Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

Ultrasonic Characterization of Interfaces in Composite Bonds

“…The objective is to determine interfacial properties separately from bulk properties of adhesives. The recursive asymptotic stiffness matrix method [7] is integrated into this model to calculate wave propagation in composite bonded structures.…”

Effective high-order approximations of layered coatings and linings of anisotropic elastic, viscoelastic and nematic materials

“…[5][6][7][8][9][10][11][12][13][14][23][24][25] We will now compare the propagator matrices obtained using impedance boundary conditions (4.1)-(4.3) and using the method of expanding the propagator matrix of the partial waves exp[i(kX − T)] with respect to the wave number, taking into account the components of higher orders. 21,29,30 We will express the normal derivatives of d and t z from the equations of elasticity and Hooke's law in dimensional form ∂ T → iω, ∂ X˛→ iką The approximate matrix B ii contains a section of a power series for B(h), and the last iterations refine this approximation. Unlike the approximation for B ii , obtained earlier, 20,21,29,30 the approximation proposed here takes into account the non-zero matrices O 2 and O 3 , which provides the same asymptotic accuracy of the displacements and stresses.…”

“…21,29,30 We will express the normal derivatives of d and t z from the equations of elasticity and Hooke's law in dimensional form ∂ T → iω, ∂ X˛→ iką The approximate matrix B ii contains a section of a power series for B(h), and the last iterations refine this approximation. Unlike the approximation for B ii , obtained earlier, 20,21,29,30 the approximation proposed here takes into account the non-zero matrices O 2 and O 3 , which provides the same asymptotic accuracy of the displacements and stresses.…”

Mapped orthogonal functions method applied to acoustic waves-based devices

“…A major drawback of the process is that it involves, by modelling the FGM by homogeneous layers, an approximation before any calculation. An alternative method consists in using geometrical integrators in the form of a Magnus expansion 12 to compute the transfer matrix for a thin vertically nonhomogeneous layer and an efficient recursive algorithm to compute from the thin layer solution the wave propagation solution for an arbitrary FGM layered structure. For an overview on approximate methods appropriate to FGM, see Ref.…”