An iterative approach for obtaining nonlinear frequency of a conservative oscillator with strong nonlinearities

• Дата: 2018
• Автори: Mohammadian, M., Pourmehran, O., Ju, P.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут механіки ім. С.П. Тимошенка НАН України 2018
• Назва видання: Прикладная механика
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/174201
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: An iterative approach for obtaining nonlinear frequency of a conservative oscillator with strong nonlinearities / M. Mohammadian, O. Pourmehran, P. Ju // Прикладная механика. — 2018. — Т. 54, № 4. — С. 113-124. — Бібліогр.: 17 назв. — англ.

An iterative procedure is suggested for obtaining the higher-order approximate solutions of a conservative system comprising an oscillator with cubic and quintic restoring force function. The proposed method is similar to the traditional harmonic balance methods but unlike them the obtained from the previous step errors are considered in the present step to increase the accuracy of the solution. A comparison of results with those obtained by exact solution and other approximate analytical techniques confirms an accuracy of the method. It is shown that the achieved approximate solutions are valid for both small and large amplitudes of oscillation and can meet the exact solutions with a high level of accuracy in the lower-order of approximations. Furthermore, using the obtained analytical solutions, the effect of cubic and quintic terms on the frequency is discussed.