Free vibration analysis of a cantilever beam with a slant edge crack

2016 ◽  
Vol 231 (5) ◽  
pp. 823-843 ◽  
Author(s):  
J Liu ◽  
YM Shao ◽  
WD Zhu
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Crack Detection ◽  
Failure Modes ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Beam Model ◽  
Equivalent Stiffness ◽  
Proposed Model ◽  
Detection And Diagnosis

As one of major failure modes of mechanical structures subjected to periodic loads, edge cracks due to fatigue can cause catastrophic failures in such structures. Understanding vibration characteristics of a structure with an edge crack is useful for early crack detection and diagnosis. In this work, a new cracked cantilever beam model is presented to study the vibration of a cantilever beam with a slant edge crack, which cannot be modeled by previous methods considering a uniform edge crack along the width of the beam in the literature. An equivalent stiffness model is proposed by dividing the beam into numerous uniform independent thin pieces along its width. The beam is assumed to be an Euler–Bernoulli beam. The crack is assumed to be distributed along the width of the beam as a straight line and a parabola. The methodology proposed in this work can also be extended to model a crack with an arbitrary curve. Effects of crack depths on the nondimensional equivalent stiffness at the crack section of the cracked cantilever beam are studied. The first three nature frequencies and mode shapes of the cracked cantilever beam are obtained using compatibility conditions at crack tips and the transfer matrix method. Effects of depths and the location of the crack on the first three natural frequencies and mode shapes of the cracked cantilever beam are studied using the proposed cracked cantilever beam model. Numerical results from the proposed model are compared with those from the finite element method and an experimental investigation in the literature, which can validate the proposed model.

An Approach to Approximate the Full Strain Field of Turbofan Blades During Operation

2018 ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu ◽  
Walter O’Brien
Keyword(s):  
Numerical Model ◽  
Cantilever Beam ◽  
Strain Field ◽  
Measured Data ◽  
Mode Shapes ◽  
Beam Model ◽  
Reference Solution ◽  
Full Field ◽  
Field Response ◽  
Critical Locations

The measurement of the aeromechanical response of the fan blades is important to quantifying their integrity. The accurate knowledge of the response at critical locations of the structure is crucial when assessing the structural condition. A reliable and low cost measuring technique is necessary. Currently, sensors can only provide the measured data at several discrete points. A significant number of sensors may be required to fully characterize the aeromechanical response of the blades. However, the amount of instrumentation that can be placed on the structure is limited due to data acquisition system limitations, instrumentation accessibility, and the effect of the instrumentation on the measured response. From a practical stand point, it is not possible to place sensors at all the critical locations for different excitations. Therefore, development of an approach that derives the full strain field response based on a limited set of measured data is required. In this study, the traditional model reduction method is used to expand the full strain field response of the structure by using a set of discrete measured data. Two computational models are developed and used to verify the expansion approach. The solution of the numerical model is chosen as the reference solution. In addition, the numerical model also provides the mode shapes of the structure. In the expansion approach, this information is used to develop the algorithm. First, a cantilever beam model is created. The influences of the sensor location, number of sensors and the number of modes included are analyzed using this cantilever beam model. The expanded full field response data is compared with the reference solution to evaluate the expansion procedure. The rotor 67 blade model is then used to test the expansion method. The results show that the expanded full field data is in good agreement with the calculated data. The expansion algorithm can be used for the full field strain by using the limited sets of strain data.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

A New Reactive Hybrid Membership Function in Fuzzy Approach for Identification of Inclined Edge Crack in Cantilever Beam Using Vibration Signatures

2014 ◽  
Vol 592-594 ◽  
pp. 1996-2000 ◽  
Author(s):  
K.B. Ranjan ◽  
Sasmita Sahu ◽  
R. Parhi Dayal
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Fuzzy Controller ◽  
Experimental Results ◽  
Mode Shapes ◽  
Crack Identification ◽  
Hybrid Technique ◽  
Membership Functions ◽  
Inclined Edge Crack ◽  
Vibration Signatures

In this paper, the crack identification using smart technique (by several hybrid membership functions in a fuzzy controller) has been developed for inverse analysis of the vibration signatures (like modal frequencies, mode shapes) and crack parameters (like crack depth, crack location and crack inclination) of an inclined edge crack cantilever beam. The modal frequencies are obtained from finite element (using ANSYS) and experimental analysis which are used as inputs to the hybrid fuzzy controller. The hybrid fuzzy system is designed by taking different types of membership functions (MF) to determine the crack parameters. The calculated first three modal frequencies are used to create number of fuzzy rules with the three output crack parameters. Finally, the proposed hybrid technique is validated by comparing the results obtained from trapezoidal and Gaussian fuzzy controllers, FEA and experimental results. The outcomes obtained from hybrid fuzzy controller are in good agreement with experimental results. Nomenclature

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.

Dynamic Modelling and Free Vibration Characteristics Analysis of Rotating Beams

2021 ◽  
Author(s):  
D. Sachin ◽  
Mallikarjuna Reddy
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Turbine Blades ◽  
Dynamic Modelling ◽  
Free Vibration Analysis ◽  
Beam Model ◽  
Plane Vibration

Abstract Turbine blades are ideally modeled as cantilever beams on a disc rotating at a constant angular velocity. A study is made to understand the dynamic relationships between a rotating cantilever beam and various factors like hub radius, rotation speed, and slenderness ratio in in-plane vibration (Chordwise motion) and out-of-plane vibration (Flapwise motion). Hub is assumed to be rigid in the study. Using Hamilton’s principle, governing differential equations of movement for free vibration analysis of Euler-Bernoulli beam (EB) and Timoshenko (TB) beam under rotation are derived. The effects of the Gyroscopic couple are taken into account in the equations. The beam model is discretized using the Finite element approach. Derived differential equations are transformed into dimensionless quantities in which dimensionless parameters are identified. Under rotation, it is observed that the natural frequencies increase with the increase in rotational speed for both flapwise and chordwise motions of the beam. An interesting phenomenon is observed in the chordwise motion results, where Natural frequencies veer off at certain rotational speeds and certain modes. Slenderness ratios also influence this phenomenon, which shifts the veer-off region and the tuned angular frequency. Numerical results are obtained for different rotational speeds with various hub radius ratios, and it was observed that hub radius directly influences the natural frequencies of the rotating uniform cantilever beam. A thorough study on the influence of the slenderness ratio showed that, for lower slenderness ratio, frequency veering region occurs at the fundamental natural frequency, but for higher slenderness ratios’ there is a shift in frequency veering region for higher modes.

Modelling of a Beam with a Breathing Edge Crack and Some Observations for Crack Detection

2002 ◽  
Vol 8 (5) ◽  
pp. 673-693 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Edge Crack ◽  
Crack Detection ◽  
Spectral Characteristics ◽  
Crack Size ◽  
Small Displacement ◽  
Harmonic Load ◽  
Cracked Beam ◽  
Frequency Spectra ◽  
Proposed Model ◽  
Cracked Beams

The breathing behaviour of closing cracks has been adequately simulated as a small-displacement, frictionless contact problem. The problem of a beam with an edge crack subjected to harmonic loading has been considered as a plane problem and an attempt is made to solve it by using finite elements employing eight-node plane isoparametric elements. The proposed model allows the crack size and position to be varied. Another physically important problem of a cantilever beam held between two heavy jaws at the top and bottom, which are not equally flushed, is considered. This beam is also excited by a harmonic load at the tip. The contact model and a simple single degree of freedom model are used to solve the problem. Both the above problems (cracked beam and beam in offset jaws) show presence of integral multiples of the forcing frequency in their frequency spectra. An important observation regarding cracked beams and beams with imperfect support is made. If the forcing frequency is such that it coincides or is close to any one of the integral sub-multiples (1/ n) of the first natural frequency of the system, then the nth harmonic of the forcing frequency will considerably shoot up. This effect is highly pronounced for the case n = 2 and this observation may be used to detect cracks in beams as small as 2.5% of the depth. For cracked beams, the even harmonics are considerably stronger than the odd ones. As the crack size decreases, the odd harmonics become weaker. For a 2.5% crack only the second and fourth harmonics are visible in an 80 dB scale, with the former being the stronger. However, it is important to note that cracked beams and beams with imperfect support have closely similar spectral characteristics and so due caution must be exercised during crack detection.

Analysis of the Dynamic Response of a Cracked Beam Structure

2012 ◽  
Vol 187 ◽  
pp. 58-62 ◽  
Author(s):  
D. N. Thatoi ◽  
J. Nanda ◽  
H.C. Das ◽  
D.R. Parhi
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Cracked Beam ◽  
Local Flexibility ◽  
Good Agreement

In this research, dynamic behaviour of a cracked cantilever beam has been analysed using finite element and experimental analysis. Deviations in mode shapes and natural frequencies have been noticed due to the presence of crack in the beam. The variation in the dynamic response is due to change in local flexibility because of the presence of crack in the beam. Finite element and experimental analyses have been carried out to find out the vibration indices of the cracked cantilever beam for validating the robustness of the theoretical model used for crack detection. The numerical results obtained through FEA are in good agreement with experimental results.

scholarly journals Computational Intelligence-Based Model for Mortality Rate Prediction in COVID-19 Patients

2021 ◽  
Vol 18 (12) ◽  
pp. 6429
Author(s):  
Irfan Ullah Khan ◽  
Nida Aslam ◽  
Malak Aljabri ◽  
Sumayh S. Aljameel ◽  
Mariam Moataz Aly Kamaleldin ◽  
...  
Keyword(s):  
Mortality Rate ◽  
Computational Intelligence ◽  
Nearest Neighbor ◽  
Gradient Boosting ◽  
K Nearest Neighbor ◽  
Detection And Identification ◽  
Proposed Model ◽  
Extreme Gradient Boosting ◽  
The World ◽  
Detection And Diagnosis

The COVID-19 outbreak is currently one of the biggest challenges facing countries around the world. Millions of people have lost their lives due to COVID-19. Therefore, the accurate early detection and identification of severe COVID-19 cases can reduce the mortality rate and the likelihood of further complications. Machine Learning (ML) and Deep Learning (DL) models have been shown to be effective in the detection and diagnosis of several diseases, including COVID-19. This study used ML algorithms, such as Decision Tree (DT), Logistic Regression (LR), Random Forest (RF), Extreme Gradient Boosting (XGBoost), and K-Nearest Neighbor (KNN) and DL model (containing six layers with ReLU and output layer with sigmoid activation), to predict the mortality rate in COVID-19 cases. Models were trained using confirmed COVID-19 patients from 146 countries. Comparative analysis was performed among ML and DL models using a reduced feature set. The best results were achieved using the proposed DL model, with an accuracy of 0.97. Experimental results reveal the significance of the proposed model over the baseline study in the literature with the reduced feature set.

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