Statistical phase analysis and Lyon statistical mode shape functions

2020 ◽  
Vol 148 (4) ◽  
pp. 2612-2612
Author(s):  
Richard DeJong
Keyword(s):  
Phase Analysis ◽  
Mode Shape ◽  
Shape Functions ◽  
Statistical Mode

Experimental System Identification of the Vibro-Impact Dynamics Towards Structural Health Monitoring and Damage Detection

2013 ◽  
Author(s):  
Heng Chen ◽  
Young S. Lee ◽  
Mehmet Kurt ◽  
D. Michael McFarland ◽  
Lawrence A. Bergman ◽  
...  
Keyword(s):  
System Identification ◽  
Structural Health Monitoring ◽  
Damage Detection ◽  
Mode Shape ◽  
Health Monitoring ◽  
Correlation Spectroscopy ◽  
Impact Dynamics ◽  
Shape Functions ◽  
Modal Assurance Criterion ◽  
Structural Health

We perform nonlinear system identification (NSI) on the acceleration signals that were experimentally measured at ten, almost evenly spaced positions along a cantilever beam undergoing vibro-impacts between two rigid stops with clearances. The NSI methodology is based on the correspondence between analytical and empirical slow-flow dynamics, with the first step requiring empirical mode decomposition (EMD) analysis of the measured time series leading to sets of intrinsic modal oscillators (IMOs) governing the vibro-impact dynamics at different time scales. By comparing the spatiotemporal variations of the nonlinear modal interactions (and hence the IMOs), we examine how vibro-impacts influence the low- and high-frequency modes in global and local senses. In applications of the NSI results to structural health monitoring and damage detection (SHM / DD), we calculate typical measures such as the modal assurance criterion (MAC) and the coordinate modal assurance criterion (COMAC) by extracting information about the mode shape functions from the spatiotemporal IMO solutions. Whereas the MAC provides a global aspect of damage occurrence (i.e., which modes are more affected by induced defects), the COMAC can narrow down the damage locations (i.e., where in the structure defects exist that yield low correlation values in specific modes). Finally, we discuss the use of the 2-dimensional correlation spectroscopy technique to SHM / DD, which is frequently used in optical chemistry areas. With the spatiotemporal IMOs the 2-D correlation intensity for the linear beam is proportional to the product of the two mode shape functions at the respective positions; hence any deviations from that may indicate the occurrence and locations of damage in the structure.

Formulating frequency of uniform beams with tip mass under various axial loads

2013 ◽  
Vol 228 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Renfan Luo
Keyword(s):  
Mode Shape ◽  
Shape Functions ◽  
Axial Loads ◽  
Concentrated Force ◽  
Element Analysis ◽  
Axial Acceleration ◽  
Free Transverse Vibration ◽  
Tip Mass ◽  
Energy Conservation Principle ◽  
Good Agreement

The energy conservation principle has been applied to derive the formulation of the frequencies of free transverse vibration of beams for a given mode shape. For uniform beams with a tip mass and with either a clamped/free or a clamped/sliding or a hinged/sliding constraint, under various loads, such a centrifugal force, axial acceleration and concentrated force, the mode shape functions for the free uniform beams have been employed to develop empirical formulae, which are capable of predicting their frequencies. The predictions show a good agreement with those given by finite element analysis.

On the Identification of Localized Losses of Stiffness in Structures

1993 ◽  
Author(s):  
Ulrich Pabst ◽  
Peter Hagedorn
Keyword(s):  
Mathematical Model ◽  
Damage Detection ◽  
Mode Shape ◽  
Measurement Errors ◽  
Mode Shapes ◽  
Shape Functions ◽  
Modal Data ◽  
Order Of Magnitude ◽  
Eigen Frequencies ◽  
Local Stiffness

Abstract In damage detection it is common to use measured modal data and a mathematical model in connection with system identification. The part of the system undergoing the largest stiffness decrease is defined to contain damage. This approach is very sensitive to measurement errors. The measurement errors are much larger for mode shape functions than for the eigen-frequencies. The errors in the mode shapes are often of the same order of magnitude as the variations due to damage leading to poor results in damage detection. Thus, the use of the mode shape functions themselves instead of their small damage induced variations would dearly be preferable. In this paper we examine the relation between the changes in the eigenfrequencies, the local stiffness losses and the mode shape functions of the undamaged system. This relation is then utilized in a damage detection procedure.

Vibration of an Euler-Bernoulli Uniform Beam Carrying Several Thin Disks

2003 ◽  
Author(s):  
S. Naguleswaran
Keyword(s):  
Finite Element ◽  
Mode Shape ◽  
Analytical Method ◽  
Frequency Equation ◽  
Shape Functions ◽  
Approximate Methods ◽  
Uniform Beam ◽  
Recurrence Relationship ◽  
Axial Dimension ◽  
Thin Disks

The Euler-Bernoulli uniform beam considered in this paper carry (n+1) thin disks, two of which are at the beam ends. For the analytical method used in the paper, n co-ordinate systems were chosen with origins at the disk locations. The mode shape of the portion of the beam between the jth and (j+1)th disk was expressed in the form Yj(Xj) = A Uj(Xj) + B Vj(Xj) in which Uj(Xj) and Vj(Xj) are ‘modified’ mode shape functions applicable to that portion but the constants A and B are common to all the portions. From the compatibility of moments and forces on the (n+1)th disk, the frequency equation was expressed in closed form as a 2nd order determinant equated to zero. Schemes are presented to compute the 4 elements of the determinant (from a recurrence relationship) and to evaluate the roots of the frequency equation. Computational difficulties were not encountered in the implementation of the schemes to beams carrying very large number of disks. The first three natural frequency parameters of 28 combinations of the boundary conditions (which includes classical clamped, pinned, sliding and free) are tabulated for beams carrying 6, 51, 201 or 1001 thin disks. The approaches in previous publications include those based on various approximate methods like finite element, Rayleighritz, Galerkin, transfer matrix etc. The results in the present paper may be used to judge the accuracy of values obtained by approximate methods. The theory developed in the paper will need modification if axial dimension of the disks are taken into account.

Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method

2018 ◽  
Vol 18 (07) ◽  
pp. 1850101 ◽  
Author(s):  
Alireza Keshmiri ◽  
Nan Wu ◽  
Quan Wang
Keyword(s):  
Free Vibration ◽  
Mode Shape ◽  
Decomposition Method ◽  
Natural Frequencies ◽  
Adomian Decomposition Method ◽  
Present Approach ◽  
Cone Beam ◽  
Mode Shapes ◽  
Shape Functions ◽  
Adomian Decomposition

In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.

Spatial Exact Actuation of Flexible Deep Double-Curvature Shells

2007 ◽  
Author(s):  
Hong-Hao Yue ◽  
Xiao-Ying Gao ◽  
Bing-Yin Ren ◽  
Horn-Sen Tzou
Keyword(s):  
Mode Shape ◽  
Mode Shapes ◽  
Shape Functions ◽  
Shell System ◽  
Control Effectiveness ◽  
Natural Modes ◽  
Double Curvature ◽  
Spatially Distributed ◽  
Control Forces ◽  
Assumed Mode

Deep double-curvature shells are commonly used as key components in many advanced aerospace structures and mechanical systems, e.g., nozzles, injectors, horns, rocket fairings. Spatially distributed micro-actuation of a laminated flexible deep double curvature shell is investigated and its control effectiveness is evaluated in this study. Dynamic equations of the smart double curvature shell system are presented and modal control forces of spatial segmented piezoelectric actuators are carried out based on a new set of assumed mode shape functions with free boundary condition. Using these assumed mode shape functions, mode shapes of a free-floating deep shell are illustrated. Finally, via numerical simulation, control effectiveness of distributed actuator patches with respect to various natural modes, actuator locations and other factors which influence precision control and active actuation behavior of flexible deep double curvature shell structronic systems is evaluated.

The Application of Non-Sinusoidal Mode Shape Function in the Identification of Modal Weight

2010 ◽  
Author(s):  
Zhibiao Rao ◽  
Shixiao Fu ◽  
Jianmin Yang ◽  
Runpei Li
Keyword(s):  
Mode Shape ◽  
Indirect Method ◽  
Shape Function ◽  
Direct Method ◽  
Superposition Method ◽  
Shape Functions ◽  
Flexible Riser ◽  
Mode Superposition Method ◽  
Mode Shape Function ◽  
Sinusoidal Function

The main objective of this paper is to study the effect of non-sinusoidal mode shape on the identification of modal weights. The simplified analytical solution of the transverse vibration equation of uniform tensioned long flexible riser was presented, and the corresponding non-sinusoidal but orthogonal mode shape function is deduced. Then the data from the VIV model tests of long flexible riser conducted by ExxonMobil at MARINTEK are analyzed by the mode superposition method. Modal weights calculated by two different mode shape functions, sinusoidal and non-sinusoidal function, with two methods, namely direct method and indirect method are compared. The comparison shows the good performance of the non-sinusoidal mode shape in the identification of modal weights.

scholarly journals Sophisticated finite strip for vibration analysis of a rotating cylindrical shell

2018 ◽  
Vol 148 ◽  
pp. 07001
Author(s):  
Ivo Senjanović ◽  
Ivan Ćatipović ◽  
Neven Alujević ◽  
Nikola Vladimir ◽  
Damjan Čakmak
Keyword(s):  
Mode Shape ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Shape Functions ◽  
Axial Mode ◽  
Beam Shape ◽  
Finite Strip ◽  
Rotating Cylindrical Shell

In this article a two-node finite strip with eight degrees of freedom for free vibration analysis of pre-stressed rotating cylindrical shells is formulated. The circumferential mode shape profiles are described exactly using trigonometric functions. The axial mode shape profiles are approximated by bar and beam shape functions for membrane and bending displacements, respectively. In this way a semi-analytical formulation is facilitated so that the discretization is required only in the axial direction. The developed finite strip is validated by comparisons with analytical results. An excellent agreement is observed both for stationary and rotating shells.

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