Category: Physics

Summary: Finding the inter-module brace strength at which the softest vibrational modes of a modular spring network stop being confined to individual modules and spread across the whole structure.

Disordered spring networks and mechanical metamaterials can host unusually soft vibrational modes that remain trapped in local regions. This experiment asks when adding braces between modules changes that picture by coupling the modules strongly enough that the lowest soft modes delocalize across the full network.

The script builds dense symmetric stiffness matrices for random modular spring systems and bisects the inter-module brace strength while increasing system size through iterative deepening. The threshold is defined by the point where the softest modes cease to look module-confined and instead become system-spanning.

That turns a qualitative design question into a quantitative spectral threshold. Rather than asking only whether the network is rigid, the experiment targets how modular mechanical structure loses its localized soft response as cross-links become stronger.

Method: Dense symmetric eigensolve with iterative deepening and bisection on inter-module brace strength in modular stiffness matrices.

What is measured: Critical brace-strength threshold, soft-mode localization, low-mode participation across modules, and bracket width.