Analysis of the Solvability of Linear Vibration Models

In this article we consider a general linear vibration problem in variational form. Models for the vibration of systems of elastic bodies can be written in this form. We show how properties of the damping term determines the time differentiability of the solution and establish classes of permissible initial conditions. The proofs are based on a direct link between the variational form and an abstract differential equation.

Keywords:

• General Linear Vibration Problem
• Damped Elastic Systems
• Abstract Differential Equation
• Semigroups