ON MODAL INTERACTION, STABILITY AND NONLINEAR DYNAMICS OF A MODEL 2 DOF MECHANICAL SYSTEM PERFORMING SNAP-THROUGH MOTION

Dynamics of a simple two degrees of freedom (d.o.f.) mechanical system is considered, to illustrate the phenomena of modal interaction. The system has a natural symmetry of shape and is subjected to symmetric l oading. Two stable equilibrium configurations are separated by an unst able one, so that the model system can perform cross-well oscillations . Nonlinear statics and dynamics are considered, with the emphasis on detecting conditions for instability of symmetric configurations and a nalysis of bi-modal non-symmetric motions. Nonlinear local dynamics is analyzed by multiple scales method. Direct numerical integration of o riginal equations of motions is carried out to validate analysis of mo dulation equations. In global dynamics (analysis of cross-well oscilla tions) Lyapunov exponents are used to estimate qualitatively a type of motion exhibited by the mechanical system. Modal interactions are dem onstrated both in the local dynamics and for snap-through oscillations , including chaotic motions. This mechanical system may be looked upon as a lumped parameters model of continuous elastic structures (spheri cal segments, cylindrical panels, buckled plates, etc.). Analyses perf ormed in the paper qualitatively describe complicated phenomena in loc al and global dynamics of original structures.