Free vibration analysis of a type of tapered beams by using Adomian decomposition method

2012 ◽  
Vol 219 (6) ◽  
pp. 3264-3271 ◽  
Author(s):  
Qibo Mao ◽  
Stanislaw Pietrzko
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Free Vibration Analysis ◽  
Adomian Decomposition

Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method

2017 ◽  
Vol 23 (9) ◽  
pp. 1345-1363 ◽  
Author(s):  
Desmond Adair ◽  
Martin Jaeger
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Free Vibration Analysis ◽  
Published Data ◽  
Bernoulli Beam ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam

The governing equations for a pre-twisted rotating cantilever beam are derived and used for free vibration analysis of a pre-twisted rotating beam whose flexural displacements are coupled in two planes. First differential equations of motion of a rotating twisted beam, including terms due to centrifugal stiffening, are derived for an Euler–Bernoulli beam undergoing free natural vibrations. The general solutions of these equations are obtained on applying the Adomian modified decomposition method (AMDM). The AMDM allows the governing differential equations to become recursive algebraic equations and the boundary conditions to become simple algebraic frequency equations suitable for symbolic computation. With additional simple mathematical operations on the model, the natural frequencies and corresponding closed-form series solution of the mode shape can be obtained simultaneously. Two main advantages of the application of the AMDM are, for the cases considered here, its fast convergence rate to the solution with the high degree of accuracy. As the AMDM technique is systematic, it is found straight-forward to modify boundary conditions from one case to the next. Comparison of results with published data showed the present calculations to be in reasonable agreement.

Solving Free Vibration of Stepped Beam by Using the Adomian Decomposition Method

2010 ◽  
Author(s):  
Anooshiravan Farshidianfar ◽  
Rassoul Tabassian ◽  
Omid Kazemzadeh Khoee ◽  
Sayed Javadorreza Noei
Keyword(s):  
Free Vibration ◽  
Cross Sections ◽  
Decomposition Method ◽  
Natural Frequencies ◽  
Adomian Decomposition Method ◽  
High Accuracy ◽  
Mode Frequency ◽  
New Approach ◽  
Stepped Beam ◽  
Adomian Decomposition

This paper studies the free vibration of Euler-Bernoulli stepped beam with different cross-sections and also different materials for each section. In this work, a new approach called Adomian decomposition method (ADM) is used to deal with vibration problem. Natural frequencies of stepped beam are obtained with high accuracy using this method. Numerical results are validated by ANSYS.10 and proper convergence is observed between results. Effects of various parameters like step ratio on natural frequency are discussed. Applying this method on free vibration of stepped beam constructs a systematic procedure which is completely straightforward and could calculate both low and high mode frequency with appropriate accuracy.

Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method

2018 ◽  
Vol 18 (07) ◽  
pp. 1850101 ◽  
Author(s):  
Alireza Keshmiri ◽  
Nan Wu ◽  
Quan Wang
Keyword(s):  
Free Vibration ◽  
Mode Shape ◽  
Decomposition Method ◽  
Natural Frequencies ◽  
Adomian Decomposition Method ◽  
Present Approach ◽  
Cone Beam ◽  
Mode Shapes ◽  
Shape Functions ◽  
Adomian Decomposition

In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.

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