Modal Analysis of Floquet Waves in Composite Materials

Abstract

A numerical method which admits discontinuous variable coefficients in the wave equation is employed for handling the wave propagation in composite materials. The resulting algebraic eigenvalue system is simplified by a rank–one matrix modification that reduces the computing time by at least one order of magnitude. The first five modes are accurately and efficiently computed as a demonstration of the method presented.

Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

“…Let us choose a pair of sectionally continuous and differentiable functions u and a which satisfy the equation of motion (1), the quasi-periodic boundary conditions (3) and (4) and continuity condition (6). The solution (uo ) which also satisfies the constitutive equation Let us choose a pair of sectionally continuous and differentiable functions u and a which satisfy the quasi-periodic boundary conditions (3) and (4) and continuity condition (5).…”

“…The solution (uo ) which also satisfies the constitutive equation Let us choose a pair of sectionally continuous and differentiable functions u and a which satisfy the quasi-periodic boundary conditions (3) and (4) and continuity condition (5). The solution (u,a)which also satisf'ies the equation of motion (1), the constitutive equation (2) and continuity condition (6) is given by the variational equation…”

“…This approach has been recently used by several authors [1-7 to study steady state wave propagation in periodic elastic composites. Of these, some [1][2][3][4][5] used variational methods while others [6][7] used direct numerical methods involving discretization of the governing differential equations and associated quasi-periodic boundary conditions.…”

An FFT-based approach for Bloch wave analysis: application to polycrystals

“…Other common numerical approaches to solve partial differential equations have also been considered, like finite differences, fast multipoles, or wavelets [6], while other common approaches as FFT-based homogenization remain almost unexplored in this context. The FS/wave plane analysis was first proposed in 1D [7] and further extended to higher dimensions in subsequent works [8][9][10]. The method is based on expressing the periodic displacement U (x) as a Fourier series expansion that corresponds to a superposition of plane waves u(x) ≈Û 0 +Û 1 e iξ 1 x + • • • +Û n e iξ n x.…”

Finite element analysis of harmonic waves in layered and fibre‐reinforced composites

“…The aim of the present paper is to develop a method of finite elements for the solution of these problems. Finite-element formulations for problems of harmonic waves in composites have been given by Yang and Lee, 6 Golub, Jenning and Yang,' and Nelson and Navi. ' Orris and Petyt' treated harmonic waves in periodic structures.…”