Nonlinear Response Analysis Research Articles

Dynamic instability and nonlinear response analysis of nanocomposite sandwich arches with viscoelastic cores

This paper presents a comprehensive study of the nonlinear dynamic behavior and snap-through phenomena in sandwich arch structures with viscoelastic cores and carbon nanotube-reinforced nanocomposite face sheets. Subjected to uniform time-dependent pressure shocks, these arches exhibit complex snap-through behavior critical for practical engineering applications. Utilizing third-order shear deformation theory, the study accurately captures nonlinear behaviors. The viscoelastic core, modeled with the Kelvin-Voigt law, enhances damping and reduces vibration amplitudes. Numerical solutions are obtained using a Chebyshev-based Ritz method, Newmark integration, and Newton-Raphson method. The Budiansky-Ruth criterion evaluates dynamic buckling loads. Key findings include significant instability near buckling loads, increased buckling loads and vibration damping due to viscoelastic effects, reduced buckling loads with foam cores, improved performance with CNTs, and more pronounced CNT effects with greater deflections. Additional conclusions highlight the sensitivity of dynamic snap-through to geometric parameters and the superior accuracy of the proposed approach compared to traditional models. This research advances the understanding and design strategies for nonlinear sandwich arch structures, enhancing predictive capabilities in complex structural systems.

Nonlinear seismic response analysis of long-span railway cable-stayed bridges crossing strike-slip faults

Active faults along railways in the mountainous regions of western China pose significant challenges to bridge safety. To ensure the safe operation of long-span railway bridges under complex geological conditions, this study investigates the synthesis of artificial ground motions for bridges crossing strike-slip faults and analyzes their nonlinear seismic response. First, we develop a theoretical method for simulating high- and low-frequency seismic motions using a finite fault and an equivalent velocity pulse model. Next, using a specific long-span railway cable-stayed bridge as a case study, we construct a nonlinear finite element model with OpenSees software. Finally, we assess the seismic response of key bridge components considering various crossing angles, seismic amplitudes, fault rupture directivity, and fling-step effects. The results show that the crossing angle significantly influences the seismic response, with longitudinal and transverse responses exhibiting opposite patterns. Additionally, the scaling factor of seismic motion significantly affects bridge response. For bridges crossing strike-slip faults, the longitudinal response exhibits a sudden increase in displacement due to instantaneous velocity pulses, while the transverse response shows notable residual displacement influenced by the fling-step effect. However, the critical section curvatures of bridge towers and piers remain within the elastic range across all crossing angles, indicating that controlling large displacement deformations is crucial for the seismic design of bridges crossing strike-slip faults.

Nonlinear Frequency Response Analysis of Distributed Parameter Systems with One Spatial Coordinate

AbstractThe objective of this paper is to investigate possible strategies for applying nonlinear frequency response (NFR) analysis based on the concept of higher‐order frequency response functions to distributed parameter systems. Three approaches are presented and compared: one based on applying the existing procedure directly to the partial differential model, and two based on approximation of the distributed parameter system with a series of lumped parameter segments. One of them treats the complete series of segments integrally, while the other treats it segment by segment, so it uses only the model of a single segment. A simple example, an isothermal plug‐flow reactor with a simple reaction mechanism, is used as a case study. Pros and cons for all three approaches are given.

Simplified site response analysis for regional seismic risk assessments

Seismic risk assessment on a regional scale requires an estimation of ground motion intensity and its spatial variation over large geographical areas. This task is particularly challenging in the presence of very soft soil deposits where significant amplification occurs at specific frequencies that are often referred to as local resonances. It is often not feasible to conduct a nonlinear site response analysis at thousands of sites of interest across a region such as an urban area due to the computational effort involved and the required detailed information on soil profiles at each site. Thus, in regional seismic risk analyses the hazard is typically represented by a field of response spectral ordinates estimated by ground motion models. This study proposes a simplified site response analysis procedure to improve the characterization of spectral ordinates to be used in regional seismic risk assessments. In the proposed procedure, reduced-order models are used to conduct site response analysis using very few parameters to transform response spectra at rock outcrop into response spectra at the surface of each of the sites. A particular emphasis is given to soft-soil sites characterized by low shear-wave velocities overlaid on rock or firm soils. A non-uniform continuous shear beam model with a parabolic variation of shear modulus along the depth and modal damping is used in combination with Random Vibration Theory. It is shown that the proposed approach provides better estimates than those of ground motion models or physics-based ground motion simulation models which often cannot capture the local resonances. Site-specific validation of the shear beam model and overall simplified site response analysis is performed at four soft-soil sites in San Francisco, California. Despite its simplicity, it is shown that the proposed procedure adequately captures the amplitudes and spectral shapes of the motions. It is also shown that in conjunction with ground motion models or physics-based models, the proposed simplified site response analysis procedure can be used to efficiently simulate the seismic hazard on a regional scale through an example of a regional seismic hazard analysis of 160 softer soil sites in Downtown San Francisco during the Loma Prieta earthquake.

Quantitative Property of MF-Discrepancy and Efficient Point-Selection Strategy for the Nonlinear Stochastic Response Analysis of Structures with Random Parameters

The response analysis of high-dimensional and strongly nonlinear systems with random parameters remains a significant challenge in stochastic computational mechanics. To address this challenge, some methods based on the high-efficacy point sets have been developed, in which efficient global-point-set methods represented by low-discrepancy are of paramount importance in generating representative point sets. Several discrepancies including the extended F-discrepancy (EF-discrepancy) and the generalized F-discrepancy (GF-discrepancy) have been introduced to assess the uniformity and the efficacy of a representative point set. In such context, a maximal marginal EF-discrepancy (MF-discrepancy), which is an extended form of the GF-discrepancy, is proposed in this paper and then the properties of the MF-discrepancy are studied in detail. The probability distribution of the MF-discrepancy is derived, including a rigorous proof for random point sets and a model based on an assumption for some generic point sets. A generalized Koksma-Hlawka inequality is established accordingly to govern the worst error estimate. The lowest bound of the MF-discrepancy is given, and two intuitive quantitative indices are proposed to measure the goodness of the MF-discrepancy. Based on the lowest bound, an enhanced point-selection strategy with a unified theoretical framework for minimizing the MF-discrepancy is proposed. In this framework, locally minimizing the MF-discrepancy yields the two-step point-selection method, and a new point-selection strategy is proposed based on the global minimization of the MF-discrepancy, which is verified to be efficient and robust, especially in high-dimensional cases. Several numerical examples, including a 2-story shear frame, a 10-story shear frame, and a 10-story reinforced concrete frame structure modeled by the finite element method, are studied, verifying the efficiency and the robustness of the proposed point-selection strategy.

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

Nonlinear seismic response analysis of liquefiable sites based on effective stress method

In this study, the one-dimensional nonlinear Matasovic model was extended to the two- and three- dimensional stress space by replacing the shear strain with the generalized shear strain. The extended Matasovic model was subsequently combined with Dobry’s excess pore water pressure generation model, and the reliability of the proposed loosely coupled effective stress analysis model was verified through undrained cyclic triaxial tests and a one-dimensional site response analysis. Finally, this method was applied to an engineering site in China to evaluate the nonlinear seismic response of liquefiable sites. The results show that the proposed effective stress analysis method can capture the dynamic behavior of the soil and the generation of pore water pressure during strong shaking. Moreover, there are differences between the proposed effective stress analysis method and the total stress analysis method for liquefiable sites, which indicates the need for careful selection in practical applications.

Nonlinear modeling and vibration response analysis of rod fastening rotor-bearing system with curvic coupling

Rod fastening combined rotor system (RFCR) are particularly popular in gas turbine rotor systems. The bolted connection introduces a discontinuity in this RFCR, which has a substantial influence on system performance.Traditional models of RFCR tend to neglect the influence of the connection structure, especially failing to fully consider the contribution of the curvic coupling to the rotor dynamics. To address this problem, this study proposes a new nonlinear analytical model of the rotor system, which focuses on the impact of the curvic coupling. This study provides a detailed analysis of the structural parameters and load forces of the curvic coupling. Based on this analysis, a mechanical model is created to assess how bolt preload and torque impact the stiffness of the curvic connection. The stiffness matrix of the curvic coupling is derived by the gear stiffness analysis method, and the accuracy of the model is confirmed using the finite element method. Furthermore, the model also considers the viscous and sliding state between the curvic coupling, which effectively describes the damping effect of the curvic coupling. On this basis, the motion control equations for the RFCR are formed, and a dynamic model considering the curvic connection in the RFCR system is introduced. The results show that the curvic coupling results in a decrease in stiffness and the occurrence of nonlinear damping phenomena in the RFCR.The RFCR exhibits a significant stiffness loss compared to the continuous rotor system, resulting in a decrease in the critical rotor speed. The nonlinear damping is mainly excited at high friction coefficient conditions and may lead to a self-excited vibration component in the rotor response at supercritical speeds. The negative impact of structural discontinuities on rotor dynamic performance can be reduced by increasing the bolt preload, decreasing the friction coefficient, and adjusting the amount of imbalance. This study offers a theoretical foundation for predicting curvic coupling-induced instability and serves as a reference for enhancing rotor system stability.

Full-, Half-, and Symmetrical Cell Analysis of Lithium-Ion Battery Using Impedance and Nonlinear Frequency Response

This study presents an in-depth analysis of the cathode and anode of a commercial 18650 lithium-ion battery by comparing their dynamic behaviors systematically with that of two additional experimental cell setups: (i) full-cell in a three-electrode setup and (ii) symmetrical cathode and anode cells. The analysis involves subjecting the cells to electrochemical impedance spectroscopy, distribution of relaxation times, and nonlinear frequency response analysis at different state-of-charges. Our findings highlight the importance of analyzing the electrodes in all three setups. The impedance and nonlinear frequency response features of the full-cell are also observed in the electrode-resolved cells. Symmetrical cells exhibit stronger impedance and nonlinear responses compared to the commercial cell and the cell with reference electrode, yet they allow identifying contributions of the single cells without artifacts from inductive loops caused by the reference electrode. By correlating nonlinear signals and characteristic peaks across different cell setups, cathode and anode processes and their respective characteristic frequencies can be clearly identified.

A general element for shell analysis based on the scaled boundary finite element method

AbstractA novel technique, the scaling surface‐based Scaled Boundary Finite Element Method (SBFEM), is introduced as a method for formulating a general element for shell analysis. This displacement‐based element includes three translational degrees of freedom (DOFs) per node. Notably, only two‐dimensional discretization for one of the two parallel shell surfaces, referred to as the scaling surface, is necessary. The interpolation scheme for the scaling surface is postulated to be applicable to all surfaces parallel to it in the thickness. The derivation strictly adheres to the 3D theory of elasticity, without making additional kinematic assumptions. As a result, the displacement field along the thickness is analytically solved, and the element formulation is immune to transverse locking, membrane locking, and other issues, eliminating the need for additional remedies. Extensive investigations into the robustness and accuracy of the elements have been conducted using well‐known benchmark problems, along with additional challenging problems. Numerical examples confirm that the element formulation is free from transverse shear locking and membrane locking. Moreover, the proposed formulation is easily extendable to cases involving shell elements with varying thickness and holds the potential for extension to the nonlinear response analysis of shell structures.

Spatial mapping of the seismic vulnerability index in Kathmandu Valley: insight from dominant frequency and amplification factor

Abstract Kathmandu Valley situated in Nepal has experienced several earthquakes in the past. The expanding population of Kathmandu Valley is driving a significant acceleration in building construction reaching record levels and posing risks to both human lives and the economy, despite this surge in development. This study aimed to spatially map the dominant frequency, amplification factor, and vulnerability index map of Kathmandu Valley, Nepal using ArcGIS. This paper presents the nonlinear response analysis of 225 boreholes using the Gorkha earthquake as input motion and DEEPSOIL software for determining the amplification ratio and dominant frequency. The results revealed a range of values for dominant frequency from 0.08 to 7.65 Hz and soil amplification ratio from 0.13 to 8.14. Furthermore, the seismic vulnerability index was derived from the dominant frequency and soil amplification ratio ranging from 0.22 to 21.84. The resulting maps acquired through this study enable the decision-makers and stakeholders, to prioritize resources and implement targeted measures for enhancing seismic resilience in the region.

Prediction of Ground Response Spectrum of Jalandhar City of Punjab using Non-Linear Ground Response Analysis

Prediction of Ground Response Spectrum of Jalandhar City of Punjab using Non-Linear Ground Response Analysis

Nonlinear transient response analysis of rotating carbon nanotube reinforced composite cylindrical shells with initial geometrical imperfection

Nonlinear transient response analysis of rotating carbon nanotube reinforced composite cylindrical shells with initial geometrical imperfection

Nonlinear dynamical modeling and response analysis of complex structures based on assumed mode weighting

The assumed mode method (AMM) is widely used for dynamical modeling but faces increasing challenges in developing low-dimensional and high-precision models of complex structures for investigations of nonlinear dynamical responses and active vibration control. This is mainly because the current complex structure has an increasing number of components, each of which needs to be discretized by multiple assumed modes in dynamical modeling, leading to increasing degrees of freedom for the system. To address this issue, this paper proposes a dimension-reduced method based on the assumed mode weighting method, referred to as Mode Weighting Method (MWM). The modeling process of a multi-beam structure is fully presented as an example to show the strategy of the MWM. During this process, the assumed mode (AM) model (the dynamic model derived in terms of a set of assumed modes) is developed first where the joints of the structure between its components are considered as artificial springs and each component is discretized by its vibration modes without constraints. The components of the eigenvector of the characteristic equation derived from the AM model are taken as the weighting coefficients to get the approximate analytical global modes of the structure by multiplying the corresponding assumed modes. Consequently, a nonlinear dynamic model with a few degree of freedom is obtained by discretizing the structure with the weighted modes. Moreover, a technique for simply obtaining the weighted mode (WM) models by directly processing the AM model through a transformation matrix is presented. To validate the proposed method, the simulations on the natural characteristics and the dynamical responses for both linear and nonlinear models, are performed respectively based on the WM and the finite element models, where both results are well matched each other. This work provides a new way of developing advanced dynamical modeling methods for structural dynamics design, optimization, and active vibration control.

Periodic foundation piles for the seismic protection of structures

This study introduces a novel solution for seismic protection of structures based on resonant metamaterials, named Periodic Foundation Piles, which can be integrated with deformable soil deposits in order to filter shear waves in a specific frequency range. A Periodic Foundation Pile consists of an array of vertical periodic structural elements containing internal resonators suitably tuned to one or more natural frequencies of the soil deposit. The proposed system is equivalent to a discontinuous foundation pile and can be installed in the ground with approximately the same procedure for piles, thus making it suitable also for applications in existing structures. The performance of the Periodic Foundation Piles in reducing the amplitude of a seismic motion has been shown through non-linear site response analyses carried out using real acceleration records as input motion. A soil deposit with an increasing shear wave velocity profile has been considered; the nonlinear behaviour of the soil has been modelled through the Iwan model, calibrated using a normalized secant shear modulus curve accounting for the influence of the confining pressure on the stress-strain relationship. Numerical results, presented in terms of peak acceleration, horizontal displacement and shear deformation profiles, as well as in terms of Fourier amplitude and response spectra, indicate that Periodic Foundation Piles may noticeably reduce the amplitudes of seismic motion in a suitable frequency range, hence potentially representing an innovative strategy to mitigate the effects of earthquakes on structures.

Nonlinear seismic response analysis of slopes considering the coupled effect of slope geometry and soil stratigraphy

SUMMARY To investigate the effects of slope geometric parameters and soil stratigraphic properties on the topographic amplification of ground motions, a large number of 2-D horizontally layered slope models are constructed. First, the linear and nonlinear seismic responses of a slope model are compared, and the result shows that the nonlinear characteristics of soils should be considered when studying the amplifying effect of slope topography on ground motions. Then, the nonlinear seismic responses of these slope models are analysed from four aspects: the maximum shear strain in the slopes, the effects of geometry and stratigraphy on the seismic response, the distance between the maximum topographic amplification indicators and the slope crest, and the influence range of slope topography behind the slope crest. The results indicate that the amplifying effect of slope topography on ground motions increases with increasing slope height or decreasing average shear wave velocity of the overlying soil layers. Besides, the variation of the topographic amplification effect with slope gradient is significantly influenced by soil stratigraphic properties. The distance between the maximum topographic amplification indicators and the slope crest is mainly in the range of 0–60 m, and the influence range of slope topography behind the slope crest is mainly in the range of 0–150 m. Subsequently, approximate relations are derived based on regression analyses of simulation results, which can provide meaningful references for the seismic design and seismic retrofitting of engineering structures behind the slope crest. Finally, the effects of slope geometric parameters and soil stratigraphic properties on ground motion modifications are further evaluated according to the prediction curves provided by the approximate relations.

Nonlinear mechanical response analysis and convolutional neural network enabled diagnosis of single-span rotor bearing system

The wide application of rotating machinery has boosted the development of electricity and aviation, however, long-term operation can lead to a variety of faults. The use of different measures to deal with corresponding malfunctions is the key to generating benefits, so it is significant to carry out the fault diagnosis of rotating machinery. In this work, a test bench for single-span rotor bearings was established, three faults, including spindle bending, spindle crack without end loading and spindle crack with end loading, are experimental analyzed with basic mechanical response. Moreover, a diagnosis is performed using a convolutional neural network, according to the differences in mechanical responses of the three faults obtained from experiments. For three faults, the change in the properties of spindle itself results in different axis trajectories and spectra. Compared with spindle bending fault, spindle crack fault not only cause 1×, 2×, 3× frequency component excitation, also 4×, 5× frequency component excitation. Additionally, the classification accuracy of the training set and the test set under machine learning for the three types of working conditions is 100%. This indicates that the network can significantly identify signal features so as to make effective fault classification.

Nonlinear Aeroelastic Response Analysis of Wing with Flared Folding Wingtip

Nonlinear Aeroelastic Response Analysis of Wing with Flared Folding Wingtip

Comparative Study of One-Dimensional Site Response Analysis on Deep Soft Clay Deposit using DEEPSOIL and NERA

Numerous high-rise buildings have been built in major cities in Indonesia. In high seismicity areas, such as Surabaya, the seismic behavior of structures is notably affected by the seismic characteristics of the subsurface soils. Typically, site-specific response analysis (SSRA) is conducted to determine the peak ground acceleration experienced at the ground surface. This paper compares one-dimensional site response analysis on deep soft clay deposits in Surabaya city using two commonly used 1D site response programs: DEEPSOIL and NERA (Non-linear Earthquake Site Response Analyse). A soil column model with 24 m thick very soft clay was developed. To represent different ground motion intensity, three levels of input motion were applied at the bedrock with peak ground accelerations (PGA) of 0.07g, 0.3g, and 0.51g. These input motions were then applied in a one-dimensional non-linear site response analysis to evaluate the seismic soil response at the surface. The evaluation involves examining the peak ground acceleration (PGA) and maximum shear strain profiles obtained from both software programs. The results indicate that the non-linear analysis conducted with NERA yielded greater amplification factors across all periods compared to the results obtained from DEEPSOIL. For the low-intensity motion, both software showed amplification of the input motion for all periods. In contrast, the spectral response obtained with DEEPSOIL demonstrated de-amplification trends for periods less than 1 s for the case of medium and high-intensity motions, whereas no de-amplification was observed from the results of NERA. This difference results in the amplification for medium and high-intensity motions can be attributed to the strength correction factors that are implemented in the DEEPSOIL software to take into account the representative shear strength of the soil layers.

Softening-based interface model and nonlinear load-settlement response analysis of piles in saturated and unsaturated multi-layered soils

This work presents a simplified method for the nonlinear analysis of the load–displacement response of piles in multi-layered soils. As a starting step, a new interface model based on the disturbed state concept (DSC) is put forth to simulate the interface shear stress-displacement relationship by considering the nonlinear hardening–softening behaviour. In the new model, input parameters can be conveniently calibrated using conventional interface shear tests or on-site tests. The good agreement between predictions and experimental data from interface direct shear tests validated the performance of the proposed DSC model. The DSC model performed better in terms of predictions when compared to the hyperbolic one. Next, the soil-structure interface model and bearing capacity theory are coupled to provide a theoretical framework for the analysis of pile load-transfer in saturated and unsaturated multi-layered soils, where the DSC model is employed to represent base resistance as well as skin friction. This work also discusses the profile of steady-state in-situ matric suction, soil–water characteristic curve, and pore-water pressure of unsaturated soils. The proposed method has the advantage of being used in practice as it is simple to obtain input parameters from laboratory tests, as well as Standard Penetration or Cone Penetration Tests. The proposed framework is finally applied to the analysis of five well-documentedcase studies. The proposed approach and the static load test results from the field measurements are found to be in satisfactory agreement, indicating that the proposed method performs well. The proposed method is suggested to be utilised for preliminary analysis, planning a suitable programme of loading tests, as well as optimizing the pile design by back analysis ofthe load test results.