Wave propagation in light weight profiles with truss-like cores: Wavenumber content, forced response and influence of periodicity perturbations

The wavenumber content of periodic light weight profile strips is investigated. Theory of wave propagation in multi-coupled periodic systems is used to extract the dispersion characteristics of typical configurations. Solving the transfer matrix eigenvalue problem forms a basis for understanding the wave propagation in (infinite) strips; six characteristic waves travelling in each direction occur, either propagating, decaying or complex. Each characteristic wave consists of multiple wavenumbers of different amplitude, forming the so called “space harmonic” series. Typical wave forms of characteristic waves are shown and form the basis for identifying their relative contributions in the space harmonic series.Based on the dynamic stiffness matrix of a single subelement of the periodic system the forced response is calculated for infinite light weight profile strips. The characteristic wave amplitudes for selected force excitations in combination with the corresponding wavenumber spectra form the basis for structural acoustic investigations. Input mobilities for the infinite strip are presented demonstrating the typical pass and stop band behaviour. A brief study of the influence of periodicity perturbations reveals that for typical profiles, even quite high random length variations up to about 10%10% have a limited effect on the structural dynamics of the strip.