A New Method for Vibration Mode Analysis

2005 ◽  
Author(s):  
David Chelidze ◽  
Wenliang Zhou
Keyword(s):  
Modal Analysis ◽  
A Priori ◽  
Normal Modes ◽  
Orthogonal Decomposition ◽  
Mode Analysis ◽  
Continuous Systems ◽  
Analysis Technique ◽  
Priori Information ◽  
Mathematical Justification ◽  
Proper Orthogonal

In this paper, a new modal analysis method based on a novel multivariate data analysis technique called smooth orthogonal decomposition (SOD) is proposed. The development of the SOD and its main properties are described. The mathematical justification for the application in modal analysis is also provided. The proper orthogonal decomposition (POD) and its application in modal analysis are provided for comparison. Numerical simulations of discrete and continuous systems are used in this comparison. It is demonstrated that the SOD-based analysis overcomes main deficiencies of the POD. The SOD identifies linear normal modes and corresponding frequencies without requiring any a priori information about the distribution of mass in the system.

Enhanced Proper Orthogonal Decomposition for the Modal Analysis of Homogeneous Structures

2002 ◽  
Vol 8 (1) ◽  
pp. 19-40 ◽  
Author(s):  
S. Han ◽  
B. F. Feeny
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Modal Analysis ◽  
Normal Modes ◽  
Orthogonality Condition ◽  
Orthogonal Decomposition ◽  
Analysis Tool ◽  
Homogeneous Structures ◽  
Proper Orthogonal ◽  
Modal Coordinates

Proper orthogonal decomposition (POD) is studied in an effort to increase its applicability as a modal analysis tool. A modification is proposed to make better use of spatial resolution and to accommodate arbitrary spacing in the discretization. The theory for this modification is rooted in the discrete approximation of the integral orthogonality condition for continuous normal modes. The modified POD is applied to a finite element beam and an experimental beam sensed with accelerometers, and the resulting proper orthogonal modes (POMs) are compared to the theoretical modes of the beam. The POMs are used as a basis for decomposing the signal ensemble into proper modal coordinates. The proper modal coordinates are used to evaluate the POMs and to match modes with modal frequencies and damping.

Macromodeling Method of Fluid-Structure Interacting MEMS Based on Modal Analysis and Proper Orthogonal Decomposition

2007 ◽  
Author(s):  
Wentao Hao ◽  
Ling Tian ◽  
Bingshu Tong
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Orthogonal Decomposition ◽  
Mems Devices ◽  
High Complexity ◽  
Fluid Structure ◽  
Fluid Field ◽  
Speed Up ◽  
Proper Orthogonal

Because of their good performance to speed up MEMS system simulation processes, macromodels have aroused lots of attentions of scientists in the last decades. However, studies on FSI (Fluid-Structure Interaction) MEMS devices still can not satisfy the macromodeling requests because of the high complexity of fluid fields. A new method based on modal analysis and POD (Proper Orthogonal Decomposition) is tentatively put forward to reduce the order of FSI MEMS models. The structure macromodeling theory is firstly reviewed. Then the fluid field macromodeling approach is discussed in detail. At last, a 2D fixed-fixed micro-beam is analyzed and the results show that the macromodel extracted in this method can highly decrease the system degrees of freedom, while its precision is still comparable with that of detailed models.

Modal Analysis With Smooth Karhunen-Loe`ve Decomposition

2009 ◽  
Author(s):  
S. Bellizzi ◽  
Rubens Sampaio
Keyword(s):  
Random Field ◽  
Modal Analysis ◽  
Covariance Matrix ◽  
Random Fields ◽  
Time Derivative ◽  
Normal Modes ◽  
Orthogonal Decomposition ◽  
White Noise Excitation ◽  
Smooth Orthogonal Decomposition ◽  
Vibrating Systems

In this paper, the Smooth Orthogonal Decomposition is formulated in term of a Smooth Karhunen-Loe`ve Decomposition (SKLD) to analyze random fields. The SKLD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random field and the covariance matrix of the associated time derivative random field. The main properties of the SKLD are described and compared to the classical Karhunen-Loe`ve decomposition. The SKLD is then applied to the responses of randomly excited vibrating systems with a view to performing modal analysis. The associated SKLD characteristics are interpreted in case of linear vibrating systems subjected to white noise excitation in terms of normal modes. Discrete and continuous mechanical systems are considered in this study.

Circumferential Mode Analysis of Axial Compressor Tip Flow Using Fourier Transform and Proper Orthogonal Decomposition

2018 ◽  
Author(s):  
Dan Yao ◽  
Jie Tian ◽  
Yadong Wu ◽  
Hua Ouyang
Keyword(s):  
Fourier Transform ◽  
Proper Orthogonal Decomposition ◽  
Axial Compressor ◽  
Orthogonal Decomposition ◽  
Mode Analysis ◽  
Rotational Instability ◽  
Flow Conditions ◽  
Mode Amplitude ◽  
Rotating Instability ◽  
Proper Orthogonal

Rotating instability (RI) of a single-stage axial compressor was studied by both numerical and experimental methods. A circumferential mode decomposition method based on spatial Fourier transform was used to analyze the circumferential pressure distribution of the tip flow. Circumferential mode characteristics were captured both on blade passing frequency (BPF) and rotational instability frequency (RIF) under several flow conditions. The characteristic spectrum of RI with broadband hump existed in a large range of flow conditions. Both frequency range and dominant circumferential mode number decreased with flow rate, while circumferential angular velocity of RI increased at the same time. On the other hand, a proper orthogonal decomposition (POD) method was applied to obtain the mode component of tip flow. The feature of tip flow was analyzed with the help of POD mode vector and mode amplitude. The influence of the decrease on the spatial monitor points in POD method was analyzed using CFD data to analysis the potential error from experimental results. It is expected to deeply understand the mechanism of the rotating instability and rotor-stator interaction phenomenon by spatial FT and POD methods in this study.

Modal analysis of wingtip vortices by means of Proper Orthogonal Decomposition

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 693-694
Author(s):  
Sebastian Dufhaus ◽  
Sarina Brautmeier ◽  
Anna Uhl ◽  
Ralf Hörnschemeyer ◽  
Eike Stumpf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Modal Analysis ◽  
Orthogonal Decomposition ◽  
Proper Orthogonal

scholarly journals Lagrangian approach for modal analysis of fluid flows

2021 ◽  
Vol 928 ◽  
Author(s):  
Vilas J. Shinde ◽  
Datta V. Gaitonde
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Modal Analysis ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Finite Time Lyapunov Exponents ◽  
Mode Decomposition ◽  
Proper Orthogonal

Common modal decomposition techniques for flow-field analysis, data-driven modelling and flow control, such as proper orthogonal decomposition and dynamic mode decomposition, are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The Eulerian description poses some difficulties, however, when the domain or the mesh deforms with time as, for example, in fluid–structure interactions. For such cases, we first formulate a Lagrangian modal analysis (LMA) ansatz by a posteriori transforming the Eulerian flow fields into Lagrangian flow maps through an orientation and measure-preserving domain diffeomorphism. The development is then verified for Lagrangian variants of proper orthogonal decomposition and dynamic mode decomposition using direct numerical simulations of two canonical flow configurations at Mach 0.5, i.e. the lid-driven cavity and flow past a cylinder, representing internal and external flows, respectively, at pre- and post-bifurcation Reynolds numbers. The LMA is demonstrated for several situations encompassing unsteady flow without and with boundary and mesh deformation as well as non-uniform base flows that are steady in Eulerian but not in Lagrangian frames. We show that application of LMA to steady non-uniform base flow yields insights into flow stability and post-bifurcation dynamics. LMA naturally leads to Lagrangian coherent flow structures and connections with finite-time Lyapunov exponents. We examine the mathematical link between finite-time Lyapunov exponents and LMA by considering a double-gyre flow pattern. Dynamically important flow features in the Lagrangian sense are recovered by performing LMA with forward and backward (adjoint) time procedures.

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