scholarly journals Detection of multiple cracks in a beam by means natural frequencies of transverse vibrations

2020 ◽  
pp. 19-26
Author(s):  
Иван Михайлович Лебедев ◽  
Ефим Ильич Шифрин
Keyword(s):  
Arbitrary Number ◽  
Natural Frequencies ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Numerical Examples ◽  
Transverse Vibrations ◽  
End Conditions

Рассматривается задача обнаружения множественных, поперечных трещин в стержне с помощью собственных частот поперечных колебаний. В недавней статье авторов доказано, что любое количество трещин однозначно восстанавливается по трем спектрам, отвечающим трем различным типам краевых условий. В статье также предложен алгоритм идентификации повреждений, вносимых трещинами. Помимо этого, высказано предположение, что для однозначной идентификации трещиноподобных дефектов на самом деле достаточно знать два спектра. Для проверки этого предположения разработана модификация предложенного ранее численного алгоритма. Рассмотрены численные примеры. Полученные результаты дают основание полагать, что высказанное предположение справедливо. A problem of detection of multiple transverse cracks in a beam by means of natural frequencies of transverse vibrations is considered. It is proved in the recent paper of the authors that an arbitrary number of cracks can be uniquely determined by three spectra corresponding to three types of the end conditions. An algorithm of reconstruction the damages corresponding the cracks is also developed. In addition, it was assumed that the cracks can be detected using only two spectra. To verify this supposition a modification of the previously developed algorithm is proposed. Numerical examples are considered. The obtained results confirm the assumption.

Vibration Analysis of a Beam with Multiple Cracks

2012 ◽  
Vol 178-181 ◽  
pp. 2505-2508 ◽  
Author(s):  
Chang Li Xiao ◽  
Ling Ling Xu
Keyword(s):  
Stiffness Matrix ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Cracked Beam ◽  
Strain Energy Density Function ◽  
Natural Frequency Analysis ◽  
Good Agreement

A new method for the natural frequency analysis of a beam with multiple transverse cracks has been carried out. The method is called reverse modal analysis in this paper. The strain energy density function is used to evaluate the additional flexibility produced due to the presence of crack. Based on the flexibility, a new stiffness matrix is deduced and subsequently that is used to calculate the natural frequencies and mode shapes of the cracked beam. It has been established that the crack depths and their positions have an important effect on its dynamic behavior. The analysis of the crack structure is done using finite element and experimental analysis. The results from numerical analysis are compared with the results from the experimental method for validation. The results are found to be in good agreement.

Transverse Vibration of a Class of Non-Uniform Beams

1968 ◽  
Vol 10 (2) ◽  
pp. 111-120 ◽  
Author(s):  
D. J. Sanger
Keyword(s):  
Transverse Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Transverse Vibrations ◽  
Special Cases ◽  
End Conditions

The free and forced transverse vibrations of a class of non-uniform beams, which includes as special cases the wedge and cone, are considered. Receptances, frequency equations, mode shapes and natural frequencies are presented for simple end conditions.

Free Vibration and Instability Analysis of Sandwich Plates with Carbon Nanotubes-Reinforced Composite Faces and Honeycomb Core

2021 ◽  
Author(s):  
Sushila Chowdhary ◽  
Mesfin Kebede Kassa ◽  
Yitbarek Gashaw Tadesse ◽  
Ananda Babu Arumugam ◽  
Rajeshkumar Selvaraj
Keyword(s):  
Finite Element ◽  
Glass Fiber ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Element Formulation ◽  
The Core ◽  
Glass Fiber Reinforced ◽  
End Conditions ◽  
Honeycomb Sandwich ◽  
Instability Regions

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight

1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
Simplified Model ◽  
Main Rotor ◽  
Numerical Examples ◽  
The Masses

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.

scholarly journals Receptance-based frequency assignment for assembled structures

2020 ◽  
pp. 107754632094545
Author(s):  
Shike Zhang ◽  
Huajiang Ouyang
Keyword(s):  
Structural Properties ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Frequency Assignment ◽  
Structural Components ◽  
Engineering Structures ◽  
Numerical Examples ◽  
Structural Modifications ◽  
Assignment Method

For engineering structures, there is a strong need to assign natural frequencies to achieve desired dynamic performance. This study proposes a receptance-based frequency assignment method for assembled structures. Very often, the substructures involved are not allowed or are difficult to change. This method uses the links between the substructures as targets of structural modifications and determines the structural properties of the links that assign the desired frequencies cast as an optimisation problem. These links could be either simple discrete structural components such as masses and springs or complex continuous structures. Only a few receptances of the substructures are required in this method, which can be measured accurately and easily in practice. Two numerical examples are presented to show the validity of this method and its strength in dealing with complex assembled structures.

scholarly journals Multiple crack identification in stepped beam by measurements of natural frequencies

2014 ◽  
Vol 36 (2) ◽  
pp. 119-132
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung ◽  
Vu Thi An Ninh
Keyword(s):  
Crack Detection ◽  
Natural Frequencies ◽  
Rayleigh Quotient ◽  
Crack Identification ◽  
Multiple Cracks ◽  
Simple Relationship ◽  
Multiple Crack ◽  
Scanning Method ◽  
New Approach ◽  
Efficient Procedure

A new approach is proposed for calculating natural frequencies and crack detection in a stepped cantilever beam with arbitrary number of cracks. This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. The proposed technique called crack scanning method is illustrated and validated by numerical results.

scholarly journals Higher-order accurate compact difference solutions for vibration problems of one dimensional continuous systems

2011 ◽  
pp. 771-794
Author(s):  
Mondher Yahiaoui
Keyword(s):  
Natural Frequencies ◽  
Continuous Systems ◽  
One Dimensional ◽  
First Order ◽  
Compact Difference ◽  
Transverse Vibrations ◽  
Seventh Order ◽  
One Step ◽  
Vibration Problems ◽  
Difference Methods

In this paper, we present a fourth-order accurate and a seventh-order accurate, one-step compact difference methods. These methods can be used to solve initial or boundaryvalue problems which can be modeled by a first-order linear system of differential equations. It is then shown in detail how these methods can be used to solve vibration problems of onedimensional continuous systems. Natural frequencies of a cantilever beam in transverse vibrations are computed and the results are compared to analytical ones to prove the high accuracy and efficiency of both methods. A comparison was also made to a finite element solution and the results have shown that both compact-difference methods yield more accurate values even with a reduced number of intervals.

Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Distribution Patterns ◽  
Continuous Systems ◽  
Cantilever Beams ◽  
Transverse Vibrations ◽  
Discretization Technique

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

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