Comparison of different models for the vibration of beams and plates

Abstract

Beam and plate models are often encountered in applications. There are a wide variety of models, ranging from the simplest one-dimensional linear model to non-linear three dimensional models. With such a wide variety of applications it may be difficult to decide which model is sufficiently realistic without introducing unnecessary complexities. Justification is needed in the decision to use a one-dimensional or two-dimensional model. There is also a need for specification to decide whether displacements are sufficiently small to use a linear model. To judge a model, comparison to other models is needed. We do this by investigating the derivation and assumptions made as well as by comparing the numerical results obtained for similar situations. We compared different linear models, different non-linear models as well as linear and non-linear models using these methods.