Effect of Nonlinear Constitutive Relations on the Large Amplitude Vibration of Elastic Structures.

摘要

The general theory of large amplitude free and forced vibration of linearly elastic structures developed previously by the author is extended to include the effects of nonlinear elastic constitutive relations. As a first approximation, it is assumed that tensile and compressive behavior are similar and that the stress-strain relations can be adequately represented as polynomial functions. Only free vibration is treated explicitly, but the extension to forced vibration is outlined. A second order approximation theory is worked out in detail and applied to the undamped free vibration of uniform simply supported beam. Numerical results are presented for several materials, for beams of varying slenderness, and for fundamental and higher vibration modes. The results indicate that nonlinear material effects are extremely important and dominantly influence the behavior for higher modes and short beams. (Author)