Interlude of operator pairs and a von Kármán plate-beam problem with rotational inertia

Abstract

In this paper we consider a non-dissipative Von Kármán plate-beam which serves as a model for the undamped transversal vibrations of a two-dimensional plate which has a beam attached to its free cdgc.Rotational moments of inertia are included for both the plate and the beam and the problem is doubly non-linear in the sensc that large deflection occur in the form of an implicit evolution problem with cause and effect in different spaces. A subtle interplay of the operator pairs acting in the evolution problem cnables us to establish the existence of a unique global classical solutions for the platc-beam problem. This is achieved by using the theory of evolution operators in cmpathy to trcat the linear evolution problem and fixed point arguments in the study of the non-lincar problem.

AMS:

• 35Q72
• 73D35

Keywords:

• Fractional powers
• empathy
• plate-beam
• Von Kármá system
• rotational inertia
• interactive
• coupled
• dynamic boundary condition