A time-dependent metric graph with a fourth-order operator on the edges

Abstract

The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution.

Keywords

• metric graph
• spectrum
• time evolution