The Influence of the Weight Loss upon Natural Frequency Changes in Case of Severe Defects (original) (raw)
Related papers
Natural Frequencies of Damaged Beams - A New Approach
This paper introduces a relation which describes the influence of discontinuities on the dynamic response of prismatic cantilever beams. The relation, providing the natural frequencies of weakaxis bending vibration modes of damaged beams, was contrived by considering the continuous model in a global approach, opposite to researches presented in literature involving mainly models based on two segments linked by a rotational spring and focusing on the local effect of the discontinuity. To demonstrate the validity of the proposed relation, a cantilever beam was analyzed both in undamaged and damaged case, being highlighted the natural frequency changes due discontinuity for various damage scenarios; finally curves representing frequency changes were plotted. Comparing the results obtained by the two approaches, a similarity for the frequency changes of the first bending vibration modes is obvious, while for higher modes the “classical” approach is not able to provide any result due to ...
The relationship between changes of deflection and natural frequencies of damaged beams
The paper describes the relationship between changes of deflection of beams due damages and the natural frequency changes. Previous papers relate the influence of damage location and severity upon the natural frequency changes of weak-axis bending vibration modes, for which the authors have found a correlation. It base on the reduction of stiffness in a slice of the beam and consequently on the reduction of the potential stored energy in that slice. While the stiffness reduction affect also the deflection under the own mass of the beam, we concluded that it can be found a relationship between deflection and frequency changes. Researches performed this direction revealed that it is a clear dependency between deflection and frequency changes, what makes deflection an important feature of beam behavior, usable in damage assessment.
Natural Frequencies Distribution on the Damaged Beams
Analele Universitatii "Eftimie Murgu" Resita - Fascicula de Inginerie, 2011
This paper presents the natural frequencies distribution on the damaged beams. The frequencies distributions was analyzed for three types of beams: cantilever, double clamped and simple supported. The analysis was performed using the finite element method (FEM), for the undamaged beam and for the beam having damages at around 190 locations, considered one by one, and nine levels of depth. The authors deduced analytical relationships for damaged beam frequency shift and presents the results.
Natural frequency changes due to damage in composite beams
Transversal cracks in structures affect their stiffness as well as the natural frequency values. This paper presents a research performed to find the way how frequencies of sandwich beams change by the occurrence of damage. The influence of the locally stored energy, for ten transverse vibration modes, on the frequency shifts is derived from a study regarding the effect of stiffness decrease, realized by means of the finite element analysis. The relation between the local value of the bending moment and the frequency drop is exemplified by a concrete case. It is demonstrated that a reference curve representing the damage severity exists whence any frequency shift is derivable in respect to damage depth and location. This curve is obtained, for isotropic and multi-layer beams as well, from the stored energy (i.e. stiffness decrease), and is similar to that attained using the stress intensity factor in fracture mechanics. Also, it is proved that, for a given crack, irrespective to its depth, the frequency drop ratio of any two transverse modes is similar. This permitted separating the effect of damage location from that of its severity and to define a Damage Location Indicator as a sequence of squared of the normalized mode shape curvatures.
Vibration-based damage detection from frequency changes requires the calculation of natural frequencies from assumed damage scenarios and conduct a comparison to the actual frequency of the structure. Analytical solutions in obtaining the natural frequency of homogeneous beams are currently limited to beams with uniform cross-sectional area. Changes in cross-sectional area might occur due to damage within the length of the beam. Finite element modeling and analysis is required in these instances, but may not be efficient in terms of time and computational effort. For the assumed damaged scenarios, there are unlimited number of possible damage combinations for which the natural frequency will be obtained. There is a need for an analytical alternative as a substitute to the finite element method to calculate these frequencies. This study presents an analytical method to estimate the natural frequencies of locally damaged homogeneous beams based on statistical data obtained from finite element modeling and analysis. The method proposes a multiplier function in terms of the extent of area reduction, length, and location of damage in order to estimate the damaged frequency. The function was derived using curve-fitting techniques of data obtained from finite element modeling and analysis of typical beams with assumed damage cases. Examples show that the method is a strong alternative to finite element analysis in estimating the natural frequencies of locally damaged homogeneous beams. The method can be used for vibration-based structural health monitoring to predict the damage state of beams given the change in frequency without the computational burden of finite element modeling and analysis.
Exact solution for the natural frequencies of slender beams with an abrupt stiffness decrease
Journal of Engineering Sciences and Innovation, 2017
In this paper, we introduce a mathematical relation which allows prediction of frequency changes of beams if a damage producing an abrupt stiffness decrease occurs in the structure. This relation is contrived from the energies stored in the beam in the intact, respectively in the damaged state. First, the analysis was performed for the damage reducing the stiffness of the slice subjected to the biggest bending moment. From this analysis, we found the damage severity evolution, reflected in a frequency drop, with the damage depth. Afterward, we replaced this damage on several locations along the beam and quantified the effect upon the natural frequencies for each of them. Based on this analysis, we found out also the effect of damage position upon the natural frequencies. The final relation resulted by aggregating the effect of the severity with that of the position. To prove the reliability of this relation, we tested it against results obtained by means of the finite element method.
Effect of severe corrosion upon natural frequencies of beam-like structures
Challenge Journal of Structural Mechanics
Corrosion, as the spontaneous process of material degradation produced by the environment, affects the reliability and safety of structures, both by reducing the section of the components, due to material loss and by diminution of the materials mechanical strength. The authors have found a mathematical relation between discontinuities in beams and changes of its natural frequencies and developed a method to identify these discontinuities. The present paper considers the more complex case of damage determined by corrosion, where beam thinning is accompanied by mass decrease. These impose considering natural frequency changes in both directions: decrease due damage and increase because of mass loss. FEM simulations and analytical investigations were carried out, in order to find the relation between mass change in different positions along the beam and the frequency increase. The results were correlated with the "classical" relation describing frequency decrease because of discontinuities. Finally, the authors developed a new relation, proper to be used for damage produced by severe corrosion, which was validated by laboratory experiments.
IJERT-Mass Loading Effect on Natural Frequency of Cracked Beam in Free-Free Condition
International Journal of Engineering Research and Technology (IJERT), 2014
https://www.ijert.org/mass-loading-effect-on-natural-frequency-of-cracked-beam-in-free-free-condition https://www.ijert.org/research/mass-loading-effect-on-natural-frequency-of-cracked-beam-in-free-free-condition-IJERTV3IS090113.pdf In this article the mass loading effect due to accelerometer on the natural frequency of cracked beam in free-free configuration has been investigated. Free-free configuration is selected as it is easier to replicate these boundary conditions in both experiment and analytical model. Also it is customary to validate the geometric model by comparing results with experiment in free-free condition. Natural frequencies obtained using accelerometer and FFT analyze are lower than obtained analytically or numerically using software based modal analysis. The difference could be attributed to the change in the boundary conditions, variation in geometric model simulating the real system, change in material properties and effect of accelerometer mass with its location on the beam. Therefore, can natural frequency alone be a detection parameter is an elusive question as on date. Nevertheless research is going on for qualitative assessment of health monitoring of the structure with natural frequency as the detection parameter due to its ease in measuring. Present work develops an analytical formulation to compute modal properties of a mass loaded beam, cracked beam and finally mass loaded cracked beam. The beam is considered as Euler-Bernoulli beam with additional mass effect is modeled by considering jump in shear force at the location. Crack is modeled as a mass less rotational spring and its flexibility parameter is obtained invoking concepts of fracture mechanics. Effects of additional mass location, crack depth and crack location on the modal properties are investigated. Keywords-Mass loading, modal analysis, FEM, free-free, cracked beam I INTRODUCTION In an attempt to extend the possibility of using modal parameters like natural frequency for detection of crack in the turbine blade, the process is validated firstly for simple beam. The intent eventually is to perform various analyses on the turbine blade model using ANSYS software so as to study mistuning effect due to cracking of blade. As sensitivity of the natural frequency to the loss of stiffness needs to be ascertained and measured accurately for it to be become indicator for presence of crack and subsequently for location and severity of the crack. All the parameters which might affect the natural frequency need to be considered. One such parameter for small and slender structure is a mass of an accelerometer itself that lowers the measured natural frequencies. Therefore, in this research paper two modeling techniques analytical and numerical using ANSYS s/w are discussed so as to consider loading effect of an accelerometer mass on the natural frequencies of the beam. It is found that the mass of an accelerometer affected the natural frequencies according to its location and the ratio of its mass to the mass of beam. The effect was studied by performing experiment using two beams of different mass whereas material is same and accelerometer of same mass. For validation of the geometric model before its use for further analyses, results of software based modal analysis have to agree closely with the experimental modal analysis of the physical or real system. It is therefore must to simulate the effect of additional mass of accelerometer in analytical and numerical i.e. software based modal analysis. Many researchers have used the vibration response to detect cracks in a structure. Dado et.al [1] have tried to figure out not only the presence of crack by studying change in modal parameters but also the crack characterization like its depth and location. These detection schemes are based on the fact that the presence of a crack in a structure reduces the stiffness of the structure, hence reducing the natural frequencies. Gounaris and Dimarogonas [2] have developed the Euler-Bernoulli beam cracked element based on the fracture mechanics approach. They have used coefficients of the compliance matrix that are computed based on available expressions of the stress intensity factor (SIF) and associated expressions of the strain energy density function (SEDF) by using the linear elastic fracture mechanics (LEFM) approach. Ostachowicz and Krawczuk [3] have considered effect of two open cracks upon natural frequencies of flexural vibration of cantilever beam. They have observed that when two cracks are near to each other then drop in natural frequency is more and if two cracks distances from each other then frequency tend to be similar to single crack beam. On the similar line of various researchers the loss of stiffness in the vicinity of the crack is estimated by calculating the additional flexibility coefficients from the relation between strain energy release rate, stress intensity factors using Castigliano"s theorem and Paris Law. Then the stiffness matrix is obtained by taking inverse of the flexibility coefficient matrix as reported by Kotambkar [4]. In many situations, the mass of accelerometer is ignored in the analytical and numerical modeling process based on a usual assumption that the accelerometer mass is negligible compared to that of the structure under test. However, when lighter structures are investigated this effect can be significant and it may be necessary to eliminate this undesirable side effect before the measured data are used for future analyses. Cakar and Sanliturk [5] discussed the new method based on Sherman Morrison identity for elimination of mass loading effect of accelerometer from the measured FRF.
The Effect of Corrosion on the Natural Frequencies of Beams
ITM Web of Conferences, 2019
Corrosion is a natural process of degradation of the mechanical properties of some materials like: metals, ceramics or polymers. The metals and their alloys corrode only because of their presence in a damp environment, but the process is more powerful in some corrosive environments. Corrosion is a diffusion process by which some chemical bonds of the base material are broken, and therefore the oxides, bases, or salts are formed, resulting in a process of mass loss but also of weak interatomic bonding forces, that means a loss of stiffness. Mass distribution and stiffness in a mechanical structure determine the natural frequencies and shape of natural modes, that is, so-called modal parameters that characterize its dynamic behavior. The purpose of this paper is to determine the influence of simultaneous loss mass and loss stiffness on natural frequencies. Applying the Finite Element Method and the Modal Analysis Module of the ANSYS software, the natural frequencies are obtained in nu...