Free and forced vibration analysis of arbitrarily supported rectangular plate systems with attachments and openings

Rectangular plates with different kinds of attachments (continuous or lumped) and various opening shapes are main constitutive parts of almost all engineering structures, e.g. aircrafts, bridges, buildings, ships, offshore structures, etc. Therefore, an assessment of their free and forced responses is generally very important for safe and rational structural design. In this paper, a range of different vibration problems inherent to rectangular plate systems, that can be solved by the energy based assumed mode method is considered. The concept of assumed mode method is outlined together with application of the mode superposition method to forced response calculation for plates under concentrated harmonic forces or enforced boundary displacement. Furthermore, complete mathematical model for vibration analysis of plate structures carrying arbitrary number of spring-mass systems is developed, based on the receptance method application. The plate is modelled by the Mindlin thick plate theory and Timoshenko beam theory is applied for stiffeners. The eigenvalue problem represented with a multi-degree-of-freedom system equation is formulated by Lagrange's equation of motion, while characteristic orthogonal polynomials having the properties of Timoshenko beam functions and satisfying the specified edge constraints are used as approximation functions. The corresponding in-house software is developed and dynamic responses of rectangular plate systems having different sets of edge constraints are analysed. Comparisons of the results with existing solutions and general finite element (FE) software are included, and very good agreement is achieved.