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Load models that account for Human-Structure Interaction (HSI) may be preferable to accurately predict the dynamic response of lightweight footbridges subjected to pedestrian actions. Representing each person within a crowd may not be practical in engineering design calculations as time-variant models with a large number of degrees of freedom have to be managed. In addition, high computational time may be required to achieve the steady-state response. In this sense, this paper proposes a novel approach to calculate the vertical steady-state response of footbridges from a time-invariant coupled crowd-structure system. Considering the model of the structure and a feedback model of the crowd, a total closed-loop Transfer Function (TF) of the coupled system is derived. Based on this frequency-domain interacting methodology, a step-by-step procedure is set to asses the vibration serviceability of lightweight footbridges due to harmonic excitations through simple algebraic operations. The proposal is used to study a Fibre Reinforced Polymer footbridge subjected to two streams of walking pedestrians. For this structure, a good compromise between experimental and numerical results is obtained in terms of vertical vibrations and TFs. To further validate the proposed approach, a pre-stressed concrete laboratory facility is also analysed, obtaining a satisfactory agreement between the experimental and numerical TFs. Thus, the proposed approach allows to evaluate lightweight footbridges under crowd-induced loads considering HSI in a simple and accurate manner, which is clearly geared to practice.

A formulation in cylindrical coordinates of the nonlinear torsional wave propagation on a hyperelastic material characterized by Hamilton's strain energy function is proposed. The objective of this formulation is to study and assess soft tissues, taking into account both geometrical and physical nonlinearity. Specifically, this work analyzes the propagation of torsional shear waves through an isotropic axisymmetric medium, so the only non-zero velocity component is associated with the angular coordinate. To transform the equations from Cartesian to cylindrical coordinates, the covariant and contravariant transformations are employed. A transverse torsional wave propagating through a quasi-incompressible hydrogel from the emitter to the receiver is considered. As the close form solution is not straightforward, a numerical simulation using the Finite Difference Time Domain method is performed. The results are obtained for a realistic range of wave frequencies and nonlinear parameters for medical applications.