This paper compares the accuracy of the power series approach with that of the modified Lindstedt-Poincare method for strongly nonlinear vibration.The free vibration of an undamped Duffing oscillator is considered bec...This paper compares the accuracy of the power series approach with that of the modified Lindstedt-Poincare method for strongly nonlinear vibration.The free vibration of an undamped Duffing oscillator is considered because it has an exact solution.In the power series approach,the time variable is transformed into an“oscillating time”which reduces the governing equation to a form well-conditioned by the power series method.The results show that the power series approach provides extremely accurate vibration frequencies,even at large values of the nonlinear parameter,compared with errors of up to nine percent for the modified Lindstedt-Poincare method.展开更多
This paper provides a power series solution to the Duffing-harmonic oscillator and compares the frequencies with those obtained by the harmonic balance method.To capture the periodic motion of the oscillator,the power...This paper provides a power series solution to the Duffing-harmonic oscillator and compares the frequencies with those obtained by the harmonic balance method.To capture the periodic motion of the oscillator,the power series expansion is used upon transforming the time variable into an“oscillating time”which reduces the governing equation to a form well-conditioned for a power series solution.A recurrence equation for the series coefficients is established in terms of the“oscillating time”frequency which is then determined by employing Rayleigh’s energy principle.The response of the oscillator is compared with a numerical solution and good agreement is demonstrated.展开更多
An analytical approach based on the power series method is used to analyze the free vibration of a cantilever beam with geometric and inertia nonlinearities.The time variable is transformed into a“harmonically oscill...An analytical approach based on the power series method is used to analyze the free vibration of a cantilever beam with geometric and inertia nonlinearities.The time variable is transformed into a“harmonically oscillating time”variable which transforms the governing equation into a form well-conditioned for a power series analysis.Rayleigh’s energy principle is also used to determine the vibration frequency.Convergence of the power series solution is demonstrated and excellent agreement is seen for the vibration response with a numerical solution.展开更多
文摘This paper compares the accuracy of the power series approach with that of the modified Lindstedt-Poincare method for strongly nonlinear vibration.The free vibration of an undamped Duffing oscillator is considered because it has an exact solution.In the power series approach,the time variable is transformed into an“oscillating time”which reduces the governing equation to a form well-conditioned by the power series method.The results show that the power series approach provides extremely accurate vibration frequencies,even at large values of the nonlinear parameter,compared with errors of up to nine percent for the modified Lindstedt-Poincare method.
文摘This paper provides a power series solution to the Duffing-harmonic oscillator and compares the frequencies with those obtained by the harmonic balance method.To capture the periodic motion of the oscillator,the power series expansion is used upon transforming the time variable into an“oscillating time”which reduces the governing equation to a form well-conditioned for a power series solution.A recurrence equation for the series coefficients is established in terms of the“oscillating time”frequency which is then determined by employing Rayleigh’s energy principle.The response of the oscillator is compared with a numerical solution and good agreement is demonstrated.
文摘An analytical approach based on the power series method is used to analyze the free vibration of a cantilever beam with geometric and inertia nonlinearities.The time variable is transformed into a“harmonically oscillating time”variable which transforms the governing equation into a form well-conditioned for a power series analysis.Rayleigh’s energy principle is also used to determine the vibration frequency.Convergence of the power series solution is demonstrated and excellent agreement is seen for the vibration response with a numerical solution.
