Free vibration of the double tapered cracked beam
13 Jan 2021-Inverse Problems in Science and Engineering (Taylor & Francis)-Vol. 29, Iss: 11, pp 1537-1564
TL;DR: In this paper, the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods, is presented.
Abstract: This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine...
Citations
More filters
TL;DR: In this article , the effect of slenderness ratio on the nonlinear vibration attributes of the rotating tapered cantilever beam in the flap-wise direction is studied and the equations of motion are derived using energy method and subsequently nonlinear governing equations are solved using the framework of minimum potential energy with the help of trail functions.
TL;DR: In this paper , the nonlinearity due to in plane stretching as a result of large deformations is taken in to consideration and nonlinear governing equations for cracked rotating tapered FGM beams are generated by optimizing the energy functional.
Abstract: Vibration-based condition monitoring for remotely located rotating blades is one of the important aspects to avoid sudden breakdown of the machinery. Vibration analysis of damaged blades provides the information to identify the damage during operation. In this work, dynamic attributes of rotating cracked tapered cantilever functionally graded material (FGM) beams for various tapered configurations are investigated using energy method. The nonlinearity due to in plane stretching as a result of large deformations is taken in to consideration. Nonlinear governing equations for cracked rotating tapered FGM beams are generated by optimizing the energy functional. An iterative algorithm is developed to solve the derived nonlinear equations. The effects corresponding to location of crack and centrifugal stiffening on the various modes has been presented for different tapered configurations, material indices, crack depths and rotational speeds. Crack compensating speeds are studied and reported for different tapered ratios and crack parameters for the first time. The effect of crack location and crack depth on the first two nonlinear frequency ratios is also investigated for different tapered configurations and material indices. The influence of centrifugal stiffening on nonlinear responses of FGM beams is presented for various crack parameters and tapered configurations.
TL;DR: In this article , a theoretical analysis of a mechanical system composed of free vibration of an Euler-Bernoulli beam with an open crack is presented, where the first three natural frequencies of a cracked beam are used to obtain the unknown crack location and depth without solving the inverse vibration problem.
Abstract: This paper presents analysis of a mechanical system composed of free vibration of an Euler-Bernoulli beam with an open crack. Two new proposals have been presented to analyse such systems: a direct crack identification method to obtain the crack properties and a theoretical margin of detection parameter to quantify the capability of the theoretical model used to detect a single crack. The direct crack identification method uses first three natural frequencies of a cracked beam to obtain the unknown crack location and depth without solving the inverse vibration problem. On the other hand, the theoretical margin of detection parameter provides capability to the analytical model to detect the location and depth of an open crack using the first three natural frequencies as a function of crack location and depth for different end conditions. To show the robustness of the direct crack identification method, errors on the first three exact values of the natural frequency parameters of the cracked beam are induced before applying the proposed method and the resulting errors were calculated. Contour plots have been developed for classical and elastically restrained end conditions to predict the detectable zones as a function of crack location and depth. The proposed analysis has been carried out on the widely used closed-form solution of the beam model.
References
More filters
TL;DR: In this paper, a crack in a structural member introduces a local flexibility that affects its vibration response, and the crack will open and close in time depending on the rotation and vibration amplitude.
1,080 citations
Book•
01 Jan 1983
422 citations
"Free vibration of the double tapere..." refers methods in this paper
...[6] proposed a method to obtain local flexibility with the stress intensity factor to demonstrate the effect of crack on the frequency of beams based on the theory of fracture mechanics....
[...]
TL;DR: In this paper, a simple but comprehensive survey of the stability behavior of a rotating shaft with a crack, and of the forced vibrations due to imbalance and to the crack, is provided, restricted to that of the Laval rotor.
414 citations
TL;DR: In this paper, a review of the field of the dynamics of cracked rotors is presented, including the modeling of the cracked part of the structure and finding different detection procedures to diagnose fracture damage.
Abstract: Propagating fatigue cracks can have detrimental effects on the reliability of rotating machinery. An early crack warning can considerably extend the durability of these very expensive machines, increasing their reliability at the same time. Vibration monitoring as a means of detecting crack initiation has been receiving much interest. A detailed study of the vibrational behavior of cracked rotating shafts, therefore, is an important problem for engineers working in the area of the dynamics of machines. This article presents a review of the field of the dynamics of cracked rotors, including the modeling of the cracked part of the structure and finding different detection procedures to diagnose fracture damage. The material should be helpful to scientists and researchers working in this area or planning to work in it in the future. Since the study of nonrotating, cracked structural elements obviously is relevant to the cracked rotor problem, the review can also be a basis for discussing the dynamics of cracked beams and columns.
387 citations
TL;DR: In this article, a new technique is proposed for calculating natural frequencies of a vibrating beam with an arbitrary finite number of transverse open cracks, and the main feature of this method is related to decreasing the dimension of the matrix involved in the calculation.
247 citations