Solvability of a Reissner–Mindlin–Timoshenko plate–beam vibration model

• Published in: IMA journal of applied mathematics Vol. 74; no. 1; pp. 149 - 162
• Main Authors: van Rensburg, N. F. J., Zietsman, L., van der Merwe, A. J.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.02.2009; Oxford Publishing Limited (England)
• Subjects: Exact sciences and technology; existence of solutions; Mathematical analysis; Mathematics; plate–beam system; Reissner–Mindlin plate; Sciences and techniques of general use; semigroups; Timoshenko beam; variational form; vibration; Reissner-Mindlin plate; Timoshenko beam; existence of solutions; plate-beam system; semigroups; vibration; variational form; Variational problem; Equation of motion; Applied mathematics; Reissner Mindlin plate
• ISSN: 0272-4960; 1464-3634
• DOI: 10.1093/imamat/hxn043

In this paper, we consider the vibration of a plate–beam system consisting of a Reissner–Mindlin plate and a Timoshenko beam. A variational form is derived directly from the equations of motion and the constitutive equations. We show how an existence result for a general linear vibration problem in variational form may be applied to the weak variational problem for this system.