Vibrations of a beam between two rigid stops: strong solutions in the framework of vector-valued measures

Abstract

We study a problem that models the dynamics of an elastic beam vibrating between two rigid stops, so we use the Signorini non-penetration condition to describe the contact process. This allows for impacts and velocity jumps. Motivated by the need to better understand this kind of dynamics, we introduce a new formulation of the problem in the framework of vector-valued measures, somewhat similar to the case of a discrete mechanical system. We prove the existence of a strong solution and establish the main properties of the reaction shear stress that acts on the system at impacts, which is a measure with a singular part.

Keywords:

• Dynamic unilateral contact
• complementarity conditions
• vector-valued measures
• existence
• elastic beam

AMS Subject Classifications:

• 35L85
• 74H45
• 74M20
• 74K10
• 28C99

Notes

No potential conflict of interest was reported by the authors.