Fourier Series Solutions to the Vibration of Rectangular Lightweight Floor/Ceiling Structures

This article presents a mathematical model of lightweight timber floor/ceiling structures. The structures studied here consist of three basic components: upper plate, joist beams and ceiling. The shape of the whole structure is rectangular with the edges simply supported. Connections between the joist beams, the upper plate and the ceiling are considered. These connections take the form of lateral and vertical elastic coupling between the plates and beams. The configuration of the structure is made progressively more complex by adding more components such as cavity air and stiffening battens. The resulting solution formulae can be directly written into computer codes, which compute the vibration of the structure.

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