A theoretical and experimental study on in-plane parametric resonance of laminated composite circular arches under a vertical base excitation

For the first time, analytical solutions for the in-plane dynamic instability of laminated composite circular arches under a vertical base excitation are developed and experimentally verified in this paper. Hamilton principle is used to derive the governing equation of motion of the laminated arch from which the principal instability region corresponding to parameter resonance can be determined. An experimental system is designed and set up to verify the developed solutions and investigate the dynamic performance of laminated arches. Comprehensive analytical and experimental results are presented, with a particular focus on the effects of rise-to-span ratio and stacking sequence on the dynamic instability region of the laminated arch. It is found that dynamic instability region mainly occurs when the excitation frequency is nearly twice the fundamental frequency. For an arch with a lower rise-to-span ratio, both the critical excitation frequency and the width of its dynamic instability region increase significantly. Under the same excitation amplitude, the dynamic instability region of an angle-ply laminated arch becomes wider as the ply-angle increases. Results also show that the critical excitation frequency is highly sensitive to the stacking sequence and quickly grows as the zero-degree ply is placed further away from the midplane.