Nonlinear pre-yield modal properties of timber structures with large-diameter steel dowel connections

• Describes laboratory measurements of an asymmetrical frequency response function in timber structures.
• Relates that asymmetry to softening behaviour in connections.
• Fits a theoretical model for a system with a cubic component of stiffness.
• The nonlinear analysis is compared with the results of a linearized modal analysis method.

In timber structures, the connections are generally flexible in comparison to the members they connect, and so contribute significantly to the dynamic properties of the structure. It is shown here that a widely-used form of connection, the dowel-type connection, exhibits nonlinear stiffness and energy dissipation, even at pre-yield loads, and that this nonlinearity affects the modal properties of structures with such connections. This study investigates that behaviour by modal analysis of a portal frame and a cantilever beam constructed from timber with steel dowel connections. The observed nonlinearity is explained qualitatively by considering the measured force–displacement response of individual connectors under cyclic load, which show a reduction in stiffness and an increase in energy dissipation with increasing amplitude of vibration. The structures were tested by modal analysis under slow sine sweep and pseudo-random excitation. Under pseudo-random excitation, a linear single degree-of-freedom curve fit was applied to estimate the equivalent linear modal properties for a given amplitude of applied force. Under slow sine sweep excitation, the frequency response function for the structures was observed to show features similar to a system with a cubic component of stiffness, and the modal properties of the structures were extracted using the equation of motion of such a system. The consequences for structural design and testing are that two key design parameters, natural frequency and damping, vary depending on the magnitude of vibration, and that parameters measured during in-situ testing of structures may be inaccurate for substantially different loads.