High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM

In the present study, the high-order buckling and free vibration behaviors of two types sandwich beams including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using generalized differential quadrature method (GDQM) are investigated. The high-order sandwich panel theory (HSAPT) for AL or PVC-foam flexible is employed and also the modified couple stress theory (MCST) for the face sheets is used. It is noted that the core of first sandwich beam is Aluminum alloy foam with variable mechanical properties and the other consists of PVC-foam core with temperature dependent mechanical properties. The governing partial differential equations of motion for two types sandwich beam are derived using Hamilton's principle and then discretized by using GDQM. These formulations yield nine partial differential equations which are coupled in axial and transverse deformations. A parametric study is carried out to investigate the effect of some important parameters such as slenderness ratio, face sheet thickness, temperature rise. Although increasing slenderness ratio, reduce the 1st natural frequency and also critical buckling load, but the treatment is different for AL-FCSB and PVC-FCSB. It is found that at high temperatures, the PVC-FCSB frequency decreases with increasing face sheet thickness whereas for AL-FCSB at high-temperatures although the frequency is less for low slenderness ratio and high face sheet thickness, but with increasing slenderness ratio frequency increases. This behavior is due to the large effect of face sheet and their temperature dependence in short sandwich beams compared with long ones.