Extension of dual criterion to periodic vibrational nonlinear systems - Nguyễn Đông Anh; Nguyễn Minh Triết (Journal of Technical Education Science, 2015)
A new approach to nonlinear problems of vibration and structural control was recently proposed by N. D. Anh. This new approach called as dual approach has a conception of balance in research which allows finding the essence of problem in fuller details. The application to the equivalent linearization leads to the technique of dual mean square minimum (dual technique in short). At beginning the dual technique was proposed for single and multi-degree-of-freedom random nonlinear vibrations. The objective of this paper is to extend the dual criterion to periodic nonlinear vibrational systems in order to find natural frequencies. A formula of dual averaged coefficient of linearization is proposed corresponding to the boundary values of weighting coefficient. Application to Duffing systems of high nonlinearity shows that the proposed formula gives less error than the classical formula does. The comparison leads to a possibility of further use of the proposed formula to find natural frequencies of more complicated nonlinear systems.