Instructions for the preparation of a numerical investigation on crack parameters of cantilever beam using FEA

2021 ◽  
Vol 109 (1) ◽  
pp. 5-10
Author(s):  
M.A. Ansari ◽  
V.K. Tiwari
Keyword(s):  
Response Surface ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Crack Depth ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
External Excitation ◽  
Taguchi Design Of Experiments ◽  
Maximum Value ◽  
Dimensional Parameters

Purpose: The operation of engineering structures may cause various type of damages like cracks, alterations. Such kind of defects can lead to change in vibration characteristics of cantilever beam. The superposition of frequency causes resonance leading to amplitude built up and failure of beam. The current research investigates the effect of crack dimensional parameters on vibrational characteristics of cantilever beam. Design/methodology/approach: The CAD design and FE simulation studies are conducted in ANSYS 20 simulation package. The natural frequencies, mode shapes and response surface plots are generated, and comparative studies are performed. The effect of crack dimensional parameters is then investigated using Taguchi Design of Experiments. The statistical method of central composite design (CCD) scheme in Response Surface Optimization is used to generated various design points based on variation of crack width and crack depth. Findings: The research findings have shown that crack depth or crack height have significant effect on magnitude of deformation and natural frequency. The deformation is minimum at 0.009 m crack height and reaches maximum value at 0.011 m crack height. Research limitations/implications: The crack induced in the cantilever beam needs to be repaired properly in order to avoid crack propagation due to resonance. The present study enabled to determine frequencies of external excitation which should be avoided. The limitation of current research is the type of crack studied which is transverse type. The effect of longitudinal cracks on vibration characteristics is not investigated. Practical implications: The study on mass participation factor has shown maximum value for torsional frequency which signifies that any external excitation along this direction should be avoided which could cause resonance and lead to amplitude build up. Originality/value: The beams are used in bridge girders and other civil structures which are continuously exposed to moist climate. The moisture present in the air causes corrosion which initiates crack. This crack propagates and alters the natural frequency of beam.

scholarly journals Influence of Crack on Modal Parameters of Cantilever Beam Using Experimental Modal Analysis

2018 ◽  
Vol 1 (1) ◽  
pp. 16-23 ◽  
Author(s):  
Siva Sankara Babu Chinka ◽  
Balakrishna Adavi ◽  
Srinivasa Rao Putti
Keyword(s):  
Numerical Analysis ◽  
Modal Analysis ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Damping Ratio ◽  
Crack Depth ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Crack Location

In this paper, the dynamic behavior of a cantilever beam without and with crack is observed. An elastic Aluminum cantilever beams having surface crack at various crack positions are considered to analyze dynamically. Crack depth, crack length and crack location are the foremost parameters for describing the health condition of beam in terms of modal parameters such as natural frequency, mode shape and damping ratio. It is crucial to study the influence of crack depth and crack location on modal parameters of the beam for the decent performance and its safety. Crack or damage of structure causes a reduction in stiffness, an intrinsic reduction in resonant frequencies, variation of damping ratios and mode shapes. The broad examination of cantilever beam without crack and with crack has been done using Numerical analysis (Ansys18.0) and experimental modal analysis. To observe the exact higher modes of beam, discretize the beam into small elements. An experimental set up was established for cantilever beam having crack and it was excited by an impact hammer and finally the response was obtained using PCB accelerometer with the help sound and vibration toolkit of NI Lab-view. After obtaining the Frequency response functions (FRFs), the natural frequencies of beam are estimated using peak search method. The effectiveness of experimental modal analysis in terms of natural frequency is validated with numerical analysis results. This paper contains the study of free vibration analysis under the influence of crack at different points along the length of the beam.

Vibration-based delamination evaluation in GFRP composite beams using ANN

2021 ◽  
pp. 096739112110033
Author(s):  
TG Sreekanth ◽  
M Senthilkumar ◽  
S Manikanta Reddy
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Composite Structures ◽  
Composite Beams ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Aviation Industry ◽  
Frequency Data ◽  
Fiber Reinforced ◽  
Back Propagation Algorithm

Delamination is definitely an important topic in the area of composite structures as it progressively worsens the mechanical performance of fiber-reinforced polymer composite structures in its service period. The detection and severity analysis of delaminations in engineering areas like the aviation industry is vital for safety and economic considerations. The existence of delaminations varies the vibration characteristics such as natural frequencies, mode shapes, etc. of composites and hence this indication can be effectively used for locating and quantifying the delaminations. The changes in vibration characteristics are considered as inputs for the inverse problem to determine the location and size of delaminations. In this paper Artificial Neural Network (ANN) is used for delamination evaluationof glass fiber-reinforced composite beams using natural frequency as typical vibration parameter. The Finite Element Analysis is used for generating the required dataset for ANN. The frequency-based delamination prediction technique is validated by finite element models and experimental modal analysis. The results indicate that the ANN-based back propagation algorithm can predict the location and size of delaminations in composites with good accuracy for numerical natural frequency data but the accuracy is comparitivelyless for experimental natural frequency data.

scholarly journals Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

2007 ◽  
Author(s):  
Nikhit N. Nair ◽  
Hamid N. Hashemi ◽  
Grant M. Warner
Keyword(s):  
Crack Opening ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Bending Moment ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Coupled Systems ◽  
Mode Shapes ◽  
Critical Speeds ◽  
Crack Location

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the disk separated by the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the critical speeds and results in a quicker onset of instability. The degree of instability caused by the crack is a function of crack depth and location. Critical speeds increase with increasing crack distance from the central clamp and decrease with increasing crack depth.

Vibration Response of Functionally Graded Rotating Disk With a Circumferential Crack

2010 ◽  
Author(s):  
Rui Liu ◽  
Hamid Nayeb-Hashemi
Keyword(s):  
Critical Speed ◽  
Crack Depth ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Campbell Diagram ◽  
Circumferential Crack ◽  
Inner Radius ◽  
The Galerkin Method

In this study, the vibration characteristics of a functionally graded rotating hollow disk with the circumferential surface crack are investigated. In order to simplify the problem, the circumferential crack of the rotating hollow disk is modeled as circumferential step indentation. The Galerkin Method is used to obtain the radial and hoop stresses for disks with clamped edge at the inner radius. Finite Difference scheme is adopted to solve the partial differential equation of motion of the rotating hollow disk to obtain the mode shapes and the Campbell Diagram. The first critical speed, which is one of the important parameters limiting the performance of the rotating disk, was obtained from the Campbell Diagram. The results show that the crack will reduce the stiffness and the critical speed of the rotating disk. Critical speed increases with decreasing the distance from inner radius to the crack and decreases with increasing crack depth. Furthermore, considering the functionally graded disk, the distribution of elastic modulus does not change significantly the effects of circumferential cracks on the vibration characteristics of the rotating.

scholarly journals Vibration-Based Damage Detection in Beams by Cooperative Coevolutionary Genetic Algorithm

2014 ◽  
Vol 6 ◽  
pp. 624949 ◽  
Author(s):  
Kittipong Boonlong
Keyword(s):  
Genetic Algorithm ◽  
Damage Detection ◽  
Cantilever Beam ◽  
Cross Section ◽  
Random Noise ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Test Problems ◽  
Uniform Cross Section ◽  
Coevolutionary Genetic Algorithm

Vibration-based damage detection, a nondestructive method, is based on the fact that vibration characteristics such as natural frequencies and mode shapes of structures are changed when the damage happens. This paper presents cooperative coevolutionary genetic algorithm (CCGA), which is capable for an optimization problem with a large number of decision variables, as the optimizer for the vibration-based damage detection in beams. In the CCGA, a minimized objective function is a numerical indicator of differences between vibration characteristics of the actual damage and those of the anticipated damage. The damage detection in a uniform cross-section cantilever beam, a uniform strength cantilever beam, and a uniform cross-section simply supported beam is used as the test problems. Random noise in the vibration characteristics is also considered in the damage detection. In the simulation analysis, the CCGA provides the superior solutions to those that use standard genetic algorithms presented in previous works, although it uses less numbers of the generated solutions in solution search. The simulation results reveal that the CCGA can efficiently identify the occurred damage in beams for all test problems including the damage detection in a beam with a large number of divided elements such as 300 elements.

Vibration characteristics analysis and structure optimization of air-pressure subsoiler

2021 ◽  
pp. 095745652110526
Author(s):  
Hongjie Su ◽  
Hongmei Cui ◽  
Feiyu Li ◽  
Chaolun Yideer ◽  
Yaxiong Zhu ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Structural Reliability ◽  
Excitation Frequency ◽  
Structure Optimization ◽  
Time Domain Analysis ◽  
Vibration Characteristics ◽  
Air Pressure ◽  
Excitation Source ◽  
External Excitation ◽  
Actual Production

Aiming at the problems of strong vibration, inconsistent subsoiling depth and high failure rate of air-pressure subsoiler, air-pressure subsoiler vibration characteristics was studied. In order to decrease the vibration, For the first time, the vibration characteristics of air-pressure subsoiler were obtained by modal analysis and vibration test. The vibration characteristics of the whole air-blown subsoiler are analyzed Through time domain analysis, it is found that the vibration acceleration of four deep loosening shovel is inconsistent. When the diesel engine is started, it is easy to cause inconsistent subsoiler depth. Then, by analyzing the vibration characteristics of the whole air-pressure subsoiler, it can be known that the external excitation source of the air-blown subsoiler is close to its own natural frequency. In order to avoid resonance caused by the vibration frequency of the external excitation source being close to the natural frequency of the air-pressure subsoiler, and to reduce the inconsistency of the subsoil depth, we optimize the design of air-pressure subsoiler. Instead of diesel engines, the steering gear box is connected with tractor power output shaft to provide power. The modal simulation of the optimized air-pressure subsoiler shows that the first-order natural frequency is obviously improved and the external excitation frequency is successfully avoided. It not only avoids resonance, reduces the damage of resonance components, but improves the service life of the subsoiler, greatly improves the structural reliability of the air-pressure subsoiler, at the same time, removes the main external excitation source, which greatly reduces the vibration in actual production and the inconsistency of subsoiling, which is of great significance in actual production. It provides a reference for the research of vibration characteristics, resonance avoidance and structure optimization of agricultural equipment.

The effect of crack geometry on non-destructive fault detection of EN 8 and EN 47 cracked cantilever beam

2019 ◽  
Vol 50 (3) ◽  
pp. 92-100 ◽  
Author(s):  
V Khalkar ◽  
S Ramachandran
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Crack Location ◽  
Crack Geometry ◽  
Shaped Crack ◽  
Non Destructive

Since long it has been observed that the size of the crack in structures increases with time, and finally, it may lead to its catastrophic failure. Hence, it is crucial to do the vibration study of cracked structures with regard to vibration-based crack detection and the classification of cracks. So far, vibration-based non-destructive testing method is applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, that is, V-shaped and U-shaped, on the applicability of these methods has been overlooked. To investigate this issue, artificially cracks are made on the cantilever beam. By free vibration analysis, the effect of crack geometry, crack depth, and crack location on natural frequency is investigated. The natural frequency results obtained from V-shaped and U-shaped models for the same crack configurations are compared with each other and it is revealed that the results are not much sensitive for the change of crack geometry. Hence, it is clear that free vibration-based crack detection method approximately predicts the crack parameters, that is, crack location and crack depth, in structures irrespective of the crack geometry. It is also found that for the same configuration, results of natural frequency are comparatively on the lower side for U-shaped crack models than V-shaped crack models. In this study, the natural frequency of each cracked case is computed by a theoretical method and numerical method and shows good agreement. Finally, it is also observed that structural integrity of a cracked cantilever beam is a function of crack location.

Coupled Transverse and Axial Vibrations of Cracked Cantilever Beams With Roving Mass and Rotary Inertia

2010 ◽  
Author(s):  
Hurang Hu ◽  
Akindeji Ojetola ◽  
Hamid Hamidzadeh
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Coupling Effect ◽  
Rectangular Cross Section ◽  
Crack Depth ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Crack Location ◽  
Axial Vibrations

The vibration behavior of a cracked cantilever beam with a stationary roving mass and rotary inertia is investigated. The beam is modeled as an Euler-Bernoulli beam with rectangular cross section. The transverse deformation and axial deformation of the cracked beam are coupled through a stiffness matrix which is determined based on fracture mechanics principles. The analytical solutions are obtained for the natural frequencies and mode shapes of a cracked cantilever beam with a roving mass and rotary inertia. The effects of the location and depth of the crack, the location and the weight of the roving mass and rotary inertia on the natural frequencies and mode shapes of the beam are investigated. The numerical results show that the coupling between the transverse and axial vibrations for moderate values of crack depth and/or roving mass and rotary inertia is weak. Increasing the crack depth and the mass and rotary inertia will increase the coupling effect. Detection of the crack location using natural frequencies and mode shapes as parameters is also discussed.

Vibration simulation for a cantilever beam including a slant vertical crack

2018 ◽  
Vol 36 (1) ◽  
pp. 147-160 ◽  
Author(s):  
Xiaohua Song ◽  
Yiming Shao
Keyword(s):  
Natural Frequency ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Analytical Modelling ◽  
Vertical Crack ◽  
Mode Shapes ◽  
Content Type ◽  
Crack Location ◽  
Minimum Value ◽  
Fixed End

Purpose Modelling methods can be helpful for understanding vibrations of beam structures including cracks, as well as for early detection of crack. This study aims to provide an analytical modelling approach for a cantilever beam considering a slant vertical crack along its height. However, previous uniform crack methods cannot be used for describing this case. The results from the analytical, finite element (FE) and experimental methods are compared to verify the vibration problem. Design/methodology/approach A massless rotational spring model is adopted to describe the crack. An extended method based on the calculation method for a uniform vertical edge crack is proposed to obtain the stiffness of the slant case. The beam is divided into a series of independent thin slices along the beam height. An Euler–Bernoulli beam model is applied to formulate each slice. The crack in each slice is considered as a uniform one. The transfer matrix method in the literature is used to obtain the beam vibration frequencies and mode shapes. Influences of crack location and sizes on the natural frequencies for the cantilever beam, as well as the mode shapes, are analysed. An established FE model and test results in the listed references are used to validate the developed method. Findings The numerical results show that the rotational stiffness at the cracked section and the natural frequencies of the beam decrease by increasing the crack sizes; the natural frequencies for the beam are greatly influenced by the crack sizes and location; the first natural frequency decreases with the distance from the beam fixed end to the crack location; the value of the first natural frequency reaches a minimum value when the crack is at the beam fixed end; the value of the second natural frequency is a minimum value when the crack is at the beam middle; and the value of the third natural frequency is a minimum value when the crack is at the beam free end. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths; but, the mode shapes of the beam are slightly influenced by the vertical crack. Originality/value This study gives a useful analytical modelling method for free vibration analysis for the cantilever beam with a vertical crack, which can overcome the disadvantages of the previous uniform crack methods.

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