Effect of bimodularity on frequency response of cylindrical panels using Galerkin time domain approach

摘要

The forced vibration analysis of bimodulus material laminated structures is a challenging problem due to non-smooth nonlinear nature of governing equations. The most commonly used direct time integration schemes show numerical instability and do not predict steady state response except for limited number of cases without considering in-plane inertia. This is due to the sudden change of restoring force from positiveegative half cycle to negative/positive half cycle exciting higher modes/harmonics at every instant of a cycle change leading to numerical instability in the time marching scheme. In the present work, Galerkin time domain approach is successfully used for the forced vibration analysis of bimodular cylindrical panels. The effect of bimodularity ratio on the frequency response of cylindrical panels for few typical geometrical and lamination parameters is studied for the first time. It is found that the positive half cycle amplitude is greater than the negative half cycle amplitude for E_(2t)/E_(2c) < 1 and is smaller for E_(2t)/E_(2c) > 1. Further, the percentage difference of positive and negative half cycle amplitudes decreases with the increase in E_(2t)/E_(2c). The stresses under dynamic loading are different for positive and negative half of a vibration cycle.