Wave propagation in light weight plates with truss-like cores
Wave propagation in light weight plates with
truss-like cores is investigated in this thesis.
In a first step, a simplified two-dimensional strip model based on analytic beam functions is established and validated experimentally. This model is also valid for line force excitation and response in the direction parallel to the intermediate webs. The model is employed to investigate the wave propagation in light weight profile strips with truss-like cores. A study using different core geometries with and without diagonal stiffeners reveals significant differences. Periodic system effects are clearly visible, most pronounced for the case of solely vertical webs. A stiffening effect of the fillets at the joints is identified, whereas their additional mass is of minor importance.
The wavenumber content of periodic light weight profile strips is investigated by using the theory of wave propagation in multi-coupled periodic systems 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 arise, 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 $5%$ have a limited effect on the structural dynamics of the strip.
The second part of the work extends the two-dimensional strip model to a full three-dimensional model of the investigated light weight plates.
For the generic light weight plates with periodicity in the lateral dimension the wavenumber content is characterized by strong directional wave propagation and resulting wave beaming in some frequency bands, where local vibrations are of primary concern. In the low frequency region, where global plate waves dominate, the vibrational behaviour can be reduced to equivalent plate models. For profiles with inclined webs, global orthotropicity is limited and global bending wave dispersion is similar irrespective of direction. For profiles with solely vertical webs, strong orthotropicity with significantly higher wavenumbers in lateral direction, normal to the webs, is demonstrated.
The strong periodic pass- and stop-band behaviour detected in the strip investigation is transformed into a spatial stop- and pass-band distribution of high and low vibration zones. As a result, the stop-bands of the two-dimensional investigation are weakened for point excitation of full plates, represented by a rising real part of the input mobilities. In these lateral stop-bands the imparted power is transmitted mainly in the longitudinal direction, parallel to the webs of the inner core.
Different methods for the extraction of theoretical and experimental dispersion characteristics are applied and discussed. Theoretical dispersion characteristics and mobilities are validated on a regional train floor section which serves as an application example.
Dissertation : http://opus.kobv.de/tuberlin/volltexte/2008/2060/ 
Supervisor : Prof. Dr.-Ing. B.A.T. Petersson