Transient vibration of visco-elastic composite plates

Quasi-static linear behavior of composite laminates is formulated by ananisotropic hygrothermal-viscoelastic constitutive model. Based on the variationalprinciple of linear viscoelasticity, a specially developed numerical model (directtime integrations) has been introduced for the solution of hygrothermal-viscoelasticboundary value problems in anisotropic laminates. The proposed model exploits arecursive approach to save both the computational time and storage. Throughout thepresent study, the material is assumed to be non-aging and thermorheologicallysimple. 2-D theories (Mindlin alld higher-order shear) and 3-D elements areemployed in the framework of viscoelastic analysis of composite structuressubjected to mechanical and hygrothermal loads. The comparative studies showgood agreement with the previous analytical and computational models. Theviscoelastic displacement fields in the transverse direction of the cross-ply andangle ply laminates are calculated, and the stacking sequence of the laminates, theskew angle, temperature and moisture effects are discussed in detail.Zocher’s recursive formula is limited only to the quasi-static analysis,therefore the proposed model exploits the aforementioned formula for analyzingdynamic responses of composite structures with time taking into account thetemperature and moisture-dependent linear viscoelastic damping. Variationalprinciples, the Newmark average acceleration method and 2-D theories (Mindlinand higher-order shear only) are used. Recursion formulas have been introduced inorder to reduce computer storage where only the previous time state is required tocompute the next time state. Verification studies were conducted to evaluate theaccuracy and convergence of the present numerical algorithm, and they show thatthe numerical solutions of the proposed model are in favorable agreement with theanalytical solutions developed for special cases. Also, the comparative study showsthat the present elastic response of cross ply unsymmetric laminates agrees wellwith the closed form solution of Reddy. Numerical results for displacement fieldsare presented showing the effects of plate side-to-thickness ratio, stacking sequence,skew angle, the environment, etc. on the dynamic response. Moreover, transientdisplacement fields for rectangular laminates as well as skew ones aloe introduced toshow the influence of load release and pulse length on the response.