Vibration of a U-shaped steel–concrete composite hollow waffle floor under human-induced excitations

The U-shaped steel–concrete composite hollow waffle floor is an innovative slender large-span floor system, where severe vibration may occur under human-induced excitations. In this research, a theoretical analysis and experimental testing are performed to explore the vibration behaviour of the composite hollow waffle floor. First, the natural frequency formula is proposed based on orthotropic thin plate theory, and the main rigidity calculation for the composite hollow waffle floor is given. Second, the mode shape, frequency and damping ratio of the composite hollow waffle floor are captured by on-site tests and validated by analytical and numerical methods, indicating that the floor has a low-frequency with a low damping ratio. Third, the vibration response of the composite hollow waffle floor is obtained by walking and running tests considering the influence of the frequency, spatial position, group size and route; in addition, the relationships between the values involved in the vibration evaluation are discussed. Finally, the composite hollow waffle floor presents satisfactory vibration performance evaluated by the threshold values among the current codes.

Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.