In the analysis, governing equations take into account both the physical nonlinearity caused by the stress-strain relation and the geometric nonlinearity resulting from the quadratic strain-displacement relation. The equations obtained are numerically evaluated by use of the extended finite difference method expanded in Taylor series. The wave sources have a form of mountain ridge with a width -2<hx<2, where hx is a distance x normalized by wave number h of P waves in the linear theory. The waves generated are then aperiodic. Only soliton-like or step-shaped simple waves (after gas-dynamics) are found numerically. Existence of these waves are also confirmed analytically by use of the second order theory. Unlike the linear theory, the velocity of the simple waves in the nonlinear theory is not exactly the same as that of P or S waves in the linear theory relying on the elastic media. Advancing speed of the waves depends on the gradient of the front simple wave. In simple waves with large amplitude, the u component (in the direction of the propagation) is more remarkably dispersed than the transverse component. This phenomenon is likely to be observed at a great distance as the P wave dispersion instead of simple wave dispersion.非線形等方性矧生体において,エネルギー関数,非線形歪-応力テンソル,非線形歪テンソルを用い,変位微分の三次項まで含む非線形動的方程式(Nonlinear dynamic equation)が導入された.
- 東京大学地震研究所,Earthquake Research Institute, University of Tokyoの論文
- 1990-09-28
東京大学地震研究所,Earthquake Research Institute, University of Tokyo | 論文
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