Free-vibration of Composite Beam-columns with Stochastic Material and Geometric Properties Subjected to Random Axial Loads

Abstract

Beam-columns made of polymer-matrix fiber-reinforced composite materials are increasingly being used in automotive, aerospace, structural, and mechanical engineering industries. The composite materials display significant variability in their material properties. The composite laminates also display significant variability in their geometric and structural properties. Randomness exists in the axial loads and in the support conditions. As a result, the natural frequencies of composite beam-columns become random variables. The present work considers such composite beam-columns with the objective of determining the mean values and variances of natural frequencies. The randomness in the material and geometric properties of the laminated beam-columns are modeled using stationary stochastic fields in space. Each natural frequency is expressed as a perturbation series. The corresponding normal mode is also expressed as a compatible perturbation series. The perturbation method is employed in the context of stochastic analysis. The equations for sample realizations of natural frequencies and normal modes are derived. Using the sample realizations and the first-order second-moment probabilistic analysis the statistics of natural frequencies are determined. A parametric study on beam-columns made of NCT-301 graphite-epoxy composite material is conducted.