Free vibration analysis of stiffened panels with lumped mass and stiffness attachments

Stiffened panels are basic constitutive members of ships and offshore structures, and in practice they often have different mass and stiffness attachments, which significantly influence their dynamic response. In this paper, a numerical procedure is presented for the free vibration analysis of stiffened panels with arbitrary sets of boundary conditions and carrying multiple lumped mass and stiffness attachments. It is based on the assumed mode method, where characteristic orthogonal polynomials having the properties of Timoshenko beam functions and satisfying the specified edge constraints are used as approximation functions. The Mindlin theory is applied for plate and the Timoshenko beam theory for stiffeners. The total potential and kinetic energies of the system are formulated in a convenient manner and further applied to derive an eigenvalue problem by means of Lagrange's equation of motion. Based on the developed numerical procedure, an in-house code is developed and is applied to a free vibration analysis of bare plates and stiffened panels carrying lumped masses and locally supported by pillars or springs. Comparisons of the results with those available in the literature and FEA solutions confirm the high accuracy and practical applicability of the presented procedure.