Radiometer Force on the Proof-Mass of a Drag-Free Satellite
V. Conclusions Whereas all previous analyses have studied the problem in the hardening regime alone"' or in the softening regime alone,' this Note unifies both formulations. The variable axial restraint at the boundary is seen to play an important role in determining the nonlinear dynamic behavior of the beam. From the present results and earlier conclusions, *~ one may conclude that the principal causes and effects of nonlinearity are a hardening effect due to axial stretching, use of exact curvature expressions, and equilibrium equations, and a softening effect due to longitudinal inertia forces. At low values of spring constant and sienderness ratios, the effect of longitudinal inertia predominates, whereas, at high values of axial restraint and sienderness ratios, the effect of axial stretching predominates.