Natural Frequencies Of Structure Research Articles

Novel rod-sprung-mass model to investigate characteristics of building structural vibration induced by railways

Railway-induced vibrations in building structures require predictions to assess the serviceability. Fundamental properties such as the predominant modes of railway-induced vibrations are critical in structural design and mitigation approaches. However, the existing numerical models are customised to specific buildings. This renders these models unsuitable for broader mechanistic investigations. To address this, this study proposes a rod-sprung-mass (RSM) model to investigate the dynamic behaviour of structures under vertical ground excitations induced by railways. The columns were modelled as axial vibration rods, with each floor suspended on the rod as a sprung mass. The model was validated using a three-story steel frame structure and a five-story concrete structure. Subsequently, the dynamic characteristics of the structures and railway-induced responses were discussed. The structural vertical modes are attributed to the interaction between the columns and slabs, and the structural natural frequencies are outside the frequency range of the individual components. Parametric studies revealed that lower-order structural modes are generally predominant. Under such circumstances, the floor response tends to first decrease and subsequently increase with the floor height. As a result, low-rise buildings exhibit the maximum amplitude on the top floor, whereas the maximum amplitude is on the ground floor for high-rise buildings. Meanwhile, when structural high-order modes become predominant owing to a high-frequency input, the responses of the middle floors intensify, and the peak responses can be altered to the middle floors. This study emphasises the necessity of considering vertical global modes, whereas existing studies have focused mainly on mode shapes on particular floors. The RSM model is an efficient tool for structural design and vibration control.

Nonlinear interactions of an n-layer X-shape low-frequency vibration isolator equipped with a nonlinear vibration absorber at 1:1 internal resonance: analytical and numerical investigations

This work addresses, for the first time, the nonlinear dynamics of an n− layers bioinspired X− shape low-frequency vibration isolation system equipped with a nonlinear vibration absorber. The comprehensive mathematical model governing the two-degree-of-freedom system has been derived using Lagrangian mechanics. The method of averaging was applied to obtain an accurate analytical solution for the derived mathematical model. Utilizing the established analytical solution, the dynamical characteristics of the X− shape vibration isolator have been explored both as a single-degree-of-freedom system and after coupling with the proposed vibration absorber, as a two-degree-of-freedom system. The influence of different system parameters, including the number of structure layers, the initial inclination angle, the X− shape rod length, and the absorber stiffness and damping coefficients, on the vibration isolation performance has been investigated. The main findings indicate that while the single-degree-of-freedom X− shape low-frequency vibration isolator performs well in eliminating low-frequency vibration excitations, it exhibits strong vibration levels when the base excitation frequency exceeds the structure's natural frequency. Additionally, it was found that coupling a highly damped linear vibration absorber to the X− shape isolator not only eliminates the strong oscillations of the structure when subjected to high-frequency base excitations but also enhances the structure's low-frequency vibration isolation performance. Moreover, it was reported that integrating a nonlinear vibration absorber with either soft or hard spring characteristics instead of a linear one may degrade the vibration isolation performance of the structure rather than enhance it. Finally, numerical validation of all the analytical results was performed, which showed excellent correspondence with the analytical findings.

Morphological analysis of a novel scissor-type deployable cable dome structure

A novel deployable scissor-type strut cable dome structure was proposed, which can improve the lateral stiffness of the traditional cable structure and achieve the characteristics of fast unfolding and closing during construction. However, the geometric stability and optimal initial prestressing theory of traditional cable dome structures cannot be applied to the new structure. Based on the equilibrium matrix theory, the geometric stability analysis was conducted and the number of self-stress modes, mechanism displacement modes, and feasible prestress modes was calculated. Then, the formula for the initial prestress distribution of the structure was derived based on the node equilibrium equation. Furthermore, the geometric stability and initial prestress distribution of the structure with different rise-to-span ratios, number of circumferential struts, and hoop cables were studied. Finally, the dynamic properties of the structure are explored by finite element simulation. The analysis results show that the structure has excellent structural stability. The rise-to-span ratios, the number of circumferential struts, and hoop cables are the important factors affecting the geometric stability and the initial prestress distribution. The rise-to-span ratios have no effect on the number of structural modes, while the number of circumferential struts and cables will cause significant changes in the number of self-stress modes. The internal force of the structural members decreases with the rise-to-span ratio and the number of circumferential struts increases, and the number of circumferential struts has the greatest influence on its internal force. The structural natural frequency exhibits a dense distribution, which indicates that the structure has good stiffness. In summary, the research has provided an idea for the application of the deployable scissor-type strut cable dome structure as a new structural system in the field of structural engineering.

A simplified approach for judging and evaluating the contribution of higher-order modes to the wind-induced acceleration of high-rise buildings

Acceleration is the control parameter for the occupant comfort, often solved in the frequency domain with modal decomposition. In general, the first-order mode response is adopted to represent the total acceleration in practice. However, considering only the first-order mode has been demonstrated to yield underestimated results up to 20 %, while no exact criterion exists to determine whether higher-order modes require to be considered or not. Hence, underlying factors, like the structural natural frequencies, the excitation dominant frequencies, and the distributions of building masses/stiffness, which may significantly affect the contribution of higher-order modes to the acceleration, are analyzed first. Notably, the ratio of the natural frequency of the higher-order mode to that of the first-order mode plays a decisive role in the contribution of the higher-order mode's acceleration. Moreover, the third-order and beyond modes can be largely disregarded. Subsequently, an empirical approach is introduced to determine the need for considering high-order modes. Finally, a simplified formula for estimating acceleration response in the frequency domain is derived to consider second-order modal response. This study provides a method for determining the contribution of higher-order vibration modes to acceleration and a simplified formula to consider the higher-order modal response.

Operational Dynamic Load Testing for Repair Recommendations Case Study of Access Road to Vehicle Weight in Motion

The indication of inaccuracies in vehicle weight measurement using Weight in Motion (WIM) technology on mining roads has been identified due to the non-fulfillment of the design criteria required by the WIM manufacturer. This study aims to identify the gap between the actual pavement conditions and the design criteria and to design improvements to eliminate this gap. The method employed involves dynamic load testing, followed by processing the test data with operational modal analysis (OMA) to obtain dynamic parameters that will serve as a reference for calculating the pavement capacity. From OMA, a natural structural frequency of 26.342 Hz was obtained, while the theoretical calculation based on the design criteria was 29.481 Hz. This frequency decrease indicates structural damage of 10.65% and a capacity reduction of 26.8% from the design criteria. This finding is reinforced by a critical damping ratio of 5.25%, which is higher than the damping for intact concrete, ranging between 2%-5%. This indicates energy dissipation through concrete cracks. It is recommended to inject the cracks in the existing pavement with a cement base and perform a 130 mm overlay with mortar grout (fc’= 50 MPa) with one layer of M12 wire mesh. The connection with the old pavement will use concrete bonding and D13-600/600 chemical anchors. With this improvement, the structural capacity will become 104% of the design criteria.

Stochastic force identification for uncertain structures based on matrix equilibration and improved Tikhonov regularization method

Accurate identification and estimation of stochastic forces applied to in-service engineering structures play a vital role in structural safety assessments. This study devised an effective force power spectral density (PSD) identification method to address the challenge of identifying multipoint stationary stochastic forces in uncertain structures. Initially, a probability model was employed to characterize structural uncertainties. Subsequently, an integral relationship was established between the probability density function (PDF) of the random structural parameters and that of the stochastic force PSD. By employing a point-selection technique based on the generalized F-discrepancy and a smoothing method, the uncertainty problem was transformed into a finite number of stochastic force PSD identification problems for deterministic structures. Simultaneously, based on the inverse pseudo-excitation method, a matrix equilibration approach and an improved Tikhonov regularization method were used to address the problem of large identification errors near structural natural frequencies. In comparison to the traditional weighting matrix method, the proposed method further reduces the condition number of frequency response function matrices, thereby enhancing the accuracy of force PSD identification. Finally, numerical examples were presented to validate the effectiveness of the proposed method in solving the stochastic force identification problem.

Research on Quantification of Structural Natural Frequency Uncertainty and Finite Element Model Updating Based on Gaussian Processes

During bridge service, material degradation and aging occur, affecting bridge functionality. Bridge health monitoring, crucial for detecting structural damage, includes finite element model modification as a key aspect. Current finite element-based model updating techniques are computationally intensive and lack practicality. Additionally, changes in loading and material property deterioration lead to parameter uncertainty in engineering structures. To enhance computational efficiency and accommodate parameter uncertainty, this study proposes a Gaussian process model-based approach for predicting structural natural frequencies and correcting finite element models. Taking a simply supported beam structure as an example, the elastic modulus and mass density of the structure are sampled by the Sobol sequence. Then, we map the collected samples to the corresponding physical space, substitute them into the finite element model, and calculate the first three natural frequencies of the model. A Gaussian surrogate model was established for the natural frequency of the structure. By analyzing the first three natural frequencies of the simply supported beam, the elastic modulus and mass density of the structure are corrected. The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model is very small. This study demonstrates that Gaussian process models can improve calculation efficiency, fulfilling the dual objectives of predicting structural natural frequencies and adjusting model parameters.

Refinement and Validation of the Minimal Information Data-Modelling (MID) Method for Bridge Management.

Various approaches have been proposed for bridge structural health monitoring. One of the earliest approaches proposed was tracking a bridge's natural frequency over time to look for abnormal shifts in frequency that might indicate a change in stiffness. However, bridge frequencies change naturally as the structure's temperature changes. Data models can be used to overcome this problem by predicting normal changes to a structure's natural frequency and comparing it to the historical normal behaviour of the bridge and, therefore, identifying abnormal behaviour. Most of the proposed data modelling work has been from long-span bridges where you generally have large datasets to work with. A more limited body of research has been conducted where there is a sparse amount of data, but even this has only been demonstrated on single bridges. Therefore, the novelty of this work is that it expands on previous work using sparse instrumentation across a network of bridges. The data collected from four in-operation bridges were used to validate data models and test the capabilities of the data models across a range of bridge types/sizes. The MID approach was found to be able to detect an average frequency shift of 0.021 Hz across all of the data models. The significance of this demonstration across different bridge types is the practical utility of these data models to be used across entire bridge networks, enabling accurate and informed decision making in bridge maintenance and management.

Structural damage detection based on structural macro-strain mode shapes extracted from non-stationary output responses

Abstract Long-gauge fiber Bragg grating strain sensors have been widely employed because of their broader measuring range and higher sensitivity. However, current structural damage detection methods using macro-strain modal parameters are based on structural frequency response function or stationary power spectrum density, which are not applicable to non-stationary responses. To overcome this limitation, an improved method is proposed in this paper for structural damage detection based on structural macro-strain responses under unknown multi-point non-stationary excitations. First, a new concept of macro-strain energy spectrum transmissibility (MEST) is proposed using structural non-stationary macro-strain responses, and it is derived that MEST at a certain system pole equals the ratio of macro-strain mode shape. Then, the singular value decomposition technique is adopted for the MEST matrix to identify structural natural frequencies and macro-strain mode shapes. Finally, two damage detection indicators are constructed based on the identified normalized macro-strain mode shape (NMMS). The first indicator is the difference in structural NMMS before and after structural damage. The second one is based on the curvatures of structural NMMS, which can be used for structures without intact baseline. Numerical verifications are conducted to identify beam-type structural damage under multi-point non-stationary excitations or vehicle loads. Five damage scenarios with different measurement noise levels are investigated, and damage detection results validate the effectiveness of the proposed method.

Structural acceleration response reconstruction based on BiLSTM network and multi-head attention mechanism

The effectiveness of structural health monitoring often relies on the precise analysis of structural response data, with data completeness directly impacting the performance of monitoring systems. Addressing the common issue of data loss in structural health monitoring systems, this study proposes a Bidirectional Long Short-Term Memory (BiLSTM) network based on a multi-head attention mechanism for the reconstruction of missing structural acceleration responses. Firstly, employing a two-layer BiLSTM network to establish an encoder-decoder framework for extracting spatio-temporal correlation features among sensor data. Subsequently, innovatively embedding a multi-head attention mechanism into the network framework enhances the modeling capability of long-distance input elements and establishes dependencies among different sensors, thereby enabling the network to better capture the global features of input information. The proposed method undergoes validation through a numerical example of a simply supported beam, practical monitoring data on the Hardanger Bridge from the Norwegian University of Science and Technology, and an experimental study of steel frame structure from our laboratory. These validations are compared with alternative response reconstruction models. The experimental results make obvious that the proposed method demonstrates superior accuracy in response reconstruction. Additionally, the suitability of this method for modal identification is validated. Through the utilization of reconstructed responses, the method effectively discerns the structural natural frequencies with accuracy.

Research on abnormal vibration of high-speed train based on wheel-rail coupling modal analysis

During dynamic line testing of a high-speed train, it was observed that the vehicle exhibited significant abnormal vertical vibrations under specific track conditions. The frequency of this vibration varies with the train speed and exhibits harmonics through analysis. As the speed approaches 400 km/h, the peak frequency is close to 44 Hz, corresponding to the system structure's natural frequency. A finite element model of the wheel-rail coupling was established for modal analysis, which revealed that the coupling between the bogie and the track will form a bogie P2 force resonance mode, which closely matches the frequency range of the abnormal vibrations. A dynamic model of vehicle-track rigid-flexible coupling was established, to simulate vibration reproduction and the bogie P2 force resonance mode variation law. Additionally, irregularities of specific wavelengths on the track can excite this mode, leading to a significant increase in amplitude. Some sections of the track line have slab warping, with a wavelength of approximately 2.45m. The frequency range of excitation formed when the vehicle speed approaches 400 km/h is close to that of the bogie P2 resonance mode. As a result, coupling resonance occurs between the vehicle and track systems, ultimately causing abnormal vibrations.

Feasibility Study of Earthquake-Induced Damage Assessment for Structures by Utilizing Images from Surveillance Cameras

Rapid and accurate structural damage assessment after an earthquake is important for efficient emergency management. The widespread application of surveillance cameras provides a new possibility for improving the efficiency of assessment. However, it is still challenging to directly assess the structural seismic damage based on videos captured by indoor surveillance cameras during earthquakes. In this study, we elaborate on the concept of estimating the structural natural frequency based on the relative pixel displacement of inter-stories. Furthermore, we propose a strategy for post-earthquake structural damage assessment that integrates the computer vision and time-frequency analysis. This approach aims to navigate the difficulties inherent in earthquake damage assessment and improve emergency responses. The relative pixel displacement between the camera and the fixed features on the floor is extracted from videos by using the Harris corner detection and Kanade–Lucas–Tomasi algorithms. The structural natural frequency is estimated using the synchroextracting transform-enhanced empirical wavelet transform. The natural frequency shift-related seismic damage index is defined and calculated for damage assessment. A shake table experiment of a small-scale steel model is conducted to verify the accuracy and feasibility of the approach, and the practicality of the proposed approach is further verified by utilizing the data from a full-scale reinforced concrete benchmark model experiment. The results demonstrate that the approach can accurately and efficiently evaluate the structural damage after an earthquake based on the video captured by surveillance cameras during the earthquake. The error of the acquired damage index is less than 0.1. We will apply more advanced algorithms in the future to alleviate this problem.

Analytical solution to a coupled system including tuned liquid damper and single degree of freedom under free vibration with modal decomposition method

This research focuses on employing a linear analytical approach to transform free surface waves and velocities into mode coordinates, with the aim of investigating the free vibration behavior of a coupled system consisting of a Single Degree of Freedom and a sloshing tank. Through a series of manipulations and simplifications of the coupled equations, a fourth-order ordinary differential equation is derived to showcase the overall response of the system, highlighting the contribution of each odd mode. Key concepts explored include system stability, mode-specific natural periods, establishment of initial boundary conditions, and formulation of the complete system response. The analytical method applied to study Tuned Liquid Dampers, a type of elevated sloshing tank, reveals that in higher modes, the lower frequency aligns with the structural natural frequency, while the higher frequency is approximately n times the structural natural frequency (where n is the odd mode number). This approach also elucidates why the system's response does not exhibit a higher-frequency component in higher modes. The study further investigates concepts such as employing an initial perturbation to excite higher frequencies and the potential for approximating the system through the first mode. Additionally, a numerical model was developed using variable separation and modal decomposition methods to complement and validate the analytical approach. Finally, further verification of the model was performed using the Preismann scheme applied to the relevant equations and the central upwind applied to nonlinear equations.

Utilizing data-driven algorithms for blind modal parameter identification of structures from output-only video measurements

In structural dynamics and vibration analysis, modal identification plays a pivotal role in understanding and characterizing the dynamic behavior of complex systems. Traditional modal analysis techniques heavily rely on accurate sensor placement and knowledge of the excitation forces, which may not always be feasible or practical in real-world scenarios. Recently, non-contact video-based modal analysis methods for structures with arbitrary complexity using computer vision techniques have gained much importance. But these methods need to know ahead of time where the structure's natural frequency ranges are, and they use steerable pyramids, which are complicated multi-scale image decomposition filters. To address these issues, a blind modal identification technique is suggested to extract the modal parameters (modal frequency and mode shapes) from the recorded structural vibration video signal. The proposed algorithm for unsupervised machine learning is the Non-Negative Matrix Factorization (NNMF) method, which is combined with the Generalized Complexity Pursuit (GCP) method for blind source separation. The NNMF algorithm is directly applied to the raw pixel-time series made from the video data to get the temporal components, which are then separated using GCP to find the individual modal frequencies and mode shapes. The above algorithm is first validated on a numerical model and then implemented on laboratory scale models (cantilever, single-degree, and multi-degree frame models). Finally, the proposed methodology is implemented on real-world recorded structural vibration videos to determine its noise sensitivity, such as the Tacoma Narrows bridge and the London Millennium footbridge. The modal parameters extracted are compared with those from the available literature for validation. The estimation errors obtained from all the validations are well below 1%, which makes the technique quite suitable and reliable for structural vibration monitoring by identifying and reproducing complex vibration modes.

A symmetric substructuring method for analyzing the natural frequencies of conical origami structures

Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorption capacity. Previous investigations have commonly focused on the static characteristics of these lightweight structures. However, the efficient analysis of the natural vibrations of these structures is pivotal for designing conical origami structures with programmable stiffness and mass. In this paper, we propose a novel method to analyze the natural vibrations of such structures by combining a symmetric substructuring method (SSM) and a generalized eigenvalue analysis. SSM exploits the inherent symmetry of the structure to decompose it into a finite set of repetitive substructures. In doing so, we reduce the dimensions of matrices and improve computational efficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis. Finite element simulations of pin-jointed models are used to validate the computational results of the proposed approach. Moreover, the parametric analysis of the structures demonstrates the influences of the number of segments along the circumference and the radius of the cone on the structural mass and natural frequencies of the structures. Furthermore, we present a comparison between six-fold and four-fold conical origami structures and discuss the influence of various geometric parameters on their natural frequencies. This study provides a strategy for efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contribute to the efficient design and customization of origami metastructures with programmable stiffness.

Numerical Investigation on the Mechanism of Solid Rocket Motor Instability Induced by Differences between On-Ground and In-Flight Conditions

A solid rocket motor (SRM) with a high aspect ratio that performs normally during ground tests may experience instability during flight. To address this issue, this study employs the pulse triggering method and the numerical approach of two-way fluid–structure interaction to investigate the mechanisms behind the SRM instability resulting from distinctions between on-ground and in-flight conditions. The results indicate that the main distinctions between the on-ground and in-flight conditions for SRMs are the strong constraints during the ground test, as well as aerodynamic forces and aerodynamic heating during flight. The strong constraints in the ground test effectively suppress structural vibrations by limiting displacements. In flight conditions, the aerodynamic heating reduces the strength of the SRM casing and aerodynamic forces provide sustained energy input for structural vibrations during flight. The mechanism for the ground/flight differences that induce SRM instability is that the structural natural frequencies are reduced by aerodynamic heating and the first-order acoustic frequency increased by the propellant regression approach reaches the resonance condition. Therefore, an instability factor Φ is proposed to represent the resonance relationship between the structural natural modes and the acoustic mode of SRMs. Furthermore, the closer the frequency of the aerodynamic forces is to the resonance frequency of the acoustic-structure coupling, the more pronounced the SRM instability.

Response of flexible structures to air-blast: nonlinear compressibility effects in fluid–structure interaction

This paper presents a coupled model that considers the nonlinear compressibility effect in fluid–structure interaction (FSI) during air-blast loading on flexible structures. In this coupled model, structural behaviour is idealized as a linear single-degree-of-freedom mass-spring-damper system whereas nonlinear fluid compressibility is considered by applying Rankine–Hugoniot jump conditions across a moving plate. The surrounding fluid medium is modelled with an ideal gas equation and hence, this model can be applied for FSI analysis with relatively strong shocks (reflection coefficient of up to 8). The nonlinear compressibility of the fluid medium at the backside of the plate is also considered in this coupled formulation and its effects on the structural responses are examined. Moreover, the negative/underpressure phase of the reflected wave profile, which is typically neglected in a decoupled model, is also considered in the proposed model and its influence on the structural response is also investigated. The study reveals that the nonlinear compressibility of fluid medium significantly influences the coupled FSI phenomena, especially in flexible lightweight structures. Numerical examples are presented to highlight the implications of the nonlinear compressibility effect in FSI on the reflected pressure profile and the response of flexible structures. Parametric dependencies of response on structural mass and natural frequency are examined thoroughly and a response spectrum is obtained. It is envisaged that the lightweight protective structure design under higher blast intensity may benefit from this study.

Analysis of free in-plane vibrations of a rectangular plate with various boundary conditions canonical form using the modified Riley-Ritz method

This paper investigates the free in-plane vibrations of rectangular sheets under various boundary conditions using an improved Riley-Ritz method. A novel approach involving graph theory and canonical forms is introduced, marking a first in the study of symmetric structures. The research presents an advanced version of Riley’s theory for accurately computing the natural frequencies of structures, showing significant improvements in efficiency and precision over traditional methods like Monte Carlo simulations. Key findings include the ability of the upgraded Riley theory and graphs to conduct comprehensive structural reliability and sensitivity analyses, particularly in evaluating changes in failure risk and aiding in precise design. Numerical analysis demonstrates the method’s rapid convergence and accuracy, proving its effectiveness in structural analysis. The study also explores the impact of geometric parameter variations on the free vibrations of rectangular sheets, offering crucial insights for various engineering applications. These findings have broad implications in mechanical, marine, aerospace, and civil engineering, particularly in the design and analysis of structural components such as fuselages, airplanes, missiles, and tank bottoms.

Research on the vibration mechanism of compressor complex exhaust pipeline based on transient flow

The periodic exhaust of the compressor often induces gas flow fluctuations within the pipeline, leading to vibrations. Excessive vibration can lead to fatigue, cracks, loosening of components, and resulting in local leakage, which may easily lead to fire, explosion, and secondary hazards. Therefore, in this paper, a computational model for the transient flow field of the compressor exhaust pipeline was established, using the pulse excitation method and Fluent software, the natural frequencies of the gas column in the pipeline were calculated, and the patterns of oscillation decay of the gas column wave propagating back and forth within three exhaust pipes were researched. The mechanism behind the pipeline pressure pulsation and the influence of pipeline structural parameters on the natural frequencies of the gas column were explored. The calculation results show that the first-order natural frequency of the gas column is very close to the double frequency of the compressor excitation frequency at 3.33Hz, and the second-order natural frequency of the gas column is very close to the quadruple frequency of the compressor excitation frequency at 3.33Hz, which may cause significant pipeline vibrations. Altering the pipeline structure, especially when influenced by airflow branching after a tee junction, results in complex changes in the natural frequencies of the gas column. Furthermore, the structural natural frequencies of the pipeline were obtained through the finite element. It has been observed that resonance phenomena exist among the structural natural frequencies and their harmonics of the pipeline and the natural frequencies of the gas column and their harmonics, as well as multiples of the excitation frequency. These results lay the foundation for understanding the vibration mechanism of the pipeline and finding ways to reduce vibration.

Wind Load Model and Response Spectra of Overbridges Subjected to Train-Induced Wind Loads

The vibration of pedestrian overbridges due to train-induced wind loads (TIWLs) during the passage of a high-speed train threatens the overbridge safety and causes pedestrian discomfort. To incorporate the structural dynamic magnification effect on overbridges under TIWLs in the design process, a framework to calculate the structural dynamic response, equivalent static TIWLs and response spectra of overbridges is established. A new simplified TIWL model with a “three-segment” wind pressure time history described by harmonic functions is proposed. This model facilitates the acquisition of analytical solutions for the structural dynamic response, streamlining the analysis process. The dynamic response and equivalent static TIWLs based on dynamic magnification factors (DMFs) of overbridges are obtained from the analytical method. The DMFs are primarily affected by the structural natural frequency and the characteristic frequency of TIWLs. Furthermore, based on the analytical solution of the overbridge dynamic response, parametric analysis is performed, and the response spectra representing the dynamic displacement and acceleration of overbridges are developed. The response spectra can be used to quickly calculate the displacement, internal force, and acceleration of the overbridges during engineering applications, which is more convenient but slightly less accurate than the analytical method.