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Bloch–Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch–Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.