{"title":"具有周期性谐振器阵列的无限束和板中弯曲波的带隙","authors":"Jing-Heng Chen, I-Chein Chao, Tungyang Chen","doi":"10.1093/jom/ufac033","DOIUrl":null,"url":null,"abstract":"The subject of seismic metamaterials, inspired from novel ideas in optics and acoustics, has attracted great attention in the last decade for potential applications in earthquake engineering. Simple structure systems, like beams and plates, with periodically attached mechanical resonators provide a simple physical model to interpret the existence of certain frequency bandgap in dispersion relations and to simulate the mechanism of flexural energy attenuation. In this work, we consider simple structure systems of beams and plates with periodically attached resonators. The resonator is composed of a spring, a damper and a mass attached along the beam direction. We utilize the Timoshenko beam model and the Mindlin plate theory to incorporate the shear effect. The plane wave expansion method together with the Bloch theorem is used to expand the governing field into an eigenvalue problem of an infinite complex system, allowing us to characterize the band structures of the dispersion relations. Local resonance and Bragg bandgaps are identified and examined. The effect of thickness ratios, the damping ratio and the shear modulus are exemplified to demonstrate how these factors will affect the formation of bandgaps. This formulation demonstrates a feasibility that a periodic array of mechanical resonators together with suitable material and geometric parameters of beams and plates can be designed to tune with the dispersion behavior in the control of flexure waves. This study may open up new potential in the control of wave propagation in complex continuum systems through the interaction of adequately designed resonators.","PeriodicalId":50136,"journal":{"name":"Journal of Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Bandgaps for flexural waves in infinite beams and plates with a periodic array of resonators\",\"authors\":\"Jing-Heng Chen, I-Chein Chao, Tungyang Chen\",\"doi\":\"10.1093/jom/ufac033\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The subject of seismic metamaterials, inspired from novel ideas in optics and acoustics, has attracted great attention in the last decade for potential applications in earthquake engineering. Simple structure systems, like beams and plates, with periodically attached mechanical resonators provide a simple physical model to interpret the existence of certain frequency bandgap in dispersion relations and to simulate the mechanism of flexural energy attenuation. In this work, we consider simple structure systems of beams and plates with periodically attached resonators. The resonator is composed of a spring, a damper and a mass attached along the beam direction. We utilize the Timoshenko beam model and the Mindlin plate theory to incorporate the shear effect. The plane wave expansion method together with the Bloch theorem is used to expand the governing field into an eigenvalue problem of an infinite complex system, allowing us to characterize the band structures of the dispersion relations. Local resonance and Bragg bandgaps are identified and examined. The effect of thickness ratios, the damping ratio and the shear modulus are exemplified to demonstrate how these factors will affect the formation of bandgaps. This formulation demonstrates a feasibility that a periodic array of mechanical resonators together with suitable material and geometric parameters of beams and plates can be designed to tune with the dispersion behavior in the control of flexure waves. This study may open up new potential in the control of wave propagation in complex continuum systems through the interaction of adequately designed resonators.\",\"PeriodicalId\":50136,\"journal\":{\"name\":\"Journal of Mechanics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1093/jom/ufac033\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1093/jom/ufac033","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
Bandgaps for flexural waves in infinite beams and plates with a periodic array of resonators
The subject of seismic metamaterials, inspired from novel ideas in optics and acoustics, has attracted great attention in the last decade for potential applications in earthquake engineering. Simple structure systems, like beams and plates, with periodically attached mechanical resonators provide a simple physical model to interpret the existence of certain frequency bandgap in dispersion relations and to simulate the mechanism of flexural energy attenuation. In this work, we consider simple structure systems of beams and plates with periodically attached resonators. The resonator is composed of a spring, a damper and a mass attached along the beam direction. We utilize the Timoshenko beam model and the Mindlin plate theory to incorporate the shear effect. The plane wave expansion method together with the Bloch theorem is used to expand the governing field into an eigenvalue problem of an infinite complex system, allowing us to characterize the band structures of the dispersion relations. Local resonance and Bragg bandgaps are identified and examined. The effect of thickness ratios, the damping ratio and the shear modulus are exemplified to demonstrate how these factors will affect the formation of bandgaps. This formulation demonstrates a feasibility that a periodic array of mechanical resonators together with suitable material and geometric parameters of beams and plates can be designed to tune with the dispersion behavior in the control of flexure waves. This study may open up new potential in the control of wave propagation in complex continuum systems through the interaction of adequately designed resonators.
期刊介绍:
The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.