Influences of the geometrical nonlinearity on the complex band structures of periodic lattice frame structures

Summary

In this study, the complex band structures of geometrically nonlinear periodic frame structures are calculated by using the Spectral Element Method (SEM). For this purpose, the spectral element matrix for a geometrically nonlinear beam element is derived. By solving the inverse eigenvalue problem for computing the complex dispersion curves k() instead of the conventional eigenvalue problem for calculating the real dispersion curves (k), the complex wave vector can be obtained, whose imaginary parts describes the evanescent behavior of the Bloch waves. Subsequently, the geometrically nonlinear effects on the evanescent behavior of the Bloch waves are investigated by evaluating the dispersion curves and the transmission spectra.

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