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- Title
Theoretical calculation and band gap characteristics of outward hierarchical local resonance Euler beam.
- Authors
Lei, Lijian; Zhang, Shiqian; Zheng, Zhigang; Ma, Minglei
- Abstract
The local resonance phononic crystals have advantages in obtaining low frequency band gaps, while the local resonance band gap obtained by traditional structures is inconvenient for engineering applications due to its narrow width. In this manuscript, a theoretical framework for the design and analysis of the Outward Hierarchical Local Resonance Euler Beam (OHLREB) structure has been introduced, which considers the foundational constraints, non-rigid interfaces, and the damping characteristics of the coating layer, leading to a significant enhancement in the low-frequency band gap properties. To analyze the band gap properties of OHLREB, the improved transfer matrix method is derived to obtain the band structure, and the spectral element method is applied to calculate the frequency response function. Furthermore, the band gap mechanism is investigated based on modal analysis of primitive cell and the time domain analysis and energy period analysis of OHLREB structure. The results indicate that improved transfer matrix method can offer a more streamlined and transparent process for solving eigenvalues and determining attenuation intervals, which can be used for the theoretical analysis of band gap regulation. It overcomes the constraints of traditional approaches by reducing the computational burden associated with matrix inversions and multiplications, thereby enhancing the efficiency of band gap analysis. The band gap mechanism investigation demonstrates that the energy conversion period is considerably longer than the load period in band gap frequency, leading to multiple conversions of the kinetic energy of the scatterer and the elastic strain energy of the coating layer within a single energy cycle, which leads to the strong local resonance and results in the attenuation of elastic waves in the band gap range. The parameter analysis is carried out to reveal the regulation laws of band gap, the results reveal that band gap intervals and attenuation efficiency can be optimized to obtain low frequency and broadband by configurating properly the control parameters, such as the matrix reaction modulus, interface stiffness, the coating layer damping, and the scatterer combination. Based on the analysis results, the design and control directions for obtaining the wider and lower frequency band gaps are given. The conclusions obtained in this manuscript can provide theoretical support and practical design perspectives for multi-frequency vibration control field.
- Subjects
TRANSFER matrix; PHONONIC crystals; BAND gaps; SPECTRAL element method; TIME-domain analysis; STRAIN energy; KINETIC energy
- Publication
Applied Physics A: Materials Science & Processing, 2024, Vol 130, Issue 7, p1
- ISSN
0947-8396
- Publication type
Article
- DOI
10.1007/s00339-024-07613-5