FREE VIBRATION ANALYSIS FOR EULER-BERNOULLI BEAM ON PASTERNAK FOUNDATION

2017 ◽  
Author(s):  
Lucas Soares ◽  
simone dos santos hoefel ◽  
Wallison Bezerra
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Pasternak Foundation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam

2013 ◽  
Vol 48 (5) ◽  
pp. 697-709 ◽  
Author(s):  
Zhifeng Liu ◽  
Yunyao Yin ◽  
Feng Wang ◽  
Yongsheng Zhao ◽  
Ligang Cai
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Differential Transform ◽  
Euler Bernoulli Beam

Free vibration analysis of Euler-Bernoulli beam with double cracks

2007 ◽  
Vol 21 (3) ◽  
pp. 476-485 ◽  
Author(s):  
Han-Ik Yoon ◽  
In-Soo Son ◽  
Sung-Jin Ahn
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

Free Vibration Analysis of Rotating Euler–Bernoulli Beam with Exponentially Varying Cross-Section by Differential Transform Method

2018 ◽  
Vol 18 (02) ◽  
pp. 1850024 ◽  
Author(s):  
Mostafa Nourifar ◽  
Ali Keyhani ◽  
Ahmad Aftabi Sani
Keyword(s):  
Free Vibration ◽  
Recurrence Relation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Differential Transform ◽  
Euler Bernoulli Beam

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.

scholarly journals Free vibration analysis on axially graded beam resting on variable Pasternak foundation

2021 ◽  
Vol 1206 (1) ◽  
pp. 012016
Author(s):  
Saurabh Kumar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Material Gradation ◽  
Euler Bernoulli Beam

Abstract Free vibration analysis is conducted on axially functionally graded Euler-Bernoulli beam resting on variable Pasternak foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying linearly along the axial direction. Two types of boundary conditions namely; clamped and simply supported are used in the analysis. The problem is formulated using Rayleigh-Ritz method and governing equations are derived with the help of Hamilton’s principle. The numerical results are generated for different material gradation parameter, foundation parameter and boundary conditions and the effect of these parameters on the free vibration behaviour of the beam is discussed.

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