Reduced-Order P.O.D. Models for Nonlinear Vibrations of Cylindrical Shells

2003 ◽  
Author(s):  
M. Amabili ◽  
A. Sarkar ◽  
M. P. Pai¨doussis
Keyword(s):  
Time Series ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Computational Effort ◽  
Inviscid Fluid ◽  
Galerkin Approach ◽  
System Behaviour ◽  
Proper Orthogonal Modes ◽  
Proper Orthogonal

The nonlinear (large-amplitude) response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of their lowest natural frequencies is investigated. The shell is assumed to be completely filled with an incompressible and inviscid fluid at rest. Donnell’s nonlinear shallow-shell theory is used, and the solution is obtained by the Galerkin method. The proper orthogonal decomposition (POD) method is used to extract proper orthogonal modes that describe the system behaviour from time-series response data. These time-series have been obtained via the conventional Galerkin approach (using normal modes as a projection basis) with an accurate model involving 16 degrees of freedom, validated in previous studies. The POD method, in conjunction with the Galerkin approach, permits a lower-dimensional model with respect to the conventional Galerkin approach. Different proper orthogonal modes computed from time-series at different excitation frequencies are used and solutions are compared. Some of these modes are capable of describing the system behaviour over the whole frequency range around the fundamental resonance with good accuracy and with only three degrees of freedom. They allow a drastic reduction in the computational effort, as compared to using the 16 degrees-of-freedom model necessary when the conventional Galerkin approach is used.

Non-Linear Vibrations of Fluid-Filled, Simply Supported Circular Cylindrical Shells: Theory and Experiments

2000 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano ◽  
M. P. Païdoussis
Keyword(s):  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Travelling Wave ◽  
Galerkin Projection ◽  
Inviscid Fluid ◽  
Simply Supported ◽  
Longitudinal Modes ◽  
Circular Cylindrical Shells

Abstract The large-amplitude response of thin, simply supported circular cylindrical shells to a harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated. Donnell’s nonlinear shallow-shell theory is used and the solution is obtained by Galerkin projection. A mode expansion including driven and companion modes, axisymmetric modes and additional asymmetric modes is used. In particular, asymmetric modes with twice the number of circumferential waves of driven and companion modes are included in the analysis. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion are studied by using a code based on the Collocation Method. Validation of the present model is obtained by comparison with other authoritative results and new experimental results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The contribution of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with harmonics of the circumferential mode number n under consideration is limited so far as the trend of nonlinearity is concerned, but is significant in the response with companion mode participation for lightly damped shells (empty shells). Results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

scholarly journals Bridge Monitoring with Harmonic Excitation and Principal Component Analysis

2018 ◽  
Vol 13 (4) ◽  
pp. 374-384
Author(s):  
Viet Ha Nguyen ◽  
Jean-Claude Golinval ◽  
Stefan Maas
Keyword(s):  
Principal Component Analysis ◽  
Prestressed Concrete ◽  
Excitation Frequency ◽  
Damage Index ◽  
Principal Component ◽  
Component Analysis ◽  
Harmonic Excitation ◽  
Health States ◽  
Proper Orthogonal Modes ◽  
Proper Orthogonal

Principal Component Analysis is used for damage detection in structures excited by harmonic forces. Time responses are directly analysed by Singular Value Decomposition to deduct two dominant Proper Orthogonal Values corresponding to two Proper Orthogonal Modes. Damage index is defined by the concept of subspace angle that a subspace is built from the two Proper Orthogonal Modes. A subspace angle reflects the coherence between two different structural health states. An example is given through the application on a part of a real prestressed concrete bridge in Luxembourg where different damage states were created by cutting a number of prestressed tendons in four scenarios with increasing levels. Results are better by using excitation frequency close to an eigenfrequency of the structure. The technique is convenient for practical application in operational bridge structures.

Large-Amplitude Vibrations of Empty and Fluid-Filled Circular Cylindrical Shells With Imperfections: Theory and Experiments

2002 ◽  
Author(s):  
M. Amabili ◽  
M. Pellegrini ◽  
F. Pellicano
Keyword(s):  
Large Amplitude ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Harmonic Excitation ◽  
Steel Shell ◽  
Nonlinear Phenomena ◽  
Inviscid Fluid ◽  
Simply Supported ◽  
Circular Cylindrical Shells ◽  
Actual Geometry

The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell’s nonlinear shallow-shell theory is used and the solution is obtained by Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement (simply supported shell at both ends) and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting nonlinear phenomena have been experimentally observed and numerically reproduced, as: softening-type nonlinearity, different types of travelling wave response in the proximity of resonances and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement.

Experimental Application of a Damage Localisation Technique Based on Smoothed Proper Orthogonal Modes

2007 ◽  
Vol 347 ◽  
pp. 121-126 ◽  
Author(s):  
U. Galvanetto ◽  
L. Monopoli ◽  
Cecilia Surace ◽  
Alessandra Tassotti
Keyword(s):  
Damage Detection ◽  
Proper Orthogonal Decomposition ◽  
Real Time ◽  
Orthogonal Decomposition ◽  
Steel Beams ◽  
Acceleration Response ◽  
Experimental Application ◽  
Lab Experiments ◽  
Proper Orthogonal Modes ◽  
Proper Orthogonal

The paper presents an experimental application of the Proper Orthogonal Decomposition (POD) to damage detection in steel beams. A damaged beam has been excited with a sinusoidal force, the acceleration response at points regularly spaced along the structure has been recorded and the relevant Proper Orthogonal Modes calculated. In this way it is possible to locate damage by comparing the measured dominant Proper Orthogonal Mode with a smoothed version of it which does not exhibit apparent peaks in correspondence with the damage. One of the principal advantages of the proposed damage detection technique is that it does not require vibration measurements to be performed on the undamaged structure. Moreover the ‘optimality’ of the proper orthogonal modes only requires the use of a few (one-two) of them which can be computed in real time during lab experiments or while the structure is functioning in the field.

Integrated Redesign of Large-Scale Structures by Large Admissible Perturbations

2003 ◽  
Vol 125 (4) ◽  
pp. 234-241 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas ◽  
Denby Morrison
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Direct Method ◽  
Computational Effort ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Performance Constraints ◽  
Large Admissible Perturbations ◽  
Design Selection

In structural redesign (inverse design), selection of the number and type of performance constraints is a major challenge. This issue is directly related to the computational effort and, most importantly, to the success of the optimization solver in finding a solution. These issues are the focus of this paper, which provides and discusses techniques that can help designers formulate a well-posed integrated complex redesign problem. LargE Admissible Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, free vibration, static deformation, and forced response amplitude constraints. The existing algorithm, referred to as the Incremental Method is improved in this paper for problems with static and forced response amplitude constraints. This new algorithm, referred to as the Direct Method, offers comparable level of accuracy for less computational time and provides robustness in solving large-scale redesign problems in the presence of damping, nonstructural mass, and fluid-structure interaction effects. Common redesign problems include several natural frequency constraints and forced response amplitude constraints at various frequencies of excitation. Several locations on the structure and degrees of freedom can be constrained simultaneously. The designer must exercise judgment and physical intuition to limit the number of constraints and consequently the computational time. Strategies and guidelines are discussed. Such techniques are presented and applied to a 2,694 degree of freedom offshore tower.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

scholarly journals Association Between PM2.5 and Daily Hospital Admissions for Heart Failure: A Time-Series Analysis in Beijing

2018 ◽  
Vol 15 (10) ◽  
pp. 2217 ◽  
Author(s):  
Man Li ◽  
Yao Wu ◽  
Yao-Hua Tian ◽  
Ya-Ying Cao ◽  
Jing Song ◽  
...  
Keyword(s):  
Heart Failure ◽  
Time Series ◽  
Degrees Of Freedom ◽  
Hospital Admissions ◽  
Scientific Evidence ◽  
Poisson Model ◽  
Sensitivity Analyses ◽  
Calendar Time ◽  
Medical Claim ◽  
Increased Risk

There is little evidence that acute exposure to fine particulate matter (PM2.5) impacts the rate of hospitalization for congestive heart failure (CHF) in developing countries. The primary purpose of the present retrospective study was to evaluate the short-term association between ambient PM2.5 and hospitalization for CHF in Beijing, China. A total of 15,256 hospital admissions for CHF from January 2010 to June 2012 were identified from Beijing Medical Claim Data for Employees and a time-series design with generalized additive Poisson model was used to assess the obtained data. We found a clear significant exposure response association between PM2.5 and the number of hospitalizations for CHF. Increasing PM2.5 daily concentrations by 10 μg/m3 caused a 0.35% (95% CI, 0.06–0.64%) increase in the number of CHF admissions on the same day. We also found that female and older patients were more susceptible to PM2.5. These associations remained significant in sensitivity analyses involving changing the degrees of freedom of calendar time, temperature, and relative humidity. PM2.5 was associated with significantly increased risk of hospitalization for CHF in this citywide study. These findings may contribute to the limited scientific evidence about the acute impacts of PM2.5 on CHF in China.

scholarly journals INFLUENCE OF SPATIAL AND TEMPORAL RESOLUTION ON TIME SERIES-BASED COASTAL SURFACE CHANGE ANALYSIS USING HOURLY TERRESTRIAL LASER SCANS

2021 ◽  
Vol V-2-2021 ◽  
pp. 137-144
Author(s):  
K. Anders ◽  
L. Winiwarter ◽  
H. Mara ◽  
R. C. Lindenbergh ◽  
S. E. Vos ◽  
...  
Keyword(s):  
Time Series ◽  
Temporal Resolution ◽  
Input Data ◽  
Laser Scanning ◽  
Poor Performance ◽  
Computational Effort ◽  
Spatial Extent ◽  
Change Analysis ◽  
Surface Change ◽  
Natural Surface

Abstract. Near-continuously acquired terrestrial laser scanning (TLS) data contains valuable information on natural surface dynamics. An important step in geographic analyses is to detect different types of changes that can be observed in a scene. For this, spatiotemporal segmentation is a time series-based method of surface change analysis that removes the need to select analysis periods, providing so-called 4D objects-by-change (4D-OBCs). This involves higher computational effort than pairwise change detection, and efforts scale with (i) the temporal density of input data and (ii) the (variable) spatial extent of delineated changes. These two factors determine the cost and number of Dynamic Time Warping distance calculations to be performed for deriving the metric of time series similarity. We investigate how a reduction of the spatial and temporal resolution of input data influences the delineation of twelve erosion and accumulation forms, using an hourly five-month TLS time series of a sandy beach. We compare the spatial extent of 4D-OBCs obtained at reduced spatial (1.0 m to 15.0 m with 0.5 m steps) and temporal (2 h to 96 h with 2 h steps) resolution to the result from highest-resolution data. Many change delineations achieve acceptable performance with ranges of ±10 % to ±100 % in delineated object area, depending on the spatial extent of the respective change form. We suggest a locally adaptive approach to identify poor performance at certain resolution levels for the integration in a hierarchical approach. Consequently, the spatial delineation could be performed at high accuracy for specific target changes in a second iteration. This will allow more efficient 3D change analysis towards near-realtime, online TLS-based observation of natural surface changes.

scholarly journals Effective Degrees of Freedom of the Pearson’s Correlation Coefficient under Autocorrelation

2018 ◽  
Author(s):  
Soroosh Afyouni ◽  
Stephen M. Smith ◽  
Thomas E. Nichols
Keyword(s):  
Time Series ◽  
Correlation Coefficient ◽  
Degrees Of Freedom ◽  
Brain Regions ◽  
Resting State Functional Connectivity ◽  
Pearson’S Correlation ◽  
Individual Level ◽  
Human Connectome Project ◽  
Pearson's Correlation ◽  
The Impact

AbstractThe dependence between pairs of time series is commonly quantified by Pearson’s correlation. However, if the time series are themselves dependent (i.e. exhibit temporal autocorrelation), the effective degrees of freedom (EDF) are reduced, the standard error of the sample correlation coefficient is biased, and Fisher’s transformation fails to stabilise the variance. Since fMRI time series are notoriously autocorrelated, the issue of biased standard errors – before or after Fisher’s transformation – becomes vital in individual-level analysis of resting-state functional connectivity (rsFC) and must be addressed anytime a standardized Z-score is computed. We find that the severity of autocorrelation is highly dependent on spatial characteristics of brain regions, such as the size of regions of interest and the spatial location of those regions. We further show that the available EDF estimators make restrictive assumptions that are not supported by the data, resulting in biased rsFC inferences that lead to distorted topological descriptions of the connectome on the individual level. We propose a practical “xDF” method that accounts not only for distinct autocorrelation in each time series, but instantaneous and lagged cross-correlation. We find the xDF correction varies substantially over node pairs, indicating the limitations of global EDF corrections used previously. In addition to extensive synthetic and real data validations, we investigate the impact of this correction on rsFC measures in data from the Young Adult Human Connectome Project, showing that accounting for autocorrelation dramatically changes fundamental graph theoretical measures relative to no correction.

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