An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
H. Al Ba'ba'a ◽  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Power Flow ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
External Disturbance ◽  
Stop Band ◽  
Bragg Scattering ◽  
Spatial Propagation ◽  
The Individual ◽  
Vibrational Power Flow

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by 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 flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic 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 treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands

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.

Wave Propagation and Power Flow Analysis of Sandwich Structures With Internal Absorbers

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
J. S. Chen ◽  
R. T. Wang
Keyword(s):  
Wave Propagation ◽  
Power Flow ◽  
Wave Attenuation ◽  
Sandwich Structures ◽  
Flow Analysis ◽  
Flow Characteristics ◽  
Continuum Models ◽  
Sandwich Beams ◽  
The Core ◽  
In Series

This study examines wave attenuation and power flow characteristics of sandwich beams with internal absorbers. Two types of absorbing systems embedded in the core are considered, namely, a conventional spring-mass-dashpot system having a mass with a spring and a dashpot in parallel, and a relaxation system containing an additional relaxation spring added in series with the dashpot. Analytical continuum models used for interpreting the attenuation behavior of sandwich structures are presented. Through the analysis of the power flowing into the structure, the correlation of wave attenuation and energy blockage is revealed. The reduction in the power flow indicates that some amount of energy produced by the external force can be effectively obstructed by internal absorbers. The effects of parameters on peak attenuation, bandwidth, and power flow are also studied.

Wave Propagation in One-Dimensional Structure of Periodic Inelasticity Composites

2011 ◽  
Author(s):  
Helio Aparecido Navarro ◽  
Meire Pereira de Souza Braun
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Stop Band ◽  
Dimensional Structure ◽  
Material Models ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Structural Problems ◽  
Plastic Damage ◽  
Non Linear

This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

Piezoelectric Networks for Vibration Suppression of Mistuned Bladed Disks

2007 ◽  
Vol 129 (5) ◽  
pp. 559-566 ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Vibration Suppression ◽  
Periodic Structures ◽  
Electric Circuit ◽  
Forced Response ◽  
Bladed Disks ◽  
Vibration Localization ◽  
Network Concept ◽  
Engine Order ◽  
The Individual ◽  
Local Circuits

Extensive investigations have been conducted to study the vibration localization phenomenon and the excessive forced response that can be caused by mistuning in bladed disks. Most previous researches have focused on analyzing∕predicting localization or attacking the mistuning issue via mechanical tailoring. Few have focused on developing effective vibration control methods for such systems. This study extends the piezoelectric network concept, which has been utilized for mode delocalization in periodic structures, to the control of mistuned bladed disks under engine order excitation. A piezoelectric network is synthesized and optimized to effectively suppress vibration in bladed disks. One of the merits of such an approach is that the optimum design is independent of the number of spatial harmonics, or engine orders. Local circuits are first formulated by connecting inductors and resistors with piezoelectric patches on the individual blades. Although these local circuits can function as conventional damped absorber when properly tuned, they do not perform well for bladed disks under all engine order excitations. To address this issue, capacitors are introduced to couple the individual local circuitries. Through such networking, an absorber system that is independent of the engine order can be achieved. Monte Carlo simulation is performed to investigate the effectiveness of the network for a bladed disk with a range of mistuning level of its mechanical properties. The robustness issue of the network in terms of detuning of the electric circuit parameters is also studied. Finally, negative capacitance is introduced and its effect on the performance and robustness of the network is investigated.

Energy flow and performance evaluation of inerter-based vibration isolators mounted on finite and infinite flexible foundation structures

2022 ◽  
Vol 14 (1) ◽  
pp. 168781402110704
Author(s):  
Zhuang Dong ◽  
Jian Yang ◽  
Chendi Zhu ◽  
Dimitrios Chronopoulos ◽  
Tianyun Li
Keyword(s):  
Power Flow ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Flow Behavior ◽  
Flexible Beam ◽  
Vibration Isolators ◽  
Force Transmissibility ◽  
And Performance ◽  
Flexible Foundation ◽  
Isolation Performance

This study investigates the vibration power flow behavior and performance of inerter-based vibration isolators mounted on finite and infinite flexible beam structures. Two configurations of vibration isolators with spring, damper, and inerter as well as different rigidities of finite and infinite foundation structures are considered. Both the time-averaged power flow transmission and the force transmissibility are studied and used as indices to evaluate the isolation performance. Comparisons are made between the two proposed configurations of inerter-based isolators and the conventional spring-damper isolators to show potential performance benefits of including inerter for effective vibration isolation. It is shown that by configuring the inerter, spring, and damper in parallel in the isolator, anti-peaks are introduced in the time-averaged transmitted power and force transmissibility at specific frequencies such that the vibration transmission to the foundation can be greatly suppressed. When the inerter is connected in series with a spring-damper unit and then in-parallel with a spring, considerable improvement in vibration isolation can be achieved near the original peak frequency while maintaining good high-frequency isolation performance. The study provides better understanding of the effects of adding inerters to vibration isolators mounted on a flexible foundation, and benefits enhanced designs of inerter-based vibration suppression systems.

Refined Theories for the Dynamic Analysis of Sandwich Structures

2017 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Wave Propagation ◽  
Dynamic Analysis ◽  
Dynamic Loading ◽  
Sandwich Structures ◽  
Harmonic Wave ◽  
Dispersion Relations ◽  
Sandwich Beams ◽  
New Models ◽  
The Individual ◽  
Selection Of

The objective of this study is to give an overview of existing theories for analyzing the behavior of sandwich beams and plates and to develop an approach for evaluating their behavior under dynamic loading. The dispersion relations for harmonic wave propagation through sandwich structures are shown to be a sound basis for evaluating whether the individual layers are modeled properly. The results provide a guide in the selection of existing models or the development of new models.

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