Walking-induced vibration control in multifamily timber buildings

Analysis of floor configurations and support conditions using classical vibration theory

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Practical combinations of floor configurations and support conditions are studied for the development of a lightweight timber building method that is suitable for multi-family residential buildings. Classical vibration theory forms the base for a methodology that is developed to assess transmittance of vibrations to adjoining floor fields. Especially when the source is out of sight, humans humans are tend to classify vibrations as annoying for low vibration levels. With the introduction of new engineered timber products made wood a more suitable and used material for residential buildings. Strength- and stiffness variation is reduced by homogenizing the material and regarding soundproofing innovative concepts have been improved, such as floating screeds and resilient materials. Based on these products and acoustic concepts, 32 design combinations are studied. A distinction between forced- and free vibrations is made and related to low- and high-frequency floors. Forced vibrations are in structural dynamics described by the particular solution, and free vibrations by the homogeneous solution of the equation of motion. This solution is found through the method of separation of variables, which multiplies the space- and time-related parts. Mode shapes are studied regarding transmittance and effective measures for prevention. Fundamental frequencies of floors supported either rigid and flexible are determined with one-dimensional undamped continuous systems where supported beams are represented by equivalent springs. All floors are transformed into Single Degree of Freedom systems to include damping. These systems are assessed making use of modal superposition, for steady-state- and transient response. The behaviour of floors under walking load harmonics provides the resonant response, and free vibration of the system due to initial conditions the transient response. Since the perception of vibrations by humans is frequency-dependent, vibrations are weighted accordingly. Eurocodes currently available are found to provide guidance regarding human-induced vibrations of lightweight structures marginally. Non-timber Eurocodes do not provide an assessment method, EN1990 only provides requirements when no assessment has to be done, and current code for timber structures prescribe criteria that are not sufficient as found in the literature. The future revision of Eurocode 5 holds several methods for assessment of vibrations but is generally focussed on rigidly supported floors. In extending to this code methods are developed to acquire fundamental frequencies of flexible, supported floors, and by transformation into SDOF systems an equation is developed for the appropriate determination of modal mass for two-span or beam supported floors using a simple formula. 32 combinations of floor configurations and support conditions are assessed at the excited field and at adjoining floor fields, where both steady-state and transient response are combined. Based on this assessment, transient responses are found to contribute significantly for low-frequency floors, where generally is assumed that the mass is sufficient to neglect this response.