Accurate semi-analytical solution for nonlinear vibration of conservative mechanical problems

2017 ◽  
Vol 61 (5) ◽  
pp. 657-661
Author(s):  
Mahmoud Bayat ◽  
Iman Pakar
Keyword(s):  
Analytical Solution ◽  
Nonlinear Vibration

scholarly journals Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

2018 ◽  
Vol 2 (3) ◽  
pp. 21 ◽  
Author(s):  
Guy Eyebe ◽  
Gambo Betchewe ◽  
Alidou Mohamadou ◽  
Timoleon Kofane
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Nonlocal Elasticity ◽  
Multiple Scales ◽  
Approximate Analytical Solution ◽  
Nonlocal Elasticity Theory ◽  
Pasternak Foundation ◽  
D’Alembert Principle

In the present study, the nonlinear vibration of a nanobeam resting on the fractional order viscoelastic Winkler–Pasternak foundation is studied using nonlocal elasticity theory. The D’Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. A detailed parametric study is conducted, and the effects of the variation of different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have a significant effect on the natural frequency and the amplitude of vibrations.

scholarly journals Analytical Solution of the Nonlinear Vibration of the Steel Skeleton Supported Membrane Structure

2020 ◽  
Vol 964 ◽  
pp. 012003
Author(s):  
Mengfei Wang ◽  
Changjiang Liu ◽  
Haibing Xie ◽  
Su Jiang ◽  
Mengjia Zhang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Nonlinear Vibration ◽  
Membrane Structure ◽  
Supported Membrane

scholarly journals Nonlinear Vibration of Axially Loaded Railway Track Systems Using Analytical Approach

2021 ◽  
pp. 146134842110041
Author(s):  
Mahmoud Bayat ◽  
Iman Pakar ◽  
Paul Ziehl
Keyword(s):  
Analytical Solution ◽  
Nonlinear Vibration ◽  
Elastic Foundation ◽  
Nonlinear Partial Differential Equation ◽  
Accurate Solution ◽  
Railway Track ◽  
Mathematical Representation ◽  
Nonlinear Frequency ◽  
Highly Nonlinear ◽  
Axially Loaded

In this paper, the nonlinear vibration of railway track systems resting on elastic foundation has been studied. An axially loaded simply supported Euler–Bernoulli beam resting on a flexible foundation has been considered to provide a mathematical representation of the railway track system. Winkler springs have been used to model the elastic foundation. Nonlinear partial differential equation of the system has been presented and solved. A new approximate analytical solution called Improved Amplitude–Frequency Formulation (IAFF) is proposed to obtain nonlinear frequency of the system and an accurate analytical solution for the whole domain. The first iteration of the IAFF leads to a highly accurate solution in comparison with the exact frequency of the problem. The exact frequency of the problem is also presented, and the results of IAFF are compared and verified. Sensitive analysis of the soil stiffness and loading condition is studied for different parameters. A full comparison of the IAFF and exact solution results are illustrated. It has been proved that the IAFF can be potentially extended to highly nonlinear conservative problems.

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