Buckling and free vibrations behaviour through differential quadrature method for foamed composites

Abstract

The current work focuses on predicting the buckling and free vibration frequencies (fn) of cenosphere reinforced epoxy based syntactic foam beam under varying loads. Critical buckling loads (Ncr) and fn are predicted using the differential quadrature method (DQM). Ncr and fn have been calculated for beams of varying cenosphere volume fractions subjected to axial load under clamped-clamped (CC), clamped-simply (CS), simply-simply (SS), and clamped-free (CF) boundary conditions (BC′s). Upon increasing the cenosphere volume fraction, Ncr and fn of syntactic foam composites increases. These numerical outcomes are compared with the theoretical values evaluated through the Euler-Bernoulli hypothesis and further compared with experimental outcomes. Results are observed to be in precise agreement. The results of the DQM numerical analysis are given out for the different BC′s, aspect ratios, cenosphere volume fractions, and varying loads. It is perceived that depending on the BC′s, the type of axial varying loads and aspect ratios has a substantial effect on the Ncr and fn behaviour of the syntactic foam beams. A comparative study of the obtained results showed that the beam subjected to parabolic load under CC boundary conditions exhibited a higher buckling load.

Keywords

• Syntactic foam
• Differential quadrature method (DQM)
• Axial varying loads