Search Results (8)

Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) systems subjected to harmonic excitation. Utilizing a classical spring–mass–damper model, Fourier decomposition is applied to derive transient and steady-state responses, highlighting the effects of damping, resonance, and excitation frequency. To overcome the uncertainties and limitations of traditional models, Extended Kalman Filters (EKFs) and Physics-Informed Neural Networks (PINNs) are incorporated, enabling precise parameter estimation even with sparse and noisy measurements. This paper uses Adam followed by LBFGS to improve accuracy while limiting runtime. Numerical experiments using 1000 time samples with a 0.01 s sampling interval demonstrate that the proposed PINN model achieves a displacement MSE of 0.0328, while the Eurocode 8 response-spectrum estimation yields 0.047, illustrating improved predictive performance under noisy conditions and biased initial guesses. Although the present study focuses on a linear SDOF system under harmonic excitation, it establishes a conceptual foundation for adaptive dynamic modeling that can be extended to performance-based seismic design and to future calibration of Eurocode 8. The harmonic framework isolates the fundamental mechanisms of amplitude modulation and damping adaptation, providing a controlled environment for validating the proposed PINN–EKF approach before its application to transient seismic inputs. Controlled-variable analyses further demonstrate that key dynamic parameters can be estimated with relative errors below 1%—specifically 0.985% for damping, 0.391% for excitation amplitude, and 0.692% for excitation frequency—highlighting suitability for real-time diagnostics, vibration-sensitive infrastructure, and data-driven design optimization. This research deepens our understanding of vibratory behavior and supports future developments in smart monitoring, adaptive control, resilient design, and structural code modernization. Full article

The motion of a heavy mass on a bridge span causes vibrations whose magnitude and frequency content depend on the mechanical properties of the structural system, including the magnitude of that mass and its speed of traverse. In order to limit vibrations that could potentially cause damage, a simple passive device configuration, namely the tuned mass damper (TMD), is introduced and its effect on the beam vibrations analyzed. Specifically, a TMD in the form of a single-degree-of-freedom (SDOF) unit comprising a mass and a spring is placed on the span to act as a secondary system for absorbing vibrations from the primary system, i.e., the bridge itself. A Lagrangian energy balance formulation is used to derive the governing equations of motion, followed by an analytical solution using the Laplace transform to investigate the transmission of vibratory energy between primary and secondary systems. Results are given in terms of time histories, Fourier spectra and spectrograms, where the influence of the TMD in reducing vibratory energy is demonstrated. The TMD is placed in the region where the beam’s transverse motion is at a maximum, while its mechanical properties are sub-optimal, in the sense that there is no separate damper present and minimal damping is provided by the spring element itself. In parallel with the analysis, a series of experiments involving a simply supported model steel bridge span traversed by a heavy mass are conducted to first gauge the analytical solution and then to confirm the validity of the proposed passive scheme. Full article

Due to its high strength-to-weight ratio, corrosion resistance, extrudability, and recyclability, there is a growing demand for the use of aluminum for sustainable bridge constructions, especially for footbridges. Owing to their light weight and lively characteristics, vibration serviceability often governs the design of aluminum footbridges. To better design these bridges, it is necessary to accurately predict pedestrian-induced walking loads. To this end, the existing design codes around the world have adopted the periodic moving force model (MF) due to its simplicity. However, the appropriateness of the MF model is being questioned, mainly in capturing the effect of the human–structure interaction (HSI), which can be pertinent to the design behavior of aluminum footbridges. A biomechanical-based spring-mass-damper (SMD) model was developed in the literature to simulate the HSI phenomena, which has never been validated for aluminum footbridges. Moreover, to simplify the complexity associated with SMD models, the experimental moving force model (EMF) was developed that can capture the effect of the HSI in an equivalent sense. This study aims to evaluate the capability of the SMD and EMF models to capture the real behavior of aluminum footbridges. To do so, the vibration responses of two aluminum footbridges are simulated numerically as a single-degree-of-freedom (SDOF) system under single-pedestrian walking loads employing the SMD, EMF, and MF models, which are then compared and validated based on already-available experimental observations. Finally, recommendations are made for the most suitable model for the vibration prediction of aluminum footbridges. Full article

A particle impact damper (PID) dissipates the vibration energy of a structure through impacts within the damper. The PID is not commonly used in practice mainly because of its low damping-to-mass ratio and the difficulty in achieving its optimal design due to its nonlinear characteristics. In contrast, a Coulomb friction damper (FD) can offer a higher damping force-to-mass ratio than other dampers, but it is also difficult to be controlled precisely due to its nonlinear characteristics and excessive frequency sensitivity regarding the resonant frequency. This paper examines a hybrid damper by combining a particle impact damper and a Coulomb friction damper (PID + FD) theoretically and experimentally. A theoretical model of the proposed damper is developed and tested numerically on a single-degree-of-freedom (SDOF) structure. The predicted results are validated by experimental tests on a prototype of the proposed damper. The damping force provided by the FD in the prototype can be varied by adjusting the normal force applied through a compression spring, while the vibration energy dissipation by the PID can be varied by changing the cavity size of the PID. A parametric analysis of the proposed hybrid damper has been performed. The proposed hybrid damper can reduce the maximum vibration amplitude of the SDOF primary structure by 66% and 43% compared with using the FD and PID only. The proposed damper is found to be effective over a wide range of excitation frequencies. Furthermore, the proposed hybrid damper achieves a similar vibration suppression performance to the traditional tuned mass damper (TMD) of a similar mass ratio. The proposed damper does not require an optimally tuned natural frequency and damping, unlike the TMD, and therefore it does not have the detuning problem associated with the TMD. In addition, the performance of the proposed damper is tested and compared with the TMD for random earthquake excitation data. Consequently, the proposed hybrid damper may be a simpler and better alternative to the TMD in passive vibration control applications. Full article

For structural design purposes, human-induced loads on pedestrian systems can be described by several simplified (i.e., deterministic equivalent-force models) or more complex computational approaches. Among others, the Spring-Mass-Damper (SMD), Single Degree of Freedom (SDOF) model has been elaborated by several researchers to describe single pedestrians (or groups) in the form of equivalent body mass m, spring stiffness k and damping coefficient c. For all these literature SMD formulations, it is proved that the biodynamic features of walking pedestrians can be realistically reproduced, with high computational efficiency for vibration serviceability assessment of those pedestrian systems mostly sensitive to human-induced loads (i.e., with vibration frequency f₁ < 8 Hz). Besides, the same SMD proposals are characterized by mostly different theoretical and experimental assumptions for calibration. On the practical side, strongly different SMD input parameters can thus be obtained for a given pedestrian. This paper focuses on a selection of literature on SMD models, especially on their dynamic effects on different structural floor systems. Four different floors are explored (F#1 and F#2 made of concrete, F#3 and F#4 of glass), with high- or low-frequency, and/or high- (>1/130th) or low- (1/4th) mass ratio, compared to the occupant. Normal walking scenarios with frequency in the range f_p = 1.5–2 Hz are taken into account for a total of 100 dynamic simulations. The quantitative comparison of typical structural performance indicators for vibration serviceability assessment (i.e., acceleration peak, RMS, CREST) shows significant sensitivity to input SMD assumptions. Most importantly, the sensitivity of structural behaviours is observed for low-frequency systems, as expected, but also for low-mass structures, which (as in the case of glazed floor solutions) can be characterized by the use of lightweight modular units with relatively high vibration frequency. As such, major attention can be required for their vibrational analysis and assessment. Full article

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects. Full article

Parametric studies on the optimization of baffles on vibration suppression of partially filled tanks coupled by structure have been widely conducted in literature. However, few studies focus on the effect of the position of the baffles on fluid flow stratification and dampening the motion. In the present study, a numerical investigation, an engineering analysis, and optimal design study were performed to determine the effect of external flow on circular obstacle baffles performance on suppressing the vibrations of coupled structure in a closed basin. The single degree of freedom model (mass–spring–damper) is used to model the structure that holds the tank. The coupled system is released from an initial displacement without a velocity. The governing mass, turbulent Navier–Stokes momentum, volume of fluid, and one degree of freedom structure equations are solved by the Pressure-Implicit with Splitting of Operators algorithm in fluids and Newmark method in structure. Based on a detailed study of transient structure motion coupled with sloshing dynamics, the optimal baffle location was achieved. Optimal position of the baffle and its width are systematically obtained with reference to the quiescent free surface. Full article

Piezoelectric ceramic Lead Zirconate Titanate (PZT) based electro-mechanicalimpedance (EMI) technique for structural health monitoring (SHM) has been successfullyapplied to various engineering systems. However, fundamental research work on thesensitivity of the PZT impedance sensors for damage detection is still in need. In thetraditional EMI method, the PZT electro-mechanical (EM) admittance (inverse of theimpedance) is used as damage indicator, which is difficult to specify the effect of damage onstructural properties. This paper uses the structural mechanical impedance (SMI) extractedfrom the PZT EM admittance signature as the damage indicator. A comparison study on thesensitivity of the EM admittance and the structural mechanical impedance to the damages ina concrete structure is conducted. Results show that the SMI is more sensitive to the damagethan the EM admittance thus a better indicator for damage detection. Furthermore, this paperproposes a dynamic system consisting of a number of single-degree-of-freedom elementswith mass, spring and damper components to model the SMI. A genetic algorithm isemployed to search for the optimal value of the unknown parameters in the dynamic system.An experiment is carried out on a two-storey concrete frame subjected to base vibrations thatsimulate earthquake. A number of PZT sensors are regularly arrayed and bonded to the framestructure to acquire PZT EM admittance signatures. The relationship between the damageindex and the distance of the PZT sensor from the damage is studied. Consequently, thesensitivity of the PZT sensors is discussed and their sensing region in concrete is derived. Full article