Waves in microstructured solids: Inverse problems

Dynamic homogenization and wave propagation in a nonlinear 1D composite material

“…Eq. (12) can be integrated exactly in elliptic functions. It may possess different solutions depending on signs of the coefficients.…”

“…In recent years, this model allowed to obtain a number of interesting results for linear [12][13][14] as well as nonlinear [15,16] dynamic properties of heterogeneous solids.…”

Internal Variables and Scale Separation in Dynamics of Microstructured Solids

“…the coefficients of the equation. In linear case, the dependence of phase velocity on microstructure gives a solid ground for solving such an inverse problem [33]. In nonlinear case, the distortion of solitary waves due to microstructure can be used [34].…”

“…It follows that the force τ should not appear in the balance of linear momentum (4) at the length scale l macro . Fortunately, the same interactive force τ together with the time derivative of the internal variable ϕ determines the intrinsic heat force in the dissipation inequality (33). Therefore, the evolution equation of the internal variable is dependent on the interactive force τ .…”

An inverse measurement of the sudden underwater movement of the sea-floor by using the time-history record of the water-wave elevation

“…In the present study, we propose a new (indirect) measurement problem for the impulsive movement, based on the time-history data acquisition. The problem introduced is involved in inverse problems that often occurs in many branches of science and engineering [5][6][7][8][9][10][11].…”