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Nonlinear oscillation analysis of a pendulum wrapping on a cylinder
, Article Scientia Iranica ; Volume 19, Issue 2 , 2012 , Pages 335-340 ; 10263098 (ISSN) ; Hosseinzadeh, A ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased....
Analytical approach to vibration analysis of a pendulum wrapping on a cylinder
, Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011, 11 November 2011 through 17 November 2011 ; Volume 7, Issue PARTS A AND B , November , 2011 , Pages 761-765 ; 9780791854938 (ISBN) ; Hosseinzadeh, A ; Ahmadian, M. T ; Barari, A ; Sharif University of Technology
Abstract
In this paper, nonlinear oscillation of a pendulum wrapping and unwrapping around two cylindrical bases is studied and an analytical solution is obtained using multiple scales method. Equations of motion are derived based on energy conservation technique. Applying perturbation method on the equations, nonlinear natural frequency of the system is calculated along with its time response. Analytical results are compared with numerical findings and good agreement is found. Effect of nonlinearity due to large amplitude and radius of cylinders on the system frequency is evaluated. Results indicate that as the radius of cylinder is increased, nonlinear frequency is enhanced. Initial amplitude plays...