Abstract
An approximate method of arriving at a solution to nonlinear vibration problems is discussed. With the technique presented which involves system discretization, solutions for free as well as forced vibrations can be derived by an application of the stationary functional method using discrete normal modes. Two examples are analyzed as follows to illustrate the applicability of the approach as a useful tool in obtaining solutions to nonlinear vibration problems. (1) A three-degree-of-freedom spring-mass system with nonlinear restoring springs, and (2) a nonuniform, rotating blade mathematically modeled as a discrete cantilevered beam vibrating in the plane of rotation. The analysis reveals a definite advantage afforded with discretization in that nonlinear modes higher than the fundamental can also be easily generated—a significant improvement over the use of shape functions in conventional nonlinear continuous system analysis.