Nonlinear Thinking in Mechanics and Design

While the spread of computer aided design tools in the last two decades has been revolutionary, much of its analytical basis in elasticity, vibrations, thermal systems etc, rests on linear models. These new ideas have found application in many areas of applied science and are now just beginning to find their ways into practical devices. (See eg, Moon (1992)). As these ideas mature, it is natural to ask if they can be introduced into the undergraduate curriculum. The Author argues that creative solutions to design problems often result from using nonlinear models and concepts. Nonlinearity, often seen as something to be avoided, can sometimes offer alternative solutions that linear models cannot do. The Author also argues the case for introducing nonlinear thinking into the engineering curriculum in mathematics, mechanics of materials and dynamics using both computational and experimental laboratories. This paper describes a program at Cornell University to introduce nonlinear dynamics concepts to mechanical engineering undergraduates through an NSF sponsored grant for curriculum development.