Theoretical Analysis on Anti-Plane Shear Response and Wave Superposition in Grillage Above Hollow

A multipoint transient input method (MTIM) is proposed based on analytical displacement field. The method mainly considers the time difference of wave propagation, and highlights the time difference of multipoint inputs. The feasibility of the method is verified by three analytical cases on wave responses of semicircular hollow-grillage model. The analytical solution on the displacement field of half space with semicircular hollow under the incidence of anti-plane shear waves (SH waves) is solved by the elastic wave theory, and the correctness and stability of the solution are verified. Based on the modified time-frequency transformation method (MTFT) and MTIM, the transient displacement responses of grillage plate are derived. The influence of incident angle, form of grillage, wave velocity ratio and other factors is discussed. The numerical results show that the surface hollow and above factors will have a significant impact on the response of grillages. This paper aims to give an effective analytical method for the wave propagation characteristics in structures and provide theoretical reference for wave protection and detection engineering of structures.