scholarly journals Measuring Strain Response Mode Shapes with a Continuous-Scan LDV

2002 ◽  
Vol 9 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Anthony B. Stanbridge ◽  
Milena Martarelli ◽  
David J. Ewins
Keyword(s):  
Mode Shape ◽  
Response Mode ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Governing Equations ◽  
Convenient Means ◽  
Straight Line ◽  
Polynomial Series ◽  
Spatial Derivatives ◽  
Derivatives Of

A continuous-scan LDV is a convenient means for measuring the response mode shape (ODS) of a vibrating surface, particularly in view of the fact that the ODS is automatically derived as a spatial polynomial series. Second spatial derivatives of the deflection equations are therefore easily derived, and these should, in principle, give curvature equations from which, for a beam or plate of known cross-section, stresses and strains can be obtained directly. Unfortunately, the stress and strain distributions depend critically on higher terms in the original ODS series, which are not accurately measured. This problem can be avoided by a method described here, which enables accurate stress and strain distributions to be derived, from a straight-line LDV scan along a uniform beam, using only five terms in the mode-shape polynomial series. A similar technique could be applied to uniform plates but the analysis and the governing equations are rather more complicated.

Damage Detection in Laminated Composite Plates and Shells Using Second Derivatives of Mode Shape Data Through Dynamic Analysis of These Structures

2015 ◽  
Author(s):  
Mahendran Govindasamy ◽  
Chandrasekaran Kesavan ◽  
Malhotra Santkumar
Keyword(s):  
Damage Detection ◽  
Mode Shape ◽  
Laminated Composite ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Experimental Investigations ◽  
Structural Elements ◽  
Plate And Shell ◽  
Second Derivatives ◽  
Derivatives Of

The main objective of this study is to evaluate the dynamics-based techniques for damage detection in laminated composite cantilevered rectangular plates and cylindrical shells with damages in the form of surface macro-level cracks using finite element analysis (FEA). However, the quantitative change in global vibration characteristics is not sufficiently sensitive to local structural damages especially to small size damages. Hence certain parameters called damage indicators based on mode shape curvature, which are the second derivatives of the vibration characteristics (mode shapes), are used in this study to detect the location and size of even small damages accurately in laminated composite structures. The commercial FEA package ANSYS is used for the theoretical modal analysis to generate the natural frequencies and normalized mode shapes of the intact and damaged structures. Experimental investigations are carried out on the laminated plate and shell structural elements to provide a validation of the analysis. Experimental investigations are carried out on the laminated composite (E-glass unidirectional fibers reinforced epoxy resin) cantilevered plate and shell structural elements to provide a validation of the analysis. The effectiveness of these methods is clearly demonstrated by the results obtained.

Damage Detection of Cantilever Beams Based on Derivatives of Mode Shapes

2014 ◽  
Vol 488-489 ◽  
pp. 817-820
Author(s):  
Jin Quan Guo ◽  
Fen Lan Ou ◽  
Jian Feng Zhong ◽  
Shun Cong Zhong ◽  
Xiao Xiang Yang ◽  
...  
Keyword(s):  
Mode Shape ◽  
Crack Detection ◽  
Shape Change ◽  
Approximation Error ◽  
Mode Shapes ◽  
Difference Approximation ◽  
Cantilever Beams ◽  
Crack Location ◽  
Displacement Mode ◽  
Derivatives Of

For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

Measuring strain response mode shapes with a continuous-scan LDV

2000 ◽  
Author(s):  
Anthony B. Stanbridge ◽  
Milena Martarelli ◽  
David J. Ewins
Keyword(s):  
Response Mode ◽  
Mode Shapes ◽  
Strain Response

Vibration attenuation of a two-link flexible arm carried by a translational stage

2018 ◽  
Vol 24 (23) ◽  
pp. 5650-5664 ◽  
Author(s):  
Shang–Teh Wu ◽  
Shan-Qun Tang ◽  
Kuan–Po Huang
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Flexible Arm ◽  
Vibration Attenuation ◽  
Shaft Encoder ◽  
High Frequency Vibrations ◽  
Spatial Derivatives ◽  
Derivatives Of

This paper investigates the vibration control of a two-link flexible manipulator carried by a translational stage. The first and the second links are each driven by a stage motor and a joint motor. By treating the joint motor as a virtual spring, the two-link manipulator can be regarded as an integral flexible arm driven by the stage motor. A noncollocated controller is devised based on feedback from the deflection of the virtual spring, which can be measured by a shaft encoder. Stability of the closed-loop system is analyzed by examining the spatial derivatives of the modal functions. By including a bandpass filter in the feedback loop, residual vibrations can be attenuated without exciting high-frequency vibrations. The control method is simple to implement; its effectiveness is confirmed by simulation and experimental results.

The effect of microscale random Alfvén waves on the propagation of large-scale Alfvén waves

1983 ◽  
Vol 29 (2) ◽  
pp. 243-253 ◽  
Author(s):  
Tomikazu Namikawa ◽  
Hiromitsu Hamabata
Keyword(s):  
Large Scale ◽  
Ponderomotive Force ◽  
Collisionless Plasma ◽  
Alfven Waves ◽  
Velocity Fields ◽  
Velocity Shear ◽  
Alfvén Waves ◽  
Spectrum Function ◽  
Spatial Derivatives ◽  
Derivatives Of

The ponderomotive force generated by random Alfvén waves in a collisionless plasma is evaluated taking into account mean magnetic and velocity shear and is expressed as a series involving spatial derivatives of mean magnetic and velocity fields whose coefficients are associated with the helicity spectrum function of random velocity field. The effect of microscale random Alfvén waves through ponderomotive and mean electromotive forces generated by them on the propagation of large-scale Alfvén waves is also investigated.

Numerical Study for Global Detection of Cracks Embedded in Beams

1999 ◽  
Author(s):  
S. A. Lipsey ◽  
Y. W. Kwon
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Natural Frequency ◽  
Mode Shape ◽  
Numerical Study ◽  
Element Model ◽  
Mode Shapes ◽  
Linear Effect ◽  
Modes Of Vibration ◽  
Damage Simulation

Abstract Damage reduces the flexural stiffness of a structure, thereby altering its dynamic response, specifically the natural frequency, damping values, and the mode shapes associated with each natural frequency. Considerable effort has been put into obtaining a correlation between the changes in these parameters and the location and amount of the damage in beam structures. Most numerical research employed elements with reduced beam dimensions or material properties such as modulus of elasticity to simulate damage in the beam. This approach to damage simulation neglects the non-linear effect that a crack has on the different modes of vibration and their corresponding natural frequencies. In this paper, finite element modeling techniques are utilized to directly represent an embedded crack. The results of the dynamic analysis are then compared to the results of the dynamic analysis of the reduced modulus finite element model. Different modal parameters including both mode shape displacement and mode shape curvature are investigated to determine the most sensitive indicator of damage and its location.

scholarly journals Modelling of the Coupled Beam-Piezoelectric Material With Hysteresis Non-Linerity Effect

2018 ◽  
Vol 217 ◽  
pp. 02001
Author(s):  
Mohd Hafiz Abdul Satar ◽  
Ahmad Zhafran Ahmad Mazlan
Keyword(s):  
Modal Analysis ◽  
Piezoelectric Material ◽  
Piezoelectric Actuator ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Sinusoidal Voltage ◽  
Correction Algorithm ◽  
Beam Structure ◽  
Piezoelectric Patch

Hysteresis is one of the non-linearity characteristics of the piezoelectric material. This characteristic is important to be characterized since it can affect the performance of the piezoelectric material as sensor or actuator in many applications. In this study, the model of the coupled aluminium beam with single piezoelectric patch material is constructed to investigate the hysteresis effect of the piezoelectric material to the whole beam structure. A P-876 DuraActTM type piezoelectric patch material is used in modelling of the piezoelectric actuator. Firstly, the modal analysis of the coupled beam-piezoelectric actuator is determined to get the natural frequencies and mode shapes. Then, the piezoelectric patch material is investigated in terms of actuator by given a sinusoidal voltage excitation and output in terms of deflection, stress and strain of the piezoelectric actuator are investigated. From the results, it is clear that, the coupled beam-piezoelectric material is affected by the hysteresis of the piezoelectric material and the natural frequencies of the beam structure. This characteristic is important for the piezoelectric actuator manufacturer and by providing the correction algorithm, it can improve the performance of the piezoelectric actuator for many applications.

scholarly journals Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 203
Author(s):  
Suzan Cival Buranay ◽  
Nouman Arshad ◽  
Ahmed Hersi Matan
Keyword(s):  
Heat Equation ◽  
Fourth Order ◽  
Boundary Value ◽  
Time Variable ◽  
Implicit Methods ◽  
First Order ◽  
Mixed Derivatives ◽  
Hexagonal Grids ◽  
Spatial Derivatives ◽  
Derivatives Of

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116,ω>0. Additionally, the methods are applied on two sample problems.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

Experimental uniaxial stress and strain derivatives of the Fermi surface of rhenium

1980 ◽  
Vol 58 (8) ◽  
pp. 1191-1199 ◽  
Author(s):  
E. Fawcett ◽  
F. W. Holroyd ◽  
J. M. Perz
Keyword(s):  
Fermi Surface ◽  
Uniaxial Stress ◽  
Stress And Strain ◽  
Strong Anisotropy ◽  
Quantum Oscillations ◽  
Band Structure Calculations ◽  
Landau Quantum ◽  
Derivatives Of ◽  
Structure Calculations ◽  
The Magnetic Field

The derivatives of the areas of extremal orbits on all the small sheets of the Fermi surface of rhenium, with respect to stress and strain along the hexad axis, have been determined from simultaneous measurements of Landau quantum oscillations in magnetostriction and torque, and also in sound velocity and torque. Strong anisotropy is observed in the stress derivatives of orbits in zones five and six as the direction of the magnetic field defining the normal to the orbit is varied; the anisotropy is most pronounced for orbits which come close to the line of degeneracy AL on the hexagonal Brillouin zone face. The derivatives of the small void in zone eight are found to be very large; this is consistent with the results of band structure calculations which show that this feature of the Fermi surface is very sensitive to small changes in the Fermi energy. Cyclotron effective masses for a number of orbits on the void have also been measured.

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