Classification of stopbands for structural waves in a periodically corrugated thin plate and comparative analysis of their mitigation efficiency

• Generation of divergence-type and flutter-type stopbands is explained • Standing waves do not feature boundaries of flutter-type stopbands • Mitigation of energy transfer in flutter-type stopbands is relatively weak • A simple model featuring flutter-type stopbands is proposed • Reported results are verified numerically and validated experimentally A thin corrugated plate is modeled as a periodically alternating sequence of segments of a cylindrical shell with constant thickness. Dispersion equations are obtained from governing equations of dynamics of individual segments in a closed analytical form. The stopband locations are identified semi-analytically using two complementary approaches: (i) Floquet analysis of an infinite periodic structure via propagation constants, and (ii) modal analysis of a symmetric periodicity cell with class-consistent boundary conditions. Direct comparison of frequency-wise stopband locations predicted by these methodologies reveals two distinct stopband-generation mechanisms, which are, referring to classical theory of dynamic stability, classified as divergence-type and flutter-type scenarios. To quantify Insertion Losses in stopband of these types and compare their mitigation efficiencies, a forcing problem for a semi-infinite plate equipped with a finite number of cells is solved. An ultimately simple model of a periodic waveguide featuring flutter-type stopbands is presented. In Appendices, (i) reported results of Floquet analysis are replicated using WFEM, (ii) solution of forcing problem is verified using COMSOL and (iii) in-house script is validated via comparison of its predictions with experimental results available in the literature.