Analytical solution for the transient response of the anisotropic multi-layered composite structure under dynamic anti-plane point loading with thermal effect

In this study analytical transient response of the anisotropic multi-layered composite structure subjected to dynamic anti-plane point loading is investigated as thermal effect considered. A linear coordinate transformation is firstly employed to convert the partial differential equation of motion when developing the transient response. By applying the double Laplace integral transformation and matrix method, analytical solution in the Laplace domain is then obtained in a form of series, where each item of the series represents a propagating path of the transient waves. With the aid of Cagniard de-Hoop method and convolution theorem, the analytical solution is finally transformed into time-space domain, and the static value is also obtained based on limit theory. Some examples are thereafter discussed in details using numeric calculation for the multi-layered composite structure. The study shows that the transition time of the transient response depends on the material parameters of the multi-layered composite structure. Most importantly, the thermal stress has significant effect both on the transition time approaching the static value and the number of head waves developed in the composite structure.