Damage Identification in Hangers of Through-Arch Bridges Using Static Deflection Difference at the Anchorage Point

This study proposes a new damage identification method for hangers of arch bridges using the static deflection difference at the anchorage point of the hanger and the tie-beam. The relationship between the ratio of cable tension loss and the deflection difference at the anchorage point is studied. For the first time, the deflection difference influence matrix for hanger damage identification is defined. The static deflection change parameter is formulated as a function of the deflection difference influence matrix and the ratio of cable tension loss. The study shows that the percentage of cable tension loss can be obtained from the changes in static deflection at the anchorage point and the deflection difference influence matrix. Therefore, by observing a plot of the ratio of cable tension loss, the damage locations can be identified conveniently. Numerical and laboratory studies show that this method can accurately locate the damaged hanger of through-arch bridges under various scenarios. The proposed damage detection method has a clear theoretical base and is simple to operate, and it is suitable for practical engineering.

Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.

A Lumped Parameter Approach for Analysing a Metamaterial Beam Based Piezoelectric Energy Harvester Around Fundamental Resonance

This paper proposes a lumped parameter approach to simplify the modelling of a metamaterial based PEH to predict its energy harvesting performance around the fundamental resonance. The metamaterial based PEH consists of a host beam with a piezoelectric patch bonded at the clamped end. A series of local resonators are attached onto the host beam. In the first case study, the local resonators are modelled as mass-spring systems. By applying Rayleigh’s method and approximating the fundamental mode shape by the static deflection, the host beam is represented by a SDOF system. The equivalent lumped parameters are assumed to concentrate at the tip of the host beam and their explicit expressions are presented. Though the local resonators are identical, they have different influences on the host beam when being attached at different positions. To reflect the interaction degree (i.e., reacting force) between the local resonator and the host beam, a scaling factor that is a function of the attaching position is derived. On the other hand, due to the action of the local resonators, the fundamental mode shape of the host beam is actually changed. Based on the linear superposition principle, the static deflection approximated fundamental mode shape is corrected and the electromechanical coupling coefficient that is sensitive to the slope of the mode shape is updated to improve the accuracy. Based on the derived equivalent lumped parameters and correction factors, a multiple-degree-of-freedom (MDOF) model is constructed to predict the dynamic behavior of the metamaterial based PEH with mass-spring resonators. A corresponding finite element model is built to verify the developed MDOF model. In the second case study, the local resonators are modelled as practical parasitic beams. The parasitic beams are converted into equivalent lumped systems as well. However, the lumped parameters are the effective parameters at the beam tip. For the force interaction at the root of a parasitic beam, a factor is derived to correct the reaction force when a parasitic beam is represented by a SDOF mass-spring system. Using the reaction force correction factor, a MDOF model for the metamaterial based PEH with beam-like resonators is also established and verified by the finite element model.

Accuracy evaluation of statically backcalculated layer properties of asphalt pavements from falling weight deflectometer data

This study is to evaluate the dynamic effects of falling weight deflectometer (FWD) loading on the surface deflection of asphalt pavement and the accuracy of statically backcalculated layer moduli from FWD data. The dynamic and static deflections were computed using the spectral element method and the layer elastic theory, respectively, for various pavement structures. The static deflection is considerably larger than the dynamic deflection for typical FWD loading and the normalized difference between static and dynamic deflections increases with increasing distance from the load center and decreases with increasing loading duration. The dynamic deflections were utilized to backcalculate the layer moduli using two static backcalculation procedures, MODULUS and EVERCALC. The backcalculated moduli can be significantly different from the actual moduli. The results indicate that the static backcalculation procedure can lead to significant errors in the backcalculated layer moduli by ignoring the dynamic effects of FWD loading.