scholarly journals Free vibration of the double tapered cracked beam

2021 ◽  
pp. 1-28
Author(s):  
Mehmet Haskul ◽  
Murat Kisa
Keyword(s):  
Free Vibration ◽  
Cracked Beam

scholarly journals Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

2018 ◽  
Author(s):  
Do Nam ◽  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Thao ◽  
Pham Thi Ba Lien
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Continuous Beam ◽  
Cracked Beam ◽  
Continuous Beams ◽  
Simplified Method ◽  
Rigid Supports ◽  
Natural Frequency Analysis ◽  
Eigenfrequency Spectrum

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

The Study of the Vibration Characteristics of the Cantilever Beam with a Surface Crack

2013 ◽  
Vol 394 ◽  
pp. 121-127
Author(s):  
Li Hua Chen ◽  
Jian Wei Duan ◽  
Yue Sun ◽  
Jing Li
Keyword(s):  
Theoretical Analysis ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Cantilever Beam ◽  
Surface Crack ◽  
Natural Frequencies ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Internal Boundary ◽  
Cracked Beam

In this paper, the physical model of the cantilever beam with a surface crack is established to study the free vibration of the cracked beam from three aspects that are theoretical analysis, FEM analysis, and experiment. At the same time, the relation between the crack parameter and the vibration characteristics, which are natural frequencies and the modes of each order, is obtained through analysis. The theoretical analysis is on the basis of the mode analysis theory and applied mechanics. The crack is regarded as a flexible hinge. Utilizing the external boundary conditions and internal boundary conditions at the crack, the free vibration characteristics are obtained combining with the vibration mechanics. With the ANSYS software, a finite element model of the cracked beam is established by the beam element. During the process of calculation, it calculates the natural frequencies and the modes of cracked beam with different parameters of crack. The results obtained from the experiment are in agreement with the results obtained from the theoretical and the FEM analysis. So the accuracy of the theoretical analysis and the numerical simulation is verified by the experiment. At last, the effects of the crack location and depth on the natural frequencies and modes of each order are shown, and it could provide the theoretical, numerical and experimental basis for the identification of cracked materials and the relevant study.

scholarly journals Free Vibration of Axially Loaded Multi-Cracked Beams Using the Transfer Matrix Method

2019 ◽  
Vol 24 (No 1) ◽  
pp. 119-138
Author(s):  
Yousef S. Al Rjoub ◽  
Azhar G. Hamad
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Beam Theory ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Cracked Beam ◽  
Axially Loaded

In this paper, an analytical method is developed to study the free vibration of multi-cracked, axially loaded beams with differing boundary conditions, namely, hinged-hinged, clamped-clamped, clamped-hinged, and clamped-free. The cracked beam system is modelled as a number of beam segments connected by massless rotational springs with sectional flexibility. Each segment is assumed to obey the Euler-Bernoulli beam theory. The characteristic equation of the cracked beam with differing boundary conditions, which is a function of the natural frequency, sizes and location of the cracks, and the physical parameters of the beam, as well as the corresponding mode shapes, is derived using a simple transfer matrix method. In this paper, a detailed parametric study is conducted to show the effects of cracks and axial load on vibrational properties of the cracked beam. The results obtained in this study agree well with analytical results available in the literature.

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