Nonlinear vibrations and stability of parametrically exited systems with cubic nonlinearities and internal boundary conditions: A general solution procedure

作者：Ghayesh Mergen H^*; Kazemirad Siavash; Reid Tyler

来源：Applied Mathematical Modelling, 2012, 36(7): 3293-3305.

DOI：10.1016/j.apm.2011.09.084

• Perturbation techniques
• The method of multiple timescales
• Nonlinear vibrations
• Parametrically excited systems

A general. form of an analytical solution algorithm for the nonlinear vibrations and stability of parametrically excited continuous systems with intermediate concentrated elements is developed in this paper. The method of multiple timescales is applied directly to the equations of the motion which are in the form of a set of nonlinear partial differential equations with nonlinear coupled terms. This yields approximate analytical expressions for the response amplitude and stability of the system. Moreover, the solution to a sample problem is obtained using the general algorithm, thus proving its effectiveness and validity.

• 出版日期2012-7