A Bloch wave reduction scheme for ultrafast band diagram and dynamic response computation in periodic structures

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

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Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations

Physical Review Letters ◽

10.1103/physrevlett.65.2650 ◽

1990 ◽

Vol 65 (21) ◽

pp. 2650-2653 ◽

Cited By ~ 416

Author(s):

Ze Zhang ◽

Sashi Satpathy

Keyword(s):

Wave Propagation ◽

Electromagnetic Wave ◽

Wave Solution ◽

Maxwell’S Equations ◽

Maxwell's Equations ◽

Electromagnetic Wave Propagation ◽

Periodic Structures ◽

Bloch Wave

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SEA Subsystem Property Identification by Periodic FEM Approach

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.94-96.1979 ◽

2011 ◽

Vol 94-96 ◽

pp. 1979-1982

Author(s):

Jie Gao ◽

Ke An Chen

Keyword(s):

Dynamic Response ◽

High Frequency ◽

Periodic Structures ◽

Low Frequency ◽

Engineering Method ◽

Complex Structures ◽

High Frequency Range ◽

Frequency Range ◽

Remarkable Improvement ◽

Property Identification

A study on SEA properties of periodically stiffened structure was accomplished based on the periodic theory. With application of certain software, a simulation was performed on a common periodically stiffened fuselage structure. The results indicate such modeling approach reflects relatively accurate property of subsystem in mid and high frequency range, while a remarkable improvement could also be expected in low frequency range, especially for complex structures. Such approach was approved as one reliable engineering method for solving dynamic response of periodic structures.

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Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands

Volume 2: Modeling, Simulation and Control; Bio-Inspired Smart Materials and Systems; Energy Harvesting ◽

10.1115/smasis2016-9277 ◽

2016 ◽

Author(s):

M. Nouh

Keyword(s):

Wave Propagation ◽

Vibration Suppression ◽

Periodic Structures ◽

External Disturbance ◽

Stop Band ◽

Bloch Wave ◽

Periodic Medium ◽

Elastic Structures ◽

Structural Intensity ◽

Wide Range

Periodic elastic structures consisting of self-repeating geometric or material arrangements exhibit unique wave propagation characteristics culminating in frequency stop bands, i.e. ranges of frequency where elastic waves can propagate the periodic medium. Such features make periodic structures appealing for a wide range of vibration suppression and noise control applications. Stop bands in periodic media are achieved via Bragg scattering of elastic which is attributed to impedance mismatches between the different constituents of the self-repeating cells. Stop band frequencies can be numerically predicted using mathematical models which generally utilize the Bloch wave theorem and a transfer matrix method to track the spatial and temporal parameters of the propagating waves from one cell to the next. Such analysis generates what is referred to as the band structure (or the dispersion curves) of the periodic medium which can be used to predict the location of the pass and stop bands. Although capable, these models become significantly more involved when analyzing structures with dissipative constituents and/or material damping and need further adjustments to account for complex elastic moduli and frequency dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power and energy transmission paths. It is shown that the steady-state spatial propagation of vibrational power caused by an external disturbance accurately reflects the wave propagation pattern in the periodic medium, and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The developed framework is mathematically applied to a one-dimensional periodic rod to validate the proposed method.

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