Large amplitude flexural vibration of the orthotropic composite plate embedded with shape memory alloy fibers

The free and forced vibration of the large deformation composite plate embedded with shape memory alloy (SMA) fibers was investigated. Based on the thermo-mechanical constitutive equation of SMA proposed by Brinson, the constitutive relationships for evaluation of the properties of a hybrid SMA composite ply were obtained following the rule of mixtures. And based on the nonlinear theory of symmetrically laminated anisotropic plates, the governing equations of flexural vibration in terms of displacement and stress functions were derived. The Galerkin method was used to reduce the original partial differential equation into a nonlinear ordinary differential equation, which was then solved by the harmonic balance method. The numerical results show that the relationship between nonlinear natural frequency ratio and temperature for the composite plate has similar characteristics to those of the linear one, and the effects of temperature on forced response behavior during phase transformation from martensite to austenite are significant. The effects of the volume fraction of the SMA fiber, aspect ratio and free vibration amplitude on the dynamical behavior of the plate were also discussed.