scholarly journals Identification of Multiple Cracks in Composite Laminated Beams Using Perturbation to Dynamic Equilibrium

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6171
Author(s):  
Aimin Deng ◽  
Maosen Cao ◽  
Qitian Lu ◽  
Wei Xu
Keyword(s):  
Dynamic Equilibrium ◽  
Structural Information ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Crack Identification ◽  
Laser Vibrometer ◽  
Multiple Cracks ◽  
Laminated Beams ◽  
Fe Method ◽  
Laminated Beam

Identification of cracks in beam-type components is significant to ensure the safety of structures. Among the approaches relying on mode shapes, the concept of transverse pseudo-force (TPF) has been well proved for single and multiple crack identification in beams made of isotropic materials; however, there is a noticeable gap between the concept of TPF and its applications in composite laminated beams. To fill this gap, an enhanced TPF approach that relies on perturbation to dynamic equilibrium is proposed for the identification of multiple cracks in composite laminated beams. Starting from the transverse equation of motion, this study formulates the TPF in a composite laminated beam for the identification of multiple cracks. The capability of the approach is numerically verified using the FE method. The applicability of the approach is experimentally validated on a carbon fiber-reinforced polymer laminated beam with three cracks, the mode shapes of which are acquired through non-contact vibration measurement using a scanning laser vibrometer. In particular, a statistic manner is utilized to enable the approach to be feasible to real scenarios in the absence of material and structural information; besides, an integrating scheme is utilized to enable the approach to be capable of identifying cracks even in the vicinity of nodes of mode shapes.

Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

2012 ◽  
Vol 28 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A. A. Khdeir ◽  
E. Darraj ◽  
O. J. Aldraihem
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
Beam Model ◽  
Laminated Beams ◽  
State Space Approach ◽  
Laminated Beam ◽  
Beam Surface

ABSTRACTAnalytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

scholarly journals Fiber Bragg Grating Sensors for Underwater Vibration Measurement: Potential Hydropower Applications

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4272
Author(s):  
Oscar de la Torre ◽  
Ignazio Floris ◽  
Salvador Sales ◽  
Xavier Escaler
Keyword(s):  
Fiber Bragg Grating ◽  
Numerical Models ◽  
Vibration Measurement ◽  
Quality Data ◽  
Bragg Grating ◽  
Laser Vibrometer ◽  
Main Concern ◽  
High Expectations ◽  
Fiber Bragg Grating Sensors ◽  
Hydraulic Machinery

The present paper assesses the performance and characteristics of fiber Bragg grating sensors, with a special interest in their applications in hydraulic machinery and systems. The hydropower industry is turning to this technology with high expectations of obtaining high quality data to validate and calibrate numerical models that could be used as digital twins of key assets, further strengthening the sector’s relevant position within industry 4.0. Prior to any validation, fiber Bragg grating sensors’ ability to perform well underwater for long periods of time with minimal degradation, and their ease of scalability, drew the authors´ attention. A simplified modal analysis of a partially submerged beam is proposed here as a first step to validate the potential of this type of technology for hydropower applications. Fiber Bragg grating sensors are used to obtain the beam’s natural frequencies and to damp vibrations under different conditions. The results are compared with more established waterproof electric strain gauges and a laser vibrometer with good agreement. The presence of several sensors in a single fiber ensures high spatial resolution, fundamental to precisely determine vibration patterns, which is a main concern in this industry. In this work, the beam’s vibration patterns have been successfully captured under different excitations and conditions.

scholarly journals Detailed Analysis of the Acoustic Mode Shapes of an Annular Combustion Chamber

1999 ◽  
Author(s):  
Günther Walz ◽  
Werner Krebs ◽  
Stefan Hoffmann ◽  
Hans Judith
Keyword(s):  
Boundary Conditions ◽  
Acoustic Mode ◽  
Mode Shapes ◽  
Maximum Deviation ◽  
Minor Importance ◽  
Velocity Of Sound ◽  
Fe Method ◽  
Shift Frequency ◽  
Space Dependence ◽  
Eigenfrequency Spectrum

To get a better understanding of the formation of thermoacoustic oscillations in an annular gasturbine combustor, an analysis of the acoustic eigenmodes has been conducted using the Finite Element (FE) method. The influence of different boundary conditions and a space dependent velocity of sound has been investigated. The boundary conditions actually define the eigenfrequency spectrum. Hence, it is crucial to know e.g. the burner impedance. In case of the combustion system without significant mixing air addition considered in this paper, the space dependence of the velocity of sound is of minor importance for the eigenfrequency spectrum leading to a maximum deviation of only 5% in the eigenvalues. It is demonstrated that the efficiency of the numerical eigenvalue analysis can be improved by making use of symmetry, by splitting the problem into several steps with alternate boundaries conditions, and by choosing the shift frequency ωs in the range of frequencies one is interested in.

scholarly journals Structural Crack Identification in Railway Prestressed Concrete Sleepers Using Dynamic Mode Shapes

Proceedings ◽  
2018 ◽  
Vol 2 (16) ◽  
pp. 1139
Author(s):  
Rims Janeliukstis ◽  
Sandris Rucevski ◽  
Sakdirat Kaewunruen
Keyword(s):  
Prestressed Concrete ◽  
Mode Shapes ◽  
Crack Identification ◽  
Dynamic Mode ◽  
Critical Component ◽  
Safety Critical ◽  
Railway Tracks

Railway prestressed concrete sleepers are a structural and safety-critical component in railway tracks. [...]

scholarly journals Crack Identification and Localization In Structural Beams Using Numerical and Experimental Modal Analysis- A Review

2020 ◽  
pp. 62-68
Keyword(s):  
Modal Analysis ◽  
Natural Frequency ◽  
Structural Damage ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Crack Identification ◽  
Engineering Structures ◽  
Aircraft Wings ◽  
Crack Location ◽  
Damaged Beams

This article presents a critical review of recent research done on crack identification and localization in structural beams using numerical and experimental modal analysis. Crack identification and localization in beams are very crucial in various engineering applications such as ship propeller shafts, aircraft wings, gantry cranes, and Turbo machinery blades. It is necessary to identify the damage in time; otherwise, there may be serious consequences like a catastrophic failure of the engineering structures. Experimental modal analysis is used to study the vibration characteristics of structures like natural frequency, damping and mode shapes. The modal parameters like natural frequency and mode shapes of undamaged and damaged beams are different. Based on this reason, structural damage can be detected, especially in beams. From the review of various research papers, it is identified that a lot of the research done on beams with open transverse crack. Crack location is identified by tracking variation in natural frequencies of a healthy and cracked beam

scholarly journals Multiple crack identification in stepped beam by measurements of natural frequencies

2014 ◽  
Vol 36 (2) ◽  
pp. 119-132
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung ◽  
Vu Thi An Ninh
Keyword(s):  
Crack Detection ◽  
Natural Frequencies ◽  
Rayleigh Quotient ◽  
Crack Identification ◽  
Multiple Cracks ◽  
Simple Relationship ◽  
Multiple Crack ◽  
Scanning Method ◽  
New Approach ◽  
Efficient Procedure

A new approach is proposed for calculating natural frequencies and crack detection in a stepped cantilever beam with arbitrary number of cracks. This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. The proposed technique called crack scanning method is illustrated and validated by numerical results.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

Nonlinear Combination Resonances in Cantilever Composite Plates

1995 ◽  
Author(s):  
Kyoyul Oh ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Low Frequency ◽  
Composite Plates ◽  
High Amplitude ◽  
Mode Shapes ◽  
Laser Vibrometer ◽  
Combination Resonance ◽  
Response Curves

Abstract We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials

2019 ◽  
Vol 19 (08) ◽  
pp. 1950084 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Young's Modulus ◽  
Mass Density ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Governing Equations ◽  
Direct Integral

This study focused on the in-plane free vibration of uniform circular arches made of axially functionally graded (AFG) materials. Based on the dynamic equilibrium of an arch element, the governing equations for the free vibration of an AFG arch are derived in this study, where arbitrary functions for the Young’s modulus and mass density are acceptable. For the purpose of numerical analysis, quadratic polynomials for the Young’s modulus and mass density are considered. To calculate the natural frequencies and corresponding mode shapes, the governing equations are solved using the direct integral method enhanced by the trial eigenvalue method. For verification purposes, the predicted frequencies are compared to those obtained by the general purpose software ADINA. A parametric study of the end constraint, rotatory inertia, modular ratio, radius parameter, and subtended angle for the natural frequencies is conducted and the corresponding mode shapes are reported.

scholarly journals Damage Identification by Using a Self-Synchronizing Multipoint Laser Doppler Vibrometer

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Chong Yang ◽  
Yu Fu ◽  
Jianmin Yuan ◽  
Min Guo ◽  
Keyu Yan ◽  
...  
Keyword(s):  
Mode Shape ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Reference Beam ◽  
Laser Doppler Vibrometer ◽  
Laser Doppler ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Interference Signal ◽  
Short Period

The vibration-based damage identification method extracts the damage location and severity information from the change of modal properties, such as natural frequency and mode shape. Its performance and accuracy depends on the measurement precision. Laser Doppler vibrometer (LDV) provides a noncontact vibration measurement of high quality, but usually it can only do sampling on a single point. Scanning LDV is normally used to obtain the mode shape with a longer scanning time. In this paper, a damage detection technique is proposed using a self-synchronizing multipoint LDV. Multiple laser beams with various frequency shifts are projected on different points of the object, reflected and interfered with a common reference beam. The interference signal containing synchronized temporal vibration information of multiple spatial points is captured by a single photodetector and can be retrieved in a very short period. Experiments are conducted to measure the natural frequencies and mode shapes of pre- and postcrack cantilever beams. Mode shape curvature is calculated by numerical interpolation and windowed Fourier analysis. The results show that the artificial crack can be identified precisely from the change of natural frequencies and the difference of mode shape curvature squares.

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