Abstract: This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.
Abstract: Currently, extensive signal analysis is performed in order to evaluate structural health of turbomachinery blades. This approach is affected by constraints of time and the availability of qualified personnel. Thus, new approaches to blade dynamics identification that provide faster and more accurate results are sought after. Generally, modal analysis is employed in acquiring dynamic properties of a vibrating turbomachinery blade and is widely adopted in condition monitoring of blades. The analysis provides useful information on the different modes of vibration and natural frequencies by exploring different shapes that can be taken up during vibration since all mode shapes have their corresponding natural frequencies. Experimental modal testing and finite element analysis are the traditional methods used to evaluate mode shapes with limited application to real live scenario to facilitate a robust condition monitoring scheme. For a real time mode shape evaluation, rapid evaluation and low computational cost is required and traditional techniques are unsuitable. In this study, artificial neural network is developed to evaluate the mode shape of a lab scale rotating blade assembly by using result from finite element modal analysis as training data. The network performance evaluation shows that artificial neural network (ANN) is capable of mapping the correlation between natural frequencies and mode shapes. This is achieved without the need of extensive signal analysis. The approach offers advantage from the perspective that the network is able to classify mode shapes and can be employed in real time including simplicity in implementation and accuracy of the prediction. The work paves the way for further development of robust condition monitoring system that incorporates real time mode shape evaluation.
Abstract: In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.
Abstract: The development in the construction of unconventional ships and the implementation of lightweight materials have shown a large impulse towards finite element (FE) method, making it a general tool for ship design. This paper briefly presents the modeling and analysis techniques of ship structures using FE method for complex boundary conditions which are difficult to analyze by existing Ship Classification Societies rules. During operation, all ships experience complex loading conditions. These loads are general categories into thermal loads, linear static, dynamic and non-linear loads. General strength of the ship structure is analyzed using static FE analysis. FE method is also suitable to consider the local loads generated by ballast tanks and cargo in addition to hydrostatic and hydrodynamic loads. Vibration analysis of a ship structure and its components can be performed using FE method which helps in obtaining the dynamic stability of the ship. FE method has developed better techniques for calculation of natural frequencies and different mode shapes of ship structure to avoid resonance both globally and locally. There is a lot of development towards the ideal design in ship industry over the past few years for solving complex engineering problems by employing the data stored in the FE model. This paper provides an overview of ship modeling methodology for FE analysis and its general application. Historical background, the basic concept of FE, advantages, and disadvantages of FE analysis are also reported along with examples related to hull strength and structural components.
Abstract: Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.
Abstract: In many applied engineering problems, structural analysis is usually conducted by assuming a rigid bed, while imposing the effect of structure bed flexibility can affect significantly on the structure response. This article focuses on investigation and evaluation of the effects arising from considering a soil-structure system in evaluation of dynamic characteristics of a steel structure with respect to elastic and inelastic behaviors. The recorded structure acceleration during Taiwan’s strong Chi-Chi earthquake on different floors of the structure was our evaluation criteria. The respective structure is an eight-story steel bending frame structure designed using a displacement-based direct method assuring weak beam - strong column function. The results indicated that different identification methods i.e. reverse Fourier transform or transfer functions, is capable to determine some of the dynamic parameters of the structure precisely, rather than evaluating all of them at once (mode frequencies, mode shapes, structure damping, structure rigidity, etc.). Response evaluation based on the input and output data elucidated that the structure first mode is not significantly affected, even considering the soil-structure interaction effect, but the upper modes have been changed. Also, it was found that the response transfer function of the different stories, in which plastic hinges have occurred in the structure components, provides similar results.
Abstract: In this study, a spatial wavelet-based crack localization technique for a thick beam is presented. Wavelet scale in spatial wavelet transformation is optimized to enhance crack detection sensitivity. A windowing function is also employed to erase the edge effect of the wavelet transformation, which enables the method to detect and localize cracks near the beam/measurement boundaries. Theoretical model and vibration analysis considering the crack effect are first proposed and performed in MATLAB based on the Timoshenko beam model. Gabor wavelet family is applied to the beam vibration mode shapes derived from the theoretical beam model to magnify the crack effect so as to locate the crack. Relative wavelet coefficient is obtained for sensitivity analysis by comparing the coefficient values at different positions of the beam with the lowest value in the intact area of the beam. Afterward, the optimal wavelet scale corresponding to the highest relative wavelet coefficient at the crack position is obtained for each vibration mode, through numerical simulations. The same procedure is performed for cracks with different sizes and positions in order to find the optimal scale range for the Gabor wavelet family. Finally, Hanning window is applied to different vibration mode shapes in order to overcome the edge effect problem of wavelet transformation and its effect on the localization of crack close to the measurement boundaries. Comparison of the wavelet coefficients distribution of windowed and initial mode shapes demonstrates that window function eases the identification of the cracks close to the boundaries.
Abstract: The objective of this article is to improve the passive vibration damping of solar array (SA) used in space structures, by the effective application of numerical optimization. A case study of a SA is used for demonstration. A finite element (FE) model was created and verified by experimental testing. Optimization was then conducted by implementing the FE model with the genetic algorithm, to find the optimal placement of aluminum circular patches, to suppress the first two bending mode shapes. The results were verified using experimental testing. Finally, a parametric study was conducted using the FE model where patch locations, material type, and shape were varied one at a time, and the results were compared with the optimal ones. The results clearly show that through the proper application of FE modeling and numerical optimization, passive vibration damping of space structures has been successfully achieved.
Abstract: A symmetrical single mass resonant gyroscope is discussed in this paper. The symmetrical design allows matched resonant frequencies for driving and sensing vibration modes, which leads to amplifying the sensitivity of the gyroscope by the mechanical quality factor of the sense mode. It also achieves decoupled vibration modes for getting a low zero-rate output shift and more stable operation environment. A new suspension beams design is developed to get a symmetrical gyroscope with matched and decoupled modes at the same time. Finite element simulations are performed using ANSYS software package to verify the theoretical calculations. The gyroscope is fabricated from aluminum alloy 2024 substrate, the measured drive and sense resonant frequencies of the fabricated model are matched and equal 81.4 Hz with 5.7% error from the simulation results.
Abstract: Structures such as buildings, bridges, dams, wind turbines etc. need to be maintained against various factors such as deterioration, excessive loads, environment, temperature, etc. Choosing an appropriate monitoring system is important for determining any critical damage to a structure and address that to avoid any adverse consequence. Structural Health Monitoring (SHM) has emerged as an effective technique to monitor the health of the structures. SHM refers to an ongoing structural performance assessment using different kinds of sensors attached to or embedded in the structures to evaluate their integrity and safety to help engineers decide on rehabilitation measures. Ability of SHM in identifying the location and severity of structural damages by considering any changes in characteristics of the structures such as their frequency, stiffness and mode shapes helps engineers to monitor the structures and take the most effective corrective actions to maintain their safety and extend their service life. The main objective of this study is to review the overall SHM process specifically determining the natural frequency of an instrumented simply-supported concrete beam using modal testing and finite element model updating.
Abstract: This paper deals with different modeling aspects of masonry infill: no infill model, Layered shell infill model, and strut infill model. These models consider the complicated behavior of the in-filled plane frames under lateral load similar to an earthquake load. Three strut infill models are used: NBCC (2005) strut infill model, ASCE/SEI 41-06 strut infill model and proposed strut infill model based on modification to Canadian, NBCC (2005) strut infill model. Pushover and modal analyses of a masonry infill concrete frame with a single storey and an existing 5-storey RC building have been carried out by using different models for masonry infill. The corresponding hinge status, the value of base shear at target displacement as well as their dynamic characteristics have been determined and compared. A validation of the structural numerical models for the existing 5-storey RC building has been achieved by comparing the experimentally measured and the analytically estimated natural frequencies and their mode shapes. This study shows that ASCE/SEI 41-06 equation underestimates the values for the equivalent properties of the diagonal strut while Canadian, NBCC (2005) equation gives realistic values for the equivalent properties. The results indicate that both ASCE/SEI 41-06 and Canadian, NBCC (2005) equations for strut infill model give over estimated values for dynamic characteristic of the building. Proposed modification to Canadian, NBCC (2005) equation shows that the fundamental dynamic characteristic values of the building are nearly similar to the corresponding values using layered shell elements as well as measured field results.
Abstract: Modal analysis of a FGM plate containing the ceramic phase of Al2O3 and metal phase of stainless steel 304 was performed using ABAQUS, with the assumptions that the material has an elastic mechanical behavior and its Young modulus and density are varying in thickness direction. For this purpose, a subroutine was written in FOTRAN and linked with ABAQUS. First, a simulation was performed in accordance to other researcher’s model, and then after comparing the obtained results, the accuracy of the present study was verified. The obtained results for natural frequency and mode shapes indicate good performance of user-written subroutine as well as FEM model used in present study. After verification of obtained results, the effect of clamping condition and the material type (i.e. the parameter n) was investigated. In this respect, finite element analysis was carried out in fully clamped condition for different values of n. The results indicate that the natural frequency decreases with increase of n, since with increase of n, the amount of ceramic phase in FGM plate decreases, while the amount of metal phase increases, leading to decrease of the plate stiffness and hence, natural frequency, as the Young modulus of Al2O3 is equal to 380 GPa and the Young modulus of stainless steel 304 is equal to 207 GPa.
Abstract: In this study, static and dynamic responses of a typical
reinforced concrete solid slab, designed to British Standard (BS 8110:
1997) and under self and live loadings for dance halls are reported.
Linear perturbation analysis using finite element method was
employed for modal, impulse loading and frequency response
analyses of the slab under the aforementioned loading condition.
Results from the static and dynamic analyses, comprising of the slab
fundamental frequencies and mode shapes, dynamic amplification
factor, maximum deflection, stress distributions among other
valuable outcomes are presented and discussed. These were gauged
with the limiting provisions in the design code with a view of
justifying valid optimization objective function for the structure that
can ensure both adequate strength and economical section for large
clear span slabs. This is necessary owing to the continued increase in
cost of erecting building structures and the squeeze on public finance
globally.
Abstract: In this study free vibration analysis of aluminum
honeycomb sandwich structures were carried out experimentally and
numerically. The natural frequencies and mode shapes of sandwich
structures fabricated with different configurations for clamped-free
boundary condition were determined. The effects of lower and upper
face sheet thickness, the core material thickness, cell diameter, cell
angle and foil thickness on the vibration characteristics were
examined. The numerical studies were performed with ANSYS
package. While the sandwich structures were modeled in ANSYS the
continuum model was used. Later, the numerical results were
compared with the experimental findings.
Abstract: An Australian manufacturer has fabricated an
innovative GFRP sandwich panel made from E-glass fiber skin and a
modified phenolic core for structural applications. Debonding, which
refers to separation of skin from the core material in composite
sandwiches, is one of the most common types of damage in
composites. The presence of debonding is of great concern because it
not only severely affects the stiffness but also modifies the dynamic
behaviour of the structure. Generally it is seen that the majority of
research carried out has been concerned about the delamination of
laminated structures whereas skin-core debonding has received
relatively minor attention. Furthermore it is observed that research
done on composite slabs having multiple skin-core debonding is very
limited. To address this gap, a comprehensive research investigating
dynamic behaviour of composite panels with single and multiple
debonding is presented. The study uses finite-element modelling and
analyses for investigating the influence of debonding on free
vibration behaviour of single and multilayer composite sandwich
panels. A broad parametric investigation has been carried out by
varying debonding locations, debonding sizes and support conditions
of the panels in view of both single and multiple debonding.
Numerical models were developed with Strand7 finite element
package by innovatively selecting the suitable elements to diligently
represent their actual behavior. Three-dimensional finite element
models were employed to simulate the physically real situation as
close as possible, with the use of an experimentally and numerically
validated finite element model. Comparative results and conclusions
based on the analyses are presented. For similar extents and locations
of debonding, the effect of debonding on natural frequencies appears
greatly dependent on the end conditions of the panel, giving greater
decrease in natural frequency when the panels are more restrained.
Some modes are more sensitive to debonding and this sensitivity
seems to be related to their vibration mode shapes. The fundamental
mode seems generally the least sensitive mode to debonding with
respect to the variation in free vibration characteristics. The results
indicate the effectiveness of the developed three dimensional finite
element models in assessing debonding damage in composite
sandwich panels.
Abstract: The aim of this paper is to perform experimental
modal analysis (EMA) of reinforced concrete (RC) square slabs.
EMA is the process of determining the modal parameters (Natural
Frequencies, damping factors, modal vectors) of a structure from a
set of frequency response functions FRFs (curve fitting). Although,
experimental modal analysis (or modal testing) has grown steadily in
popularity since the advent of the digital FFT spectrum analyzer in
the early 1970’s, studying all types of members and materials using
such method have not yet been well documented. Therefore, in this
work, experimental tests were conducted on RC square slab
specimens of dimensions 600mm x 600mmx 40mm. Experimental
analysis was based on freely supported boundary condition.
Moreover, impact testing as a fast and economical means of finding
the modes of vibration of a structure was used during the
experiments. In addition, Pico Scope 6 device and MATLAB
software were used to acquire data, analyze and plot Frequency
Response Function (FRF). The experimental natural frequencies
which were extracted from measurements exhibit good agreement
with analytical predictions. It is showed that EMA method can be
usefully employed to investigate the dynamic behavior of RC slabs.
Abstract: This paper presents small signal stability study carried
over the 140-Bus, 31-Machine, 5-Area MEPE system and validated
on free and open source software: PSAT. Well-established linearalgebra
analysis, eigenvalue analysis, is employed to determine the
small signal dynamic behavior of test system. The aspects of local
and interarea oscillations which may affect the operation and
behavior of power system are analyzed. Eigenvalue analysis is carried
out to investigate the small signal behavior of test system and the
participation factors have been determined to identify the
participation of the states in the variation of different mode shapes.
Also, the variations in oscillatory modes are presented to observe the
damping performance of the test system.
Abstract: This paper presents the details of a numerical study of
buckling and post buckling behaviour of laminated carbon fiber
reinforced plastic (CFRP) thin-walled cylindrical shell under axial
compression using asymmetric meshing technique (AMT) by
ABAQUS. AMT is considered to be a new perturbation method to
introduce disturbance without changing geometry, boundary
conditions or loading conditions. Asymmetric meshing affects both
predicted buckling load and buckling mode shapes. Cylindrical shell
having lay-up orientation [0^o/+45^o/-45^o/0^o] with radius to thickness
ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is
analysed numerically. A series of numerical simulations
(experiments) are carried out with symmetric and asymmetric
meshing to study the effect of asymmetric meshing on predicted
buckling behaviour. Asymmetric meshing technique is employed in
both axial direction and circumferential direction separately using
two different methods, first by changing the shell element size and
varying the total number elements, and second by varying the shell
element size and keeping total number of elements constant. The
results of linear analysis (Eigenvalue analysis) and non-linear
analysis (Riks analysis) using symmetric meshing agree well with
analytical results. The results of numerical analysis are presented in
form of non-dimensional load factor, which is the ratio of buckling
load using asymmetric meshing technique to buckling load using
symmetric meshing technique. Using AMT, load factor has about 2%
variation for linear eigenvalue analysis and about 2% variation for
non-linear Riks analysis. The behaviour of load end-shortening curve
for pre-buckling is same for both symmetric and asymmetric meshing
but for asymmetric meshing curve behaviour in post-buckling
becomes extraordinarily complex. The major conclusions are:
different methods of AMT have small influence on predicted
buckling load and significant influence on load displacement curve
behaviour in post buckling; AMT in axial direction and AMT in
circumferential direction have different influence on buckling load
and load displacement curve in post-buckling.
Abstract: Over the last few decades, oilfield service rolling
equipment has significantly increased in weight, primarily because of
emissions regulations, which require larger/heavier engines, larger
cooling systems, and emissions after-treatment systems, in some
cases, etc. Larger engines cause more vibration and shock loads,
leading to failure of electronics and control systems.
If the vibrating frequency of the engine matches the system
frequency, high resonance is observed on structural parts and mounts.
One such existing automated control equipment system comprising
wire rope mounts used for mounting computers was designed
approximately 12 years ago. This includes the use of an industrialgrade
computer to control the system operation. The original
computer had a smaller, lighter enclosure. After a few years, a newer
computer version was introduced, which was 10 lbm heavier. Some
failures of internal computer parts have been documented for cases in
which the old mounts were used. Because of the added weight, there
is a possibility of having the two brackets impact each other under
off-road conditions, which causes a high shock input to the computer
parts. This added failure mode requires validating the existing mount
design to suit the new heavy-weight computer.
This paper discusses the modal finite element method (FEM)
analysis and experimental modal analysis conducted to study the
effects of vibration on the wire rope mounts and the computer. The
existing mount was modelled in ANSYS software, and resultant
mode shapes and frequencies were obtained. The experimental modal
analysis was conducted, and actual frequency responses were
observed and recorded.
Results clearly revealed that at resonance frequency, the brackets
were colliding and potentially causing damage to computer parts. To
solve this issue, spring mounts of different stiffness were modeled in
ANSYS software, and the resonant frequency was determined.
Increasing the stiffness of the system increased the resonant
frequency zone away from the frequency window at which the engine
showed heavy vibrations or resonance. After multiple iterations in
ANSYS software, the stiffness of the spring mount was finalized,
which was again experimentally validated.
Abstract: This paper focuses on the dynamic behavior of
reinforced concrete (RC) slabs. Therefore, the theoretical modal
analysis was performed using two different types of boundary
conditions. Modal analysis method is the most important dynamic
analyses. The analysis would be modal case when there is no external
force on the structure. By using this method in this paper, the effects
of freely and simply supported boundary conditions on the
frequencies and mode shapes of RC square slabs are studied. ANSYS
software was employed to derive the finite element model to
determine the natural frequencies and mode shapes of the slabs.
Then, the obtained results through numerical analysis (finite element
analysis) would be compared with the exact solution. The main goal
of the research study is to predict how the boundary conditions
change the behavior of the slab structures prior to performing
experimental modal analysis. Based on the results, it is concluded
that simply support boundary condition has obvious influence to
increase the natural frequencies and change the shape of the mode
when it is compared with freely supported boundary condition of
slabs. This means that such support conditions have the direct
influence on the dynamic behavior of the slabs. Thus, it is suggested
to use free-free boundary condition in experimental modal analysis to
precisely reflect the properties of the structure. By using free-free
boundary conditions, the influence of poorly defined supports is
interrupted.