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This study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.

Timoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.

The results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.

The combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks.

The design of compliant towers in deep waters is greatly affected by their dynamic response to wave loads as well as by the geometrical and material nonlinearities that appear. In general, a nonlinear time history dynamic analysis is the most appropriate one to be applied to capture the exact response of the structure under wave loading. However, this type of analysis is complex and time-consuming. This paper aims to develop a simplified methodology, which can adequately approximate the maximum response yielded by a dynamic analysis by means of a static analysis.

Various types of time history dynamic analysis are first applied on a detailed structural model, ranging from linear to fully nonlinear, that are used as reference solutions. In the sequel, a simplified analysis model is formulated, capable of reproducing the response of the entire structure with significantly reduced computational cost. In the next stage, this model is used to obtain the linear and nonlinear response spectra of the structure. Finally, these spectra are used to formulate a simplified design approach, based on equivalent static loads.

This simplified design approach produces good results in cases that the response is mainly governed by the first eigenmode, which is the case when compliant towers are considered.

The present paper borrows ideas from the area of earthquake engineering, where simplified methodologies can be used for the design of a certain class of structures. However, the development of a simplified methodology for the approximation of the dynamic behavior of offshore structures under wave loading is a much more complex problem, which, to the authors’ knowledge, has not been addressed till now.

Structural stress and strain in the key components of aircraft structure is important for structural health monitoring and strength assessment. However, the measure of dynamic strain is often difficult to implement because of the complex test equipment and inconvenient measure points, especially in flight test. This study aims to propose an algorithm of dynamic strain estimation using the acceleration response in time domain to simplify the measure of dynamic strain.

The relationship between the strain and acceleration response is established through the sinusoidal response or modal analysis, which is insensitive to the excitation position and form. A band-pass filter is used to obtain the modal acceleration response, and a filter frequency band selection method is proposed. Then, the dynamic strain at the concerned points can be estimated based on the modal superposition principle.

Simulation and experiment are implemented to validate the applicability and effectiveness of the strain estimation method. The estimated strain results agree well with numerical simulation as well as the experimental results. The simplicity and accuracy of the strain estimation method show practicability for dynamic strength and fatigue analysis in engineering applications.

An algorithm of dynamic strain estimation using the acceleration response in time domain is developed. A band-pass filter is used to obtain the modal acceleration response, and a filter frequency band selection method is proposed. The dynamic strain at the concerned points can be estimated based on the modal superposition principle.

This study aims to ensure reliable analysis of dynamic responses in asphalt pavement structures. It investigates noise reduction and data mining techniques for pavement dynamic response signals.

The paper conducts time-frequency analysis on signals of pavement dynamic response initially. It also uses two common noise reduction methods, namely, low-pass filtering and wavelet decomposition reconstruction, to evaluate their effectiveness in reducing noise in these signals. Furthermore, as these signals are generated in response to vehicle loading, they contain a substantial amount of data and are prone to environmental interference, potentially resulting in outliers. Hence, it becomes crucial to extract dynamic strain response features (e.g. peaks and peak intervals) in real-time and efficiently.

The study introduces an improved density-based spatial clustering of applications with Noise (DBSCAN) algorithm for identifying outliers in denoised data. The results demonstrate that low-pass filtering is highly effective in reducing noise in pavement dynamic response signals within specified frequency ranges. The improved DBSCAN algorithm effectively identifies outliers in these signals through testing. Furthermore, the peak detection process, using the enhanced findpeaks function, consistently achieves excellent performance in identifying peak values, even when complex multi-axle heavy-duty truck strain signals are present.

The authors identified a suitable frequency domain range for low-pass filtering in asphalt road dynamic response signals, revealing minimal amplitude loss and effective strain information reflection between road layers. Furthermore, the authors introduced the DBSCAN-based anomaly data detection method and enhancements to the Matlab findpeaks function, enabling the detection of anomalies in road sensor data and automated peak identification.

The purpose of this paper is to focus on the influences of the uncertain dynamic responses on the reconstruction of loads.

Based on the assumption of unknown-but-bounded (UBB) noise, a time-domain approach to estimate the uncertain time-dependent external loads is presented by combining the inverse system method in modern control theory and interval analysis in interval mathematics. Inspired by the concept of set membership identification in control theory, an interval analysis model of external loads time history, which is indeed a region or feasible set containing all possible loads being consistent with the bounded structural acceleration responses is established and further solved by two interval algorithms.

Unlike traditional loads identification methods which only give a point estimation, an interval estimation of external loads time history, which is a region containing all the possible loads being consistent with the uncertain structural responses, is determined. The correlation characteristics among the responses of acceleration, velocity, and displacement are also discussed in consideration of the UBB uncertainty.

For one hand, the solution of the inverse problem in original system is transformed to the solution of the direct problem in inverse system; for another, the authors deal with the uncertainty by use of interval analysis method, and the identified interval process, which contains any possible external loads time history being consistent with the bounded structural responses can be approximately obtained.

The dynamic response of the nuclear power plants (NPPs) with pile foundation reinforcement have not yet been systemically investigated in detail. Thus, there is an urgent need to improve evaluation methods for nonlithological foundation reinforcements, as this issue is bound to become an unavoidable task.

A nonlinear seismic wave input method is adopted to consider both a nonlinear viscoelastic artificial boundary and the nonlinear properties of the overburden layer soil. Subsequently, the effects of certain vital parameters on the structural response are analyzed.

A suitable range for the size of the overburden foundation is suggested. Then, when piles are used to reinforce the overburden foundation, the peak frequencies in the floor response spectra (FRS) in the horizontal direction becomes higher (38%). Finally, the Poisson ratio of the foundation soil has a significant influence on the FRS peak frequency in the vertical direction (reduce 35%–48%).

The quantifiable results are performed to demonstrate the seismic responses with respect to key design parameters, including foundational dimensions, the Poisson Ratio of the soil and the depth of the foundation. The results can help guide the development of seismic safety requirements for NPPs.

The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE).

A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally.

The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load.

This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

The purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.

In this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.

The numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.

The paper provides a useful reference for further theoretical research and engineering application.

The purpose of this paper is to propose a new method of robust parameter design for dynamic multi‐response system. The objectives are to resolve the correlations among multiple responses and the uncertainty of system with incomplete information.

First, desirability function is used to measure dynamic system sensitivity and system variation, and principal component analyses on the two indices are conducted. Second, the grey relational grade (GRD) between principal component sequences of the two indices and their respective ideal sequences, gained by grey relational analysis, is converted to an integrated GRD (IGRD) index by means of TOPSIS method, and then the optimal level combination of controllable factors is identified based on the IGRD index.

It was found that the optimal factor level combination obtained by the proposed method is nearest the ideal solution and farthest from the negative ideal solution. The validity and superiority of the proposed method are confirmed through two illustrative examples.

It should be noted that the proposed method fails to consider the interaction effects between controllable factors and noise factors.

The method proposed in the paper effectively integrates several common methods to optimize a dynamic multiple responses system based on Taguchi's robust parameter design. These methods do not involve complicated mathematical theory, and are therefore easy for practitioners to use in engineering practice.

The purpose of this paper is to establish a simplified model of the closed hydrostatic guideway for the rapid analysis of static and dynamic characteristics. Further, the influence of compressibility and dynamic frequency are taken into consideration in the new dynamic model.

The new model is based on the second kind of Lagrange equation. In this model, the closed hydrostatic guideway is supported by 12 pads, and each oil pad is equivalent to a nonlinear spring-damper system. The equivalent spring coefficient and damper coefficient of the oil pad are extracted by the three different equivalent methods. Finally, the validation experiments of step load response and dynamic stiffness are conducted on a hydrostatic guideway.

For solving the step response, the linear spring-damper model and the nonlinear spring-damper Model 1 are better than the nonlinear spring-damper Model 2. The accuracy of the three methods are very high for static stiffness calculation. For the calculation of dynamic stiffness, the nonlinear spring-damper Model 2 is better than the nonlinear spring-damper Model 1. The linear spring-damper model has low precision for dynamic stiffness calculation, especially at high frequency. The accuracy of the new model is validated by experiments.

The equivalent method of nonlinear spring-damper system has higher accuracy. Different equivalent methods should be adopted for different load types. The computational speeds of the new dynamic model with the three methods are much better than finite element method (about ten times).