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

TL;DR

This paper introduces a novel integrated method using a general spring-boundary model to analyze the multiple mechanical configurations possible in nonlinear stiffness systems combining linear springs with nonlinear boundaries.

Contribution

It presents a new modeling approach that reveals nonlinear stiffness systems can have six or eight distinct mechanical configurations, expanding understanding of their design possibilities.

Findings

Systems with nonnegative or nonpositive potential energy have six configurations.

Other systems can have eight configurations.

The method considers various pre-tensioned and pre-compressed conditions.

Abstract

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.