Dynamic analysis of rectangular plate structures with arbitrary edge supports subjected to harmonic point excitation force or enforced boundary displacement

Abstract eng:
Rectangular plates with different kinds of attachments and/or various openings are main constitutive parts of almost all engineering structures, e.g. aircrafts, bridges, buildings, ships, offshore structures, etc. Therefore, an assessment of their natural and forced dynamic responses is generally very important for safe and rational structural design. In this paper, an overview of different vibration problems inherent to rectangular plate structures and considered in the recent references published by the authors, that can be solved by the energy based assumed mode method is presented. The concept of assumed mode method is briefly described together with application of the mode superposition method to forced response assessment. Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners and carlings. Lagrange’s equation of motion is used to formulate an eigenvalue problem represented with a multi-degree-of-freedom system equation. Characteristic orthogonal polynomials having the properties of Timoshenko beam functions and satisfying the specified edge constraints are used as approximation functions. Rectangular plate structures subjected to harmonic point excitation force or boundary displacement loading are considered. Comparisons of the results with general Finite Element (FE) software are included, and very good agreement is obtained.

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