An equivalent beam and equivalent plane strain method for bang gap analysis of metamaterials

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (8) : 319-325.

MAO Xiang1, YANG Deqing1,2, LI Qing1

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Abstract

Based on the barrel bending theory of rectangular thin plates, an equivalent beam element method is proposed for the calculation of bandgap properties of metamaterials that can be simplified in plane strain mechanical problem. The equivalent beam element method and the conventional equivalent plane strain method are applied to numerically calculate the bandgap characteristics of various typical configurations of negative Poisson's ratio metamaterials (re-entrant hexagonal, star-shaped, double arrowhead and rotating triangle), comparing the differences between the two methods in terms of bandgap calculation accuracy, calculation efficiency and applicability in topology optimization, and verified by experimental test results. It is shown that both the equivalent beam element method and the equivalent plane strain method have a high bandgap calculation accuracy, within 7% of the experimental measurements. The equivalent beam element method is about 50% more efficient than the equivalent plane strain method in bandgap calculation, but the scale of the topology optimization base structure model is larger and suitable for topology optimization of rod-like metamaterial structures. The equivalent plane strain method is less efficient in bandgap calculation and the size of the base structure model is smaller for topology optimization of continuum and skeleton metamaterials. This study can provide a reference for the design of bandgap topology optimization of metamaterials.

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metamaterial / bandgap characteristics / finite element analysis / plane strain / thin plate theory

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MAO Xiang1, YANG Deqing1,2, LI Qing1. An equivalent beam and equivalent plane strain method for bang gap analysis of metamaterials[J]. Journal of Vibration and Shock, 2023, 42(8): 319-325

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