On the number of mechanical configurations for nonlinear stiffness systems designed based on a linear spring with a nonlinear boundary

In this paper, we present a novel integrated method for designing nonlinear stiffness systems based on a general spring-boundary model (GSBM) to study the number of mechanical configurations for nonlinear stiffness systems designed by the combination of a linear spring with a nonlinear boundary. GSBM consists of a lumped mass, a special-shaped track, a roller rolling in the track and GLSM with either positive or negative stiffness. The integrated method considers pre-tensioned, pre-compressed and original length conditions of GLSM to design roller trajectories to customize nonlinear stiffness systems. It is proved that the mechanical configurations of nonlinear stiffness systems designed by the combination of a linear spring with a nonlinear boundary are not limited to one, but six or eight forms: for systems with nonnegative or nonpositive potential energy, there are six independent mechanical configurations, and for other systems, there are eight independent mechanical configurations.