Thermal stability design for flexural wave bandgap of metamaterial plates with perforated and pre-curved patterns

doi:10.1007/s10483-026-3359-6

摘要/Abstract

Abstract:

A design idea for single-component metamaterial plates is proposed to achieve the thermal stability of flexural wave bandgap by the perforated and pre-curved patterns. The band structure analysis suggests that perforation can release part of the in-plane thermal expansion to weaken the softening effect of thermal stress. Introducing pre-curved components to the perforated structure will stop the decrement of the bandgap frequency in thermal environment, and even make the frequency higher with appropriate structural parameters. The bending stiffness of the heated plate is enhanced by the thermal deflection induced stiffening effect of the pre-curved components. The segmented pre-curved component presents a strong ability to resist the thermal influence on the flexural wave bandgap. A simplified model is established for the local structure of the pre-curved component. The theoretical calculations explain the thermally induced frequency increment of the bandgap and the discrepancy in the thermal response between the two pre-curved models. The transmittance of flexural wave validates the effectiveness of the proposed design.

Key words: metamaterial plate, flexural vibration, bandgap, perforation, pre-curved pattern, thermal stability

中图分类号:

O343

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 443-472.

Qian GENG, Xing ZHOU, Mengyang WANG, Xiongwei YANG, Zhushan SHAO, Yueming LI. Thermal stability design for flexural wave bandgap of metamaterial plates with perforated and pre-curved patterns[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 443-472.

图/表 24

Material	Young’s modulus/GPa	Poisson’s ratio	Mass density/(kg·m^-3)	Thermal expansion coefficient/°C
Aluminum	69	0.34	2 700	$2.3 × 10 − 5$

Type	Geometric parameter	Value
Perforation enveloped area	a	$b − 0.3$ mm
Perforation enveloped area	b	6 mm, 8 mm, 10 mm
Root size of perforation	a	7.4 mm, 7.1 mm, 6 mm
Root size of perforation	b	8 mm

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