The Rayleigh-Ritz solution to estimate vibration characteristics of building floors

An approximate solution for floor vibration is proposed as an aid to structural design. The building floor is approximated as a thin rectangular plate in order to use the Rayleigh-Ritz method in the analysis. To represent various structural types of building floors, the plate may be simultaneously subjected to many different factors, including orthotropy of the plate material, the presence of in-plane forces, uniform elastic edge supports, elastic point supports, reinforcement by flexural and torsional beams and vibration control by tuned mass dampers (TMDs). Beam functions, for which free edge conditions of the plate are generally difficult to represent, are used in practice as admissible functions in the Rayleigh-Ritz method under various boundary conditions, in consideration of the approximate approach for only free edge conditions of the plate. The accuracy and applicability of the approximate solution are confirmed in comparison with the results obtained by earlier studies and the finite element method (FEM). (C) 1998 Academic Press Limited.