Effects of “Finiteness” on Wave Propagation and Vibration in Elastic Periodic Structures

Aerospace ◽  
2004 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Frequency Band ◽  
Vibration Isolation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Stop Band ◽  
Forced Response ◽  
Band Frequency ◽  
Mode Localization ◽  
Unit Cells ◽  
Frequency Behavior

The dynamics of finite elastic periodically layered structures is compared to that of the constituent periodic media. The focus is on both the frequency behavior and the spatial response. Through simulations of harmonically induced wave motion within a finite number of unit cells, the frequency band structure and attenuation characteristics of infinite and finite periodic systems are shown to conform under certain conditions. It is concluded that only one or two unit cells of a periodic material are required for “frequency bandness” to carry through to a finite structure, and only three to four unit cells are necessary for significant wave attenuation to take place when the structure is excited at a stop-band frequency. Furthermore, vibration analyses are conducted on a bounded fully periodic structure. The natural frequency spread is shown to conform with the frequency band layout of the infinite periodic material, and the steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium. These results could be used for setting guidelines for the design of periodic structures for vibration isolation and frequency filtering.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

scholarly journals Optimization of a type of elastic metamaterial for broadband wave suppression

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210337
Author(s):  
Kun Wu ◽  
Haiyan Hu ◽  
Lifeng Wang
Keyword(s):  
Vibration Isolation ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Mass Unit ◽  
Super Cell ◽  
Unit Cells ◽  
Sequential Quadratic Programming Method ◽  
Continuous Frequency ◽  
Quadratic Programming Method

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

Geometric Mistuning Reduced Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

Abstract By design, Integrally Bladed Rotors (IBRs) are meant to be tuned, rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, referred to as mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned-structure analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model. To overcome this expense, Reduced Order Models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. This method, referred to as the Surrogate Modal Analysis for Geometry Mistuning Assessments (SMAGMA), will propagate the uncertainties of the surrogate prediction to the forced response. Assessments of the ROM accuracy are made by comparing results to the true forced response levels and results computed by a frequency-based ROM.

Broadband Vibration Isolation for Rods and Beams Using Periodic Structure Theory

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Extreme Case ◽  
Unit Cell ◽  
Structure Theory ◽  
Seismic Excitations ◽  
Stiffness Properties ◽  
Selection Of

The alternating stop-band characteristics of periodic structures have been widely used for narrow band vibration control applications. The objective of this work is to extend this idea for broadband excitations. Toward this end, we seek to synthesize a longitudinal and a flexural periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. Such a periodic structure when subjected to broadband excitation has minimal transmission of the response away from the source of excitation. The unit cell of such a periodic structure is constituted of two distinct regions having different inertial and stiffness properties. We derive guidelines for suitable selection of inertial and stiffness properties of the two regions in the unit cell such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that maximal dissimilarity between the neighboring regions of the unit cell leads to maximal attenuating frequencies. In the extreme case, it is found that more than 98% of the frequencies are blocked. For seismic excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure.

Design of Disordered Periodic Structures for Mode Localization

2017 ◽  
Author(s):  
Gabriele Cazzulani ◽  
Emanuele Riva ◽  
Edoardo Belloni ◽  
Francesco Braghin
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Unit Cell ◽  
Band Gaps ◽  
Mode Shapes ◽  
Mode Localization ◽  
Geometrical Properties ◽  
Unit Cells ◽  
The Mean ◽  
Propagation Properties

Periodic structures are the repetition of unit cells in space, that provide a filtering behavior for wave propagation. In particular, it is possible to tailor the geometrical, physical and elastic properties of the unit cells, in order to attenuate certain frequency bands, called band-gaps or stop-bands. Having each element characterized with the same parameters, the filtering behavior of the system can be described through the wave propagation properties of the unit cell. This is technologically impossible to obtain, therefore the Lyapunov factor is used, in order to define the mean attenuation of a quasi-periodic structure. Tailoring Gaussian unit cell properties potentially allows to extend the stop-bands width in the frequency domain. A drawback is that some unexpected resonance peaks may lie in the neighborhood of the extended regions. However, the correspondent mode-shapes are localized in a particular region of the structure, and they partially decrease the global attenuating behavior. In this paper, the aperiodicity introduced in the otherwise perfect repetition is investigated, providing an explanation for the mode-localization problem and for the stop-bands extension. Then, the proposed approach is applied to a passive quasi-periodic beam, characterized from a localized peak within a designed band-gap. The geometrical properties of its aperiodic parts are changed in order to deterministically move the localization peak in the frequency response. Numerical and experimental results are compared.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

2016 ◽  
Vol 230 (16) ◽  
pp. 2840-2850 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Hongxing Hua ◽  
Hui Zheng
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps ◽  
Stiffened Plate ◽  
Frequency Range ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

scholarly journals Wideband Metamaterial Absorber Based on Combination of Unit Cells

2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Puji Handayani ◽  
Gamantyo Hendrantoro ◽  
Eko Setijadi ◽  
Ahmad Mauludiyanto ◽  
Muhammad Rendy Anggara
Keyword(s):  
Frequency Band ◽  
Wide Band ◽  
Split Ring Resonator ◽  
Metamaterial Absorber ◽  
Simulation Software ◽  
Resonant Frequencies ◽  
Band Frequency ◽  
Wide Frequency Band ◽  
Unit Cells ◽  
Multiple Unit

Metamaterial absorber is an electromagnetic wave absorber made from metamaterial. It basically works in narrow band frequency as it is designed in a particular shape that related to its resonance frequency. However, some applications, e.g., anechoic chamber, require metamaterial absorber that can work in a wide frequency band. This paper discussed the design of wide band metamaterial absorber using the combination of multiple unit cells. The unit cells type was split ring resonator (SRR). SRR had advantages in terms of its simple shape, it could have more than one resonant frequencies depending on the number of its ring, and its shape could be modified easily to obtain the desired resonant frequencies. We designed metamaterial absorber having good absorbtion rate in 2-10 GHz frequency band. To cover this wide frequency band, we used five unit cells which were arranged on a flat plane. Each unit cell had several resonant frequencies. The design was carried out using simulation software of CST (Computer Simulation System). The fabricated design was measured and the results shown that it had an absorbtion rate of 99% in the measured frequency band.

Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part I: Free Vibrations

1988 ◽  
Vol 110 (4) ◽  
pp. 429-438 ◽  
Author(s):  
S.-T. Wei ◽  
C. Pierre
Keyword(s):  
Periodic Structures ◽  
Coupled System ◽  
Companion Paper ◽  
Free Vibrations ◽  
Forced Response ◽  
Cyclic Symmetry ◽  
Coupling Ratio ◽  
Mode Localization ◽  
Weakly Coupled ◽  
Weakly Coupled System

An investigation of the effects of small structural irregularities on the dynamics of nearly periodic structures with cyclic symmetry is presented. The system studied may be regarded as a simple model of a continuously shrouded blade assembly accounting for one structural mode per blade. A key aspect of the approach is the use of perturbation methods that lead to a physical insight into the effects of mistuning. The study shows that the sensitivity to mistuning depends primarily upon the ratio of mistuning strength to coupling strength. For a small mistuning to coupling ratio, the mistuned system behaves like a perturbation of the corresponding tuned system, in which case mistuning has a relatively small effect on both the free and forced responses. On the other hand, for a large mistuning to coupling ratio (i.e., weak coupling), the mistuned system behaves like a perturbation of the corresponding decoupled mistuned system, in which case small mistuning dramatically changes the dynamics of the system. This paper, Part I, investigates the effects of small mistuning on the free response of the system. Specifically, it is shown that strong mode localization and eigenvalue loci veering phenomena occur in the weakly coupled system when mistuning is introduced. The effects of mistuning on the forced response are studied in the companion paper, Part II (Wei and Pierre, 1987).

Angle and polarization-independent miniaturized UWB FSS design

2021 ◽  
pp. 1-9
Author(s):  
Yanning Yuan ◽  
Yuchen Zhao ◽  
Xiaoli Xi
Keyword(s):  
Design Method ◽  
Incident Angle ◽  
Stop Band ◽  
Single Layer ◽  
Wireless Systems ◽  
Frequency Selective Surface ◽  
Ultra Wideband ◽  
Band Frequency ◽  
Gain Enhancement ◽  
Polarization Independent

Abstract A single-layer ultra-wideband (UWB) stop-band frequency selective surface (FSS) has several advantages in wireless systems, including a simple design, low debugging complexity, and an appropriate thickness. This study proposes a miniaturized UWB stop-band FSS design. The proposed FSS structure consists of a square-loop and metalized vias that are arranged on a single layer substrate; it has an excellent angle and polarization-independent characteristics. At an incident angle of 60°, the polarization response frequencies of the transverse electric and magnetic modes only shifted by 0.003 f0 and 0.007 f0, respectively. The equivalent circuit models of the square-loop and metallized vias structure are analysed and the accuracy of the calculation is evaluated by comparing the electromagnetic simulation. The 20 × 20 array constitutes an FSS reflector with a unit size of 4.2 mm × 4.2 mm (less than one-twentieth of the wavelength of 3 GHz), which realizes an UWB quasi-constant gain enhancement (in-band flatness is <0.5 dB). Finally, the simulation results were verified through sample processing and measurement; consistent results were obtained. The FSS miniaturization design method proposed in this study could be applied to the design of passband FSS (complementary structure), antennas and filters, among other applications.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

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