A finite-element model for the study of vibration of a beam with a closing crack

Bovsunovskii, O. A.

doi:10.1007/s11223-008-9072-5

Cited by 6 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, their analytical method is only applicable to beams with uniform cross-sections. The finite element method has been developed and applied to solve the natural frequency and vibration mode of curved beams with cracks (Palash and Talukdar, 2016;Karaagac et al, 2011;Bovsunovskii, 2008). Kisa et al (1998) integrated the finite element method and component mode synthesis to analyse the free vibration characteristics of cracked Timoshenko beams.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams

Wang

2023

View full text Add to dashboard Cite

PurposeThis study aimed to solve the engineering problem of free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams. The accurate identification of the crack damage depth, number and location depends on high-precision frequency and vibration mode solutions; therefore, it is critical to obtain these reliable solutions. The high-precision finite element method for the free vibration of cracked beams needs to be developed to grasp and control error information in the conventional solutions and the non-uniform mesh generation near the cracks. Moreover, the influence of multi-crack damage on the natural frequency and vibration mode of a circularly curved beam needs to be detected.Design/methodology/approachA scheme for cross-sectional damage defects in a circularly curved beam was established to simulate the depth, location and the number of multiple cracks by implementing cross-section reduction induced by microcrack damage. In addition, the h-version finite element mesh adaptive analysis method of the Timoshenko beam was developed. The superconvergent solution of the vibration mode of the cracked curved beam was obtained using the superconvergent patch recovery displacement method to determine the finite element solution. The superconvergent solution of the frequency was obtained by computing the Rayleigh quotient. The superconvergent solution of the eigenfunction was used to estimate the error of the finite element solution in the energy norm. The mesh was then subdivided to generate an improved mesh based on the error. Accordingly, the final optimised meshes and high-precision solution of natural frequency and mode shape satisfying the preset error tolerance can be obtained. Lastly, the disturbance behaviour of multi-crack damage on the vibration mode of a circularly curved beam was also studied.FindingsNumerical results of the free vibration and damage disturbance of cracked curved beams with cracks were obtained. The influences of crack damage depth, crack damage number and crack damage distribution on the natural frequency and mode of vibration of a circularly curved beam were quantitatively analysed. Numerical examples indicate that the vibration mode and frequency of the beam would be disturbed in the region close to the crack damage, and a greater crack depth translates to a larger frequency change. For multi-crack beams, the number and distribution of cracks also affect the vibration mode and natural frequency. The adaptive method can use a relatively dense mesh near the crack to adapt to the change in the vibration mode near the crack, thus verifying the efficacy, accuracy and reliability of the method.Originality/valueThe proposed combination of methodologies provides an extremely robust approach for free vibration of beams with cracks. The non-uniform mesh refinement in the adaptive method can adapt to changes in the vibration mode caused by crack damage. Moreover, the proposed method can adaptively divide a relatively fine mesh at the crack, which is applied to investigating free vibration under various curved beam angles and crack damage distribution conditions. The proposed method can be extended to crack damage detection of 2D plate and shell structures and three-dimensional structures with cracks.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The finite element method has been developed and applied to solve the natural frequency and vibration mode of curved beams with cracks (Palash and Talukdar, 2016; Karaagac et al. , 2011; Bovsunovskii, 2008). Kisa et al.…”

Section: Introductionmentioning

confidence: 99%

Free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams

Wang

2023

View full text Add to dashboard Cite

show abstract

“…The numerical results were obtained by using the experimentally verified finite-element model of a cracked rod proposed in [23]. The model consists of 21 elements (Fig.…”

mentioning

confidence: 99%

Diagnostics of closing cracks in rodlike elements at nonlinear resonances by the method of variation of the asymmetry of driving forces

Bovsunovskii

2010

Strength Mater

Self Cite

View full text Add to dashboard Cite

The vibrations of elastic bodies with closing cracks are essentially nonlinear. As a specific feature of these vibrations, we can mention the manifestation of so-called nonlinear effects, in particular, sub-and superharmonic resonances and the nonlinearity of vibrations at these resonances. We propose a method for the diagnostics of cracks based on the variation of the asymmetry of driving forces. The static component of the concentrated harmonic driving force changes the state of a crack: it becomes partially or completely open or closed. Moreover, the degree of nonlinearity of vibrations for any nonlinear resonance varies from the maximum level (in the absence of static component) to its almost complete absence in the case where the crack becomes open or closed in the course of vibrations under the action of the static component. The proposed method enables one to detect the presence of cracks without any preliminary data on the analyzed object in the intact state.Keywords: closing crack, sub-and superharmonic vibrations, diagnostics of cracks, nonlinear effects, asymmetry of the driving force.Introduction. The problem of detection of the cracks of subcritical sizes with an aim of prevention of the failures of machines and structures of different kinds is one of the most urgent problems of engineering diagnostics. The last decades were marked by the rapid development of the vibration methods of diagnostics of defects based, as a rule, on the analysis of the changes in the natural frequencies of vibrations and distortions of their shapes caused by the cracks [1, 2]. However, the sensitivity of these methods proved to be insufficient for practical application. Higher sensitivities to the presence of cracks are exhibited by the so-called nonlinear effects [3], i.e., sub-and superharmonic resonances, and the well-pronounced nonlinearity of vibrations at these resonances.In the case of vibration of a body containing a crack, the events of crack opening and closure are accompanied by the variations of stiffness of the entire structure simulated, for the sake of simplicity, by an asymmetric piecewise linear characteristic of the restoring force. The analytic investigations of forced vibrations of the mechanical systems with one degree of freedom and the indicated characteristic of the restoring force reveal the possibility of appearance of sub-[4-13] and superharmonic [7,8,10,12,14,15] resonance vibrations of various orders. Similar results were also obtained in the numerical investigations of the forced vibrations of rods with closing cracks [10,[16][17][18].The idea of modeling of the process of vibrations in cracked structural elements subjected to the action of static forces was realized by analyzing free [19,20] and forced [21] vibrations of rods. These investigations were carried out due to the necessity of more exact analysis of the conditions of loading of structural elements either operating in the fields of significant centrifugal forces (e.g., blades of gas-turbine engines) or carrying large static loads ...

show abstract

“…The numerical analyses of the influence of the place of application of the driving force on the nonlinearity of vibrations at the superharmonic resonance of order 2/1 and the subharmonic resonance of order 1/2 are carried out by using a finite-element model of a rod with closing crack [32]. The model consists of 21 elements (Fig.…”

mentioning

confidence: 99%

Application of nonlinear resonances for the diagnostics of closing cracks in rodlike elements

Bovsunovskii

2010

Strength Mater

Self Cite

View full text Add to dashboard Cite

The vibrations of elastic bodies with closing cracks are essentially nonlinear. As a specific feature of these vibrations, one can mention the manifestation of so-called nonlinear effects, e.g., nonlinear (i.e., sub-and superharmonic) resonances and the nonlinearity of vibrations for these resonances. The proposed method for the evaluation of the parameters of cracks (their sizes and location) is based on the analysis of the nonlinearity of vibrations in the neighborhood of a superharmonic resonance of order 2/1 and/or a subharmonic resonance of order 1/2 in the case of variation of the site of application of the driving force because, as follows from the results of numerical and experimental investigations, the level of nonlinearity of the vibrations of rods with closing cracks for nonlinear resonances depends not only on the parameters of the crack but also on the site of application of the driving forces.Keywords: closing crack, sub-and superharmonic vibrations, diagnostics of the crack, nonlinear effects. Introduction.Fatigue cracks form one of the most widespread types of defects in machines and structures operating under dynamic loads. As follows from the results of numerous experimental and theoretical investigations, cracks lead to a decrease in the natural frequencies of these objects and distort the form of vibrations. The relationship between the parameters of the crack (sizes and location), on the one hand, and the changes in the natural frequencies and forms of vibrations, on the other hand, is studied in numerous works [1,2]. However, the sensitivity of the methods of diagnostics of the cracks based on the changes in the natural frequencies and forms of vibrations appeared to be to be quite low. Later, it was shown that the so-called nonlinear effects [3], i.e., the sub-and superharmonic resonances, a strong nonlinearity of vibrations at these resonances, and the characteristics of damping of vibrations, are characterized by a higher sensitivity to the presence of cracks [4].In order to simplify the analysis of nonlinear effects, it is customary to assume that the stiffness of structures suffers instantaneous changes at the times of crack closure and opening. As a rule, this phenomenon is modeled by asymmetric piecewise-linear characteristics of the restoring forces. The analytic investigations of the forced vibrations of a mechanical system with one degree of freedom and the indicated characteristic of restoring forces make it possible to reveal sub-[5-14] and superharmonic [8,9,11,13,15,16] resonances of different orders. In addition, as shown in [3,7,8], the nonlinear effects strongly depend on the dissipative properties of the investigated system: the higher the level of damping of vibrations in the system, the lower the amplitudes of nonlinear resonances and the level of nonlinearity of vibrations at these resonances.The data of experimental investigations [4,[17][18][19] demonstrate that the growth of fatigue cracks is accompanied by a significant increase in the characteristics of damping o...

show abstract

A finite-element model for the study of vibration of a beam with a closing crack

Cited by 6 publications

References 5 publications

Free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams

Free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams

Diagnostics of closing cracks in rodlike elements at nonlinear resonances by the method of variation of the asymmetry of driving forces

Application of nonlinear resonances for the diagnostics of closing cracks in rodlike elements

Contact Info

Product

Resources

About