Quantification of Vibration Localization in Periodic Structures

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
A. Chandrashaker ◽  
S. Adhikari ◽  
M. I. Friswell
Keyword(s):  
Complex Geometry ◽  
Periodic Structures ◽  
Random Noise ◽  
Computational Effort ◽  
Mode Shapes ◽  
Engineering Structures ◽  
Modal Assurance Criterion ◽  
Mode Localization ◽  
Modal Data ◽  
Wide Range

The phenomenon of vibration mode localization in periodic and near periodic structures has been well documented over the past four decades. In spite of its long history, and presence in a wide range of engineering structures, the approach to detect mode localization remains rather rudimentary in nature. The primary way is via a visual inspection of the mode shapes. For systems with complex geometry, the judgment of mode localization can become subjective as it would depend on visual ability and interpretation of the analyst. This paper suggests a numerical approach using the modal data to quantify mode localization by utilizing the modal assurance criterion (MAC) across all the modes due to changes in some system parameters. The proposed MAC localization factor (MACLF) gives a value between 0 and 1 and therefore gives an explicit value for the degree of mode localization. First-order sensitivity based approaches are proposed to reduce the computational effort. A two-degree-of-freedom system is first used to demonstrate the applicability of the proposed approach. The finite element method (FEM) was used to study two progressively complex systems, namely, a coupled two-cantilever beam system and an idealized turbine blade. Modal data is corrupted by random noise to simulate robustness when applying the MACLF to experimental data to quantify the degree of localization. Extensive numerical results have been given to illustrate the applicability of the proposed approach.

scholarly journals Vibration of carbon nanotubes with defects: order reduction methods

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170555 ◽  
Author(s):  
Robert B. Hudson ◽  
Alok Sinha
Keyword(s):  
Carbon Nanotubes ◽  
Periodic Structures ◽  
Order Reduction ◽  
Domain Analysis ◽  
Computational Effort ◽  
Mode Shapes ◽  
Mode Localization ◽  
Reduction Techniques ◽  
Reduction Methods ◽  
The Impact

Order reduction methods are widely used to reduce computational effort when calculating the impact of defects on the vibrational properties of nearly periodic structures in engineering applications, such as a gas-turbine bladed disc. However, despite obvious similarities these techniques have not yet been adapted for use in analysing atomic structures with inevitable defects. Two order reduction techniques, modal domain analysis and modified modal domain analysis, are successfully used in this paper to examine the changes in vibrational frequencies, mode shapes and mode localization caused by defects in carbon nanotubes. The defects considered are isotope defects and Stone–Wales defects, though the methods described can be extended to other defects.

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 Linear Finite Element Modeling of Joined Structures With Riveted Connections

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
J. S. Kim ◽  
Y. F. Xu ◽  
W. D. Zhu
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Modeling Method ◽  
Test Structure ◽  
Mode Shapes ◽  
Fe Model ◽  
Fe Modeling ◽  
Engineering Structures ◽  
Modal Assurance Criterion ◽  
Linear Finite Element

Abstract Riveted connections are widely used to join basic components, such as beams and panels, for engineering structures. However, accurately modeling joined structures with riveted connections can be a challenging task. In this work, an accurate linear finite element (FE) modeling method is proposed for joined structures with riveted connections to estimate modal parameters in a predictive manner. The proposed FE modeling method consists of two steps. The first step is to develop nonlinear FE models that simulate riveting processes of solid rivets. The second step is to develop a linear FE model of a joined structure with the riveted connections simulated in the first step. The riveted connections are modeled using solid cylinders with dimensions and material properties obtained from the nonlinear FE models in the first step. An experimental investigation was conducted to study accuracy of the proposed linear FE modeling method. A joined structure with six riveted connections was prepared and tested. A linearity investigation was conducted to validate that the test structure could be considered to be linear. A linear FE model of the test structure was constructed using the proposed method. Natural frequencies and corresponding mode shapes of the test structure were measured and compared with those from the linear FE model. The maximum difference of the natural frequencies was 1.63% for the first 23 out-of-plane elastic modes, and modal assurance criterion values for the corresponding mode shapes were all over 95%, which indicates high accuracy of the proposed linear FE modeling method.

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.

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.

Novel Vibration-Based Methods for Detecting Delamination Damage in Composite Plate and Shell Laminates

2005 ◽  
Vol 293-294 ◽  
pp. 289-296 ◽  
Author(s):  
Marco Gherlone ◽  
Massimiliano Mattone ◽  
Cecilia Surace ◽  
Alessandra Tassotti ◽  
Alexander Tessler
Keyword(s):  
Composite Plate ◽  
Research Effort ◽  
Random Noise ◽  
Damage Index ◽  
Structural Response ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Modal Data ◽  
Plate And Shell ◽  
Delamination Damage

The paper describes an on-going research effort aimed at detecting the presence of delamination damage in composite panels based upon their higher-frequency structural response. Two alternative damage indexes are examined that facilitate the identification of the location and extent of delaminations. The damage indexes do not require vibration measurements to be performed on the undamaged structure. Use is made of the bending and twisting curvatures corresponding to the higher-frequency mode shapes that are post-processed via two different smoothing techniques. The modal data are obtained via finite element models based on Mindlin theory and including delaminations. These are introduced using a sub-laminate strategy that permits multiple damages to be modelled through the thickness. Various delamination sizes and locations are examined with a random noise superposed on the data in order to ascertain the degree of sensitivity of the damage index to the noise in the experimental data.

Compressor Performance and Operability in Swirl Distortion

2010 ◽  
Author(s):  
Yogi Sheoran ◽  
Bruce Bouldin ◽  
P. Murali Krishnan
Keyword(s):  
Gas Turbine ◽  
Complex Geometry ◽  
Full Range ◽  
Axial Compressor ◽  
Cfd Model ◽  
Generator System ◽  
Sliding Mesh ◽  
Wide Range ◽  
Compressor Performance ◽  
The Impact

Inlet swirl distortion has become a major area of concern in the gas turbine engine community. Gas turbine engines are increasingly installed with more complicated and tortuous inlet systems, like those found on embedded installations on Unmanned Aerial Vehicles (UAVs). These inlet systems can produce complex swirl patterns in addition to total pressure distortion. The effect of swirl distortion on engine or compressor performance and operability must be evaluated. The gas turbine community is developing methodologies to measure and characterize swirl distortion. There is a strong need to develop a database containing the impact of a range of swirl distortion patterns on a compressor performance and operability. A recent paper presented by the authors described a versatile swirl distortion generator system that produced a wide range of swirl distortion patterns of a prescribed strength, including bulk swirl, twin swirl and offset swirl. The design of these swirl generators greatly improved the understanding of the formation of swirl. The next step of this process is to understand the effect of swirl on compressor performance. A previously published paper by the authors used parallel compressor analysis to map out different speed lines that resulted from different types of swirl distortion. For the study described in this paper, a computational fluid dynamics (CFD) model is used to couple upstream swirl generator geometry to a single stage of an axial compressor in order to generate a family of compressor speed lines. The complex geometry of the analyzed swirl generators requires that the full 360° compressor be included in the CFD model. A full compressor can be modeled several ways in a CFD analysis, including sliding mesh and frozen rotor techniques. For a single operating condition, a study was conducted using both of these techniques to determine the best method given the large size of the CFD model and the number of data points that needed to be run to generate speed lines. This study compared the CFD results for the undistorted compressor at 100% speed to comparable test data. Results of this study indicated that the frozen rotor approach provided just as accurate results as the sliding mesh but with a greatly reduced cycle time. Once the CFD approach was calibrated, the same techniques were used to determine compressor performance and operability when a full range of swirl distortion patterns were generated by upstream swirl generators. The compressor speed line shift due to co-rotating and counter-rotating bulk swirl resulted in a predictable performance and operability shift. Of particular importance is the compressor performance and operability resulting from an exposure to a set of paired swirl distortions. The CFD generated speed lines follow similar trends to those produced by parallel compressor analysis.

Investigating the vibrational behaviour of a rotating two-blade propeller by using a self-tracking method

2018 ◽  
Vol 233 (3) ◽  
pp. 835-847 ◽  
Author(s):  
Mohammad-Reza Ashory ◽  
Farhad Talebi ◽  
Heydar R Ghadikolaei ◽  
Morad Karimpour
Keyword(s):  
Natural Frequency ◽  
Measurement Errors ◽  
Mode Shapes ◽  
Model Parameters ◽  
Test Results ◽  
Modal Assurance Criterion ◽  
Tracking Method ◽  
Strong Resemblance ◽  
Test Scenarios ◽  
Good Agreement

This study investigated the vibrational behaviour of a rotating two-blade propeller at different rotational speeds by using self-tracking laser Doppler vibrometry. Given that a self-tracking method necessitates the accurate adjustment of test setups to reduce measurement errors, a test table with sufficient rigidity was designed and built to enable the adjustment and repair of test components. The results of the self-tracking test on the rotating propeller indicated an increase in natural frequency and a decrease in the amplitude of normalized mode shapes as rotational speed increases. To assess the test results, a numerical model created in ABAQUS was used. The model parameters were tuned in such a way that the natural frequency and associated mode shapes were in good agreement with those derived using a hammer test on a stationary propeller. The mode shapes obtained from the hammer test and the numerical (ABAQUS) modelling were compared using the modal assurance criterion. The examination indicated a strong resemblance between the hammer test results and the numerical findings. Hence, the model can be employed to determine the other mechanical properties of two-blade propellers in test scenarios.

scholarly journals Multi-stable composite twisting structure for morphing applications

2012 ◽  
Vol 468 (2141) ◽  
pp. 1230-1251 ◽  
Author(s):  
X. Lachenal ◽  
P. M. Weaver ◽  
S. Daynes
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Degrees Of Freedom ◽  
Design Parameters ◽  
Engineering Structures ◽  
The Past ◽  
Wide Range ◽  
Morphing Structure ◽  
Low Mass ◽  
Unstable States

Conventional shape-changing engineering structures use discrete parts articulated around a number of linkages. Each part carries the loads, and the articulations provide the degrees of freedom of the system, leading to heavy and complex mechanisms. Consequently, there has been increased interest in morphing structures over the past decade owing to their potential to combine the conflicting requirements of strength, flexibility and low mass. This article presents a novel type of morphing structure capable of large deformations, simply consisting of two pre-stressed flanges joined to introduce two stable configurations. The bistability is analysed through a simple analytical model, predicting the positions of the stable and unstable states for different design parameters and material properties. Good correlation is found between experimental results, finite-element modelling and predictions from the analytical model for one particular example. A wide range of design parameters and material properties is also analytically investigated, yielding a remarkable structure with zero stiffness along the twisting axis.

A periodic seismic isolation foundation with an extremely broad low-frequency attenuation zone: Theoretical analysis and experimental verification

2021 ◽  
pp. 136943322110646
Author(s):  
Peng Zhou ◽  
Shui Wan ◽  
Xiao Wang ◽  
Yingbo Zhu ◽  
Muyun Huang
Keyword(s):  
Seismic Isolation ◽  
Seismic Waves ◽  
Periodic Structures ◽  
Finite Size ◽  
Low Frequency ◽  
Bridge Structure ◽  
Engineering Structures ◽  
P Waves ◽  
New Type ◽  
Dominant Frequencies

The attenuation zones (AZs) of periodic structures can be used for seismic isolation design. To cover the dominant frequencies of more seismic waves, this paper proposes a new type of periodic isolation foundation (PIF) with an extremely wide low-frequency AZ of 3.31 Hz–17.01 Hz composed of optimized unit A with a wide AZ and optimized unit B with a low-frequency AZ. The two kinds of optimized units are obtained by topology optimization on the smallest periodic unit with the coupled finite element-genetic algorithm (GA) methodology. The transmission spectra of shear waves and P-waves through the proposed PIF of finite size are calculated, and the results show that the AZ of the PIF is approximately the superposition of the AZs of the two kinds of optimized units. Additionally, shake tests on a scale PIF specimen are performed to verify the attenuation performance for elastic waves within the designed AZs. Furthermore, numerical simulations show that the acceleration responses of the bridge structure with the proposed PIF are attenuated significantly compared to those with a concrete foundation under the action of different seismic waves. Therefore, the newly proposed PIF is a promising option for the reduction of seismic effects in engineering structures.

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