Analysis of Bloch’s Method in Structures With Energy Dissipation

2010 ◽  
Author(s):  
Farhad Farzbod ◽  
Michael J. Leamy
Keyword(s):  
Energy Dissipation ◽  
Vibration Analysis ◽  
General Framework ◽  
Periodic Potential ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Periodic Systems ◽  
Crystalline Solid ◽  
Structural Damping ◽  
Electron Wave

Bloch analysis was originally developed to solve Schro¨dinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schro¨dinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straight-forward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

Analysis of Bloch’s Method in Structures with Energy Dissipation

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Farhad Farzbod ◽  
Michael J. Leamy
Keyword(s):  
Energy Dissipation ◽  
Periodic Potential ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Periodic Systems ◽  
Crystalline Solid ◽  
Structural Damping ◽  
Electron Wave ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Bloch analysis was originally developed to solve Schrödinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schrödinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straightforward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

scholarly journals “Fuzzy Band Gaps”: A Physically Motivated Indicator of Bloch Wave Evanescence in Phononic Systems

Crystals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 66
Author(s):  
Connor D. Pierce ◽  
Kathryn H. Matlack
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Quantitative Measure ◽  
Bloch Wave ◽  
Phononic Crystals ◽  
Wave Transmission ◽  
Band Gaps ◽  
Dissipative Systems ◽  
Frequency Range ◽  
Wave Modes

Phononic crystals (PCs) have been widely reported to exhibit band gaps, which for non-dissipative systems are well defined from the dispersion relation as a frequency range in which no propagating (i.e., non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Various measures have been proposed to quantify the “evanescence” of frequency ranges and/or wave propagation directions, but these measures are not based on measurable physical quantities. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite PC from the infinite dispersion relation is elusive. In this paper, we propose an “evanescence indicator” for PCs with 1D periodicity that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed “fuzzy band gaps” due to the smooth (rather than abrupt) transition between evanescent and propagating wave characteristics. The indicator is capable of identifying polarized fuzzy band gaps, including fuzzy band gaps which exists with respect to “hybrid” polarizations which consist of multiple simultaneous polarizations. We validate the indicator using simulations and experiments of wave transmission through highly viscoelastic and finite phononic crystals.

Elastic wave band gaps in 2D fractal phononic crystals

2021 ◽  
Author(s):  
Victor Gustavo Ramos Costa Dos Santos ◽  
Edson Jansen Pedrosa de Miranda Junior ◽  
Jose Maria Campos dos Santos
Keyword(s):  
Elastic Wave ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Wave Band

Tunable Band Gaps of Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Band Structures

2009 ◽  
Author(s):  
Zi-Gui Huang ◽  
Yunn-Lin Hwang ◽  
Pei-Yu Wang ◽  
Yen-Chieh Mao
Keyword(s):  
Acoustic Waves ◽  
Composite Structures ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Sound Insulation ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Elastic Band ◽  
Band Structures ◽  
Elastic Band Gaps

The excellent applications and researches of so-called photonic crystals raise the exciting researches of phononic crystals. By the analogy between photon and phonon, repetitive composite structures that are made up of different elastic materials can also prevent elastic waves of some certain frequencies from passing by, i.e., the frequency band gap features also exist in acoustic waves. In this paper, we present the results of the tunable band gaps of acoustic waves in two-dimensional phononic crystals with reticular band structures using the finite element method. Band gaps variations of the bulk modes due to different thickness and angles of reticular band structures are calculated and discussed. The results show that the total elastic band gaps for mixed polarization modes can be enlarged or reduced by adjusting the orientation of the reticular band structures. The phenomena of band gaps of elastic or acoustic waves can potentially be utilized for vibration-free, high-precision mechanical systems, and sound insulation.

scholarly journals Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model

Crystals ◽  
2016 ◽  
Vol 6 (5) ◽  
pp. 52 ◽  
Author(s):  
Yan-Feng Wang ◽  
Alexei Maznev ◽  
Vincent Laude
Keyword(s):  
Lattice Model ◽  
Phononic Crystals ◽  
Band Gaps

scholarly journals Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

2008 ◽  
Vol 45 (14-15) ◽  
pp. 4203-4210 ◽  
Author(s):  
Yi-Ze Wang ◽  
Feng-Ming Li ◽  
Wen-Hu Huang ◽  
Xiaoai Jiang ◽  
Yue-Sheng Wang ◽  
...  
Keyword(s):  
Phononic Crystals ◽  
Band Gaps ◽  
Wave Band ◽  
Two Dimensional

Optimizing Distributed-Contact Friction in Ring Dampers

2005 ◽  
Author(s):  
X. W. Tangpong ◽  
J. A. Wickert ◽  
A. Akay ◽  
Yuri Karpenko
Keyword(s):  
Energy Dissipation ◽  
Vibration Analysis ◽  
Excitation Frequency ◽  
Contact Friction ◽  
Friction Damping ◽  
End Effects ◽  
Noise And Vibration ◽  
Disk Brake ◽  
Brake Rotors ◽  
Base Structure

This paper describes the vibration analysis and optimization of a base structure and a beam-like attached damper sub-system that couple in vibration through distributed-contact friction damping. The objective is to tune the characteristics of the damper sub-system to maximize energy dissipation, and therefore to control vibration of the base structure. Applications of the concept to noise and vibration phenomena associated with automotive disk brake rotors are discussed. Per-cycle energy dissipation is examined as a function of damper preload for two classes of sub-systems: dampers that are split rings, and dampers that are continuous rings. End-effects and the manner in which energy dissipation is distributed spatially along the damper are also discussed. Of potential technological application, for a given excitation frequency, the damper sub-system’s design can be optimized to reduce vibration of the base structure.

scholarly journals EXPERIMENTAL ANALYSIS OF STRUCTURAL DAMPING FOR BOLTED AND WELDED SPLICE CONNECTION JOINT FOR IPE-80 STEEL PROFILE

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Ognjen Mijatović ◽  
Zoran Mišković ◽  
Ratko Salatić ◽  
Rastislav Mandić ◽  
Valentina Golubović-Bugarski ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Experimental Analysis ◽  
Damping Capacity ◽  
Dynamic Problems ◽  
Structural Damping ◽  
Structural Joints

Progress and demands of all types of constructions imposed the need for the development of modernstructures that are lightweight, but at the same time have high damping capacity and stiffness. Theconsequences of these requirements are increased dynamic problems related to vibrations anddissipative processes in structure connection joints. Structural joints are the main reason for thesignificant reduction of the level of energy dissipation and source of structural damping so thereforethey have become a subject of interest to many researchers. The aim of this paper is to present someproblems regarding research of structural damping and the importance of study Contact Mechanicsto better understand the problem of structural damping.

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