NATURAL FREQUENCIES, SENSITIVITY AND MODE SHAPE DETAILS OF AN EULER–BERNOULLI BEAM WITH ONE-STEP CHANGE IN CROSS-SECTION AND WITH ENDS ON CLASSICAL SUPPORTS

2002 ◽  
Vol 252 (4) ◽  
pp. 751-767 ◽  
Author(s):  
S. NAGULESWARAN
Keyword(s):  
Cross Section ◽  
Mode Shape ◽  
Natural Frequencies ◽  
Step Change ◽  
Bernoulli Beam ◽  
One Step ◽  
Euler Bernoulli Beam

scholarly journals Elliptical Crack Identification in a Nonrotating Shaft

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
B. Muñoz-Abella ◽  
L. Rubio ◽  
P. Rubio ◽  
L. Montero
Keyword(s):  
Cross Section ◽  
Direct Problem ◽  
Natural Frequencies ◽  
Fatigue Cracks ◽  
Circular Cross Section ◽  
Crack Identification ◽  
Bernoulli Beam ◽  
Bending Vibration ◽  
Euler Bernoulli Beam ◽  
Cracked Shaft

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses. This work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler–Bernoulli beam, with circular cross section under pinned-pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.

scholarly journals On the compression softening effect of prestressed beams

2006 ◽  
Vol 28 (3) ◽  
pp. 145-154 ◽  
Author(s):  
Nguyen Van Khang ◽  
Nguyen Phong Dien ◽  
Nguyen Thi Van Huong
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Axial Strain ◽  
Detailed Comparison ◽  
Bernoulli Beam ◽  
Softening Effect ◽  
Euler Bernoulli Beam ◽  
Prestressed Beam ◽  
Prestressed Beams

The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed, in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam. The forced transverse vibration of the beam with a moving external force has been considered. From this it follows compression softening effect of prestressed beams. A detailed comparison between the calculating results for the prestressed and the non-prestressed beam is also presented.

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

2006 ◽  
Vol 20 (4) ◽  
pp. 467-472 ◽  
Author(s):  
Youngjae Shin ◽  
Jonghak Yun ◽  
Kyeongyoun Seong ◽  
Jaeho Kim ◽  
Sunghwang Kang
Keyword(s):  
Natural Frequencies ◽  
Bernoulli Beam ◽  
Elastic Foundations ◽  
Euler Bernoulli Beam

scholarly journals A Structured Approach to Solve the Inverse Eigenvalue Problem for a Beam with Added Mass

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Farhad Mir Hosseini ◽  
Natalie Baddour
Keyword(s):  
Natural Frequencies ◽  
Point Of View ◽  
Inverse Eigenvalue Problem ◽  
Bernoulli Beam ◽  
Combined System ◽  
Vibrational System ◽  
Single Mass ◽  
Inverse Eigenvalue ◽  
Euler Bernoulli Beam ◽  
Structured Approach

The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem). A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem). In this paper, a method to impose two natural frequencies on a dynamical system consisting of an Euler-Bernoulli beam and carrying a single mass attachment is evaluated.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

Effects of Different Models on Natural Frequencies of Short Span Bridges Used in High Speed Rail

2015 ◽  
Author(s):  
Said I. Nour ◽  
Mohsen A. Issa
Keyword(s):  
Timoshenko Beam ◽  
High Speed ◽  
Natural Frequencies ◽  
Bernoulli Beam ◽  
High Speed Rail ◽  
Vertical Stiffness ◽  
Short Span ◽  
Elastically Supported ◽  
Euler Bernoulli Beam ◽  
Track Modulus

The natural frequencies of vibration of short span bridges used in high-speed rail were investigated. Three different models of increasing complexity were evaluated and their effects on the vibration frequency were compared to the first basic model of simply supported Euler-Bernoulli beam. In the second and third cases, the bridge was modeled as an Euler-Bernoulli and Timoshenko beam supported at its two ends by identical spring elements with an equivalent vertical stiffness to simulate elastomeric bearings and soil foundation. The boundary value problem was solved numerically to extract the bridge eigenfrequencies. In the case of Euler-Bernoulli beam, curve fitting techniques were used to deduce accurate simple empirical formulae to calculate the first six natural frequencies of an elastically supported bridge. In the case of a Timoshenko beam, graphical solutions were proposed to compute the fundamental frequency. Results confirmed that the use of Timoshenko beam theory reduces the natural frequency and the consideration of flexible supports further decreases the natural frequency. In the fourth model, the interaction of the track and the bridge was included. The bridge was modeled as an elastically supported beam and the track was modeled as a spring-damper element with an equivalent vertical stiffness resulting from track components like rail pads, cross-ties and ballast. A parametric study was performed to analyze the effects of the track stiffness on the natural frequencies of the bridge. Graphical solutions were presented to quantify the change of the normalized natural frequencies of the system with the increase in the track modulus. Results indicated that the changes in the track modulus have no significant effects in models with rigid supports. A decrease in the fundamental frequency was noticeable with softer track modulus as the support flexibility increased.

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