Nonlinear Dynamic Analysis Research Articles

Performance-based seismic design of sliding gusset plate braced frames incorporating thermodynamic models

A sliding gusset plate braced frame (SGBF) is proposed to enhance the seismic resilience of steel concentrically braced frames (CBFs). The symmetric friction connection (SFC) is used at the brace-to-gusset plate connection to create a sliding gusset plate brace. The sliding gusset plate brace offers high initial stiffness to withstand wind and service level earthquake loads. It also absorbs energy through friction beyond service level earthquakes, which mitigates performance degradation caused by brace buckling. Besides, replaceable links are added to the beam ends where plastic hinges are anticipated to form, creating a dual system that allows for damage control and rapid repair. The paper first presents the design concepts and performance objectives of SGBFs. Subsequently, a thermodynamic model is established to reveal the energy–temperature–coefficient of friction (CoF) (E-T-μ) relationship based on quasi-static tests of SFCs. The model partially tackles and addresses the challenge of temperature-dependent variations in CoF during sliding. By incorporating the model into performance-based seismic design, the overstrength ratio of SFC due to temperature-induced hardening can be quantified, according to the energy absorption demand of a specific SGBF during an earthquake. In this manner, unexpected damage and failure of members adjacent to the SFC and sliding gusset plate braces can be avoided. To demonstrate the application of the thermodynamic model and verify the seismic performance of SGBF, a prototype is designed based on a practical four-story hospital and validated through an excessive array of nonlinear dynamic analyses. The results show that the proposed SGBF can achieve the targeted performance objectives under different seismic shaking intensities. In addition, the SGBF has a sufficient margin of safety against collapse. Hence, the proposed SGBF can be used as an efficient and resilient structural system in high seismic zones.

Analysis of Progressive Collapse Resistance in Precast Concrete Frame with a Novel Connection Method

The configuration of beam–column joints in precast concrete (PC) building structures varies widely, and different connection methods significantly affect the progressive collapse resistance of the structure. This study investigates the progressive collapse resistance of an innovative beam–column connection node frame. Finite element models of four-story, two-span space frame structures made of reinforced concrete (RC) and PC were developed using ANSYS 14.0/LS-DYNA R5.x software, employing nonlinear dynamic and static analysis to examine structural collapse behavior under bottom middle or corner column damage. Numerical results indicate that following the failure of the middle or corner column due to explosion loading, the vertical displacement and collapse rate of the PC structure with the novel connection method are less than those of the RC structure during collapse progression. Furthermore, upon removal of the middle or corner column, the residual load-carrying capacity of the PC structure with the innovative connection increased by 7% and 3.7%, respectively, compared to the RC structure. This suggests that PC structures with this type of connection demonstrate superior performance in resisting progressive collapse, offering valuable insights for future engineering applications.

Seismic fragility and resilience assessment of steel frame with replaceable T-stub connection components

Based on a rational design, steel beam-column joints with replaceable T-stub connection components (SBCJ-RTCCs) possess superior structural fuse performance and seismic resilience performance. To further evaluate the benefits of steel frames using RTCCs in terms of dynamic response, structural and non-structural components damage as well as seismic resilience, a 12-story steel frame equipped with RTCCs (SF-RTCCs) and a steel moment resisting frame (SMRF) were designed and established. On the basis of validating the simulation results with the experimental findings, the nonlinear dynamic analyses and incremental dynamic analysis (IDA) based seismic fragility analysis was performed. The results confirm that the introducing RTCCs into steel frames can significantly mitigate base shear and floor acceleration as well as produce a more uniform inter-story deformation and a more rational yielding mechanism. Meanwhile, the SF-RTCCs can obtain comparable collapse-resistant performance compared to SMRF, and both frames possess sufficient redundancy to resist structural collapse. Thanks to the lower floor acceleration responses, the SF-RTCCSs performs much better than SMRF in controlling non-structural components damage. After DBE excitations, the probabilities of RTCCs can be replaced by 1st class and 2nd class was 17.2 % and 84.9 %, respectively. After MCE excitations, RTCCs has about 29.3 % and 67.2 % probability that it can be replaced by 2nd class and 3rd class, respectively. Considering the lower economic losses, short repair time and fewer casualties, the rating of seismic resilience of SF-RTCCs was enhanced from one-star of SMRF to two-star.

An asymmetric rotor model under external, parametric, and mixed excitations: Nonlinear bifurcation, active control, and rub-impact effect

This article explores the nonlinear dynamical analysis and control of a [Formula: see text] DOF system that emulates the lateral vibration of an asymmetric rotor model under external, multi-parametric, and mixed excitation. The linear integral resonant controller ([Formula: see text]) has been coupled to the rotor as an active damper through a magnetic actuator. The complete mathematical model, governing the nonlinear interaction among the rotor, controller, and actuator, is derived based on electromagnetic theory and the principle of solid mechanics. This results in a discontinuous [Formula: see text] DOF system coupled with two [Formula: see text] DOF systems, incorporating the rub-impact effect between the rotor and stator. The complicated mathematical model is investigated using analytical techniques, employing the perturbation method, and validated numerically through time response, basins of attraction, bifurcation diagrams, [Formula: see text] chaotic test, and Poincaré return map. The main findings indicate that the asymmetric system model may exhibit nonzero bistable forward whirling motion under external excitation. Additionally, it can whirl either forward or backward under multi-parametric excitation, besides the trivial stable solution. Furthermore, in the case of mixed excitation, the rotor displays nontrivial tristable solutions, with two corresponding to forward whirling orbits and the other one corresponding to backward whirling oscillation. These findings are validated through the establishment of different basins of attraction. Finally, the performance of the [Formula: see text] in mitigating rotor vibrations and averting nonlinear catastrophic bifurcations under various excitation conditions. Furthermore, the rotor’s dynamical behavior and stability are explored in the event of an abrupt failure of one of the connected controllers. The outcomes demonstrate that the proposed [Formula: see text] effectively eliminates dangerous nonlinearities, steering the system to respond akin to a linear system with controllable oscillation amplitudes. However, the sudden controller failure induces a local rub-impact effect, leading to a nonlocal quasiperiodic oscillation and restoring the dominance of the nonlinearities on the system’s response.

Lambert W Functions in the Analysis of Nonlinear Dynamics and Bifurcations of a 2D γ-Ricker Population Model

The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ-Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter γ is even or odd. In addition, the analysis of the bifurcation structure of this γ-Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results.

Constant-strength inelastic displacement ratio spectra for assessment of superstructures in seismically isolated buildings

A reliable estimation of maximum displacement demands of seismically isolated inelastic superstructures is crucial for assessment of base-isolated buildings under beyond-design earthquakes. Constant-strength inelastic displacement ratio, CR, spectra, as applied in the performance-based seismic assessment procedure, can be used to estimate the inelastic displacement demands of structures. Currently, a suitable analytical expression of CR is lacking for base-isolated structures considering the influencing parameters comprehensively. This paper seeks to fill this gap. The constant-strength spectra are computed from nonlinear dynamic analyses of simplified two-degree-of-freedom models considering the inelastic behavior of the superstructure and isolator system, using a set of earthquake ground motions recorded on stiff soil sites. The effects of strength reduction factor of superstructure, superstructure elastic period, secondary stiffness ratio of superstructure, mass ratio, isolation period, normalized strength of isolation system and superstructure viscous damping on the mean and dispersion of CR are investigated. In particular, the effects of variations in earthquake intensity and isolator strength on CR are taken into account by the normalized strength of isolation system. Besides, limiting values of CR as the superstructure elastic period tends to zero or infinity are discussed and verified using the statistical values of CR. Finally, based on the trends of CR with respect to the design parameters of the superstructure and isolation system, and the boundary conditions to the CR formula, an analytical estimating equation with reasonable accuracy is developed to approximate the mean constant-strength inelastic displacement ratios during seismic assessment of base-isolated building structures built on stiff soil sites.

Extending the concepts of response spectrum analysis to nonlinear static analysis: Does it make sense?

The study presented in this paper aims to assess the recent novelties proposed by new generation building codes about the extension of some concepts at the base of linear analyses to the procedures of nonlinear static analysis. The nonlinear static analysis (pushover) is an extensively adopted approach by engineers and practitioners for purpose of assessing the seismic performance of new and existing buildings, although several drawbacks characterize this methodology, as evidenced by the existing scientific literature. In order to overcome the well-known limitations characterizing nonlinear static analysis, and to offer an alternative to nonlinear dynamic analysis, the recent upgrades of some building codes, such as the Italian one, provide different rules to employ in nonlinear static procedures. Among these new provisions, one regards the possibility to use a horizontal load profile proportional to the storey forces derived from a response spectrum analysis in all cases (i.e., also for irregular buildings). The main goal of this study is to demonstrate the reliability of this new load profile when strong irregularities arise. To this scope, the seismic behaviour of a sample of archetype buildings characterized by increasing in-height irregularity was investigated. The sample of buildings was subdivided in two subsets characterized by different design levels, one conceived by considering the prescriptions of the new Italian building code and one designed according to the oldest Italian building code (i.e., without considering anti-seismic details). The sample of buildings, simulating new and existing cases, was firstly modelled and after investigated through nonlinear static analyses by employing both traditional (i.e., inverse triangular- and uniform-like) and new (i.e., derived from response spectrum analysis) load profiles. After, nonlinear dynamic analyses were run, in order to assess the capacity of both traditional and new load profiles to capture the dynamic behaviour of the investigated archetype buildings. The performed analysis campaign demonstrated the efficiency of the new load profile proposed by the code, and the output of the work provided an answer to the main question posed by the authors: does it make sense to extend the concepts of response spectrum analysis to nonlinear static analysis?

Ductility demand estimation of high-rise steel special moment frames due to structure-pile-soil interaction

ABSTRACT This study is concerned with variation of ductility demands in a range of tall buildings comprising 15, 20, 25, and 30-story steel special moment frames resting on pile groups in a flexible soil medium. Nonlinear soil–structure interaction analysis is performed using the direct method by considering an adequate extent of soil around the structures terminating at appropriate boundaries. Eleven consistent ground motions are used for nonlinear dynamic analysis of the systems and the ductility demands are evaluated by tracing the rotation history of the plastic hinges. It is concluded that simultaneous contribution of soil–structure interaction and p-∆ effect results in more than 40% increase of the ductility demand and 20% increase of the story drifts in the worst case that includes the lower stories of the tallest building.

Seismic Evaluation of Step-Back Building and Regular Building by Using Nonlinear Static and Nonlinear Dynamic Analysis

Seismic Evaluation of Step-Back Building and Regular Building by Using Nonlinear Static and Nonlinear Dynamic Analysis

Study on multi-state of meshing-impacting dynamic characteristics of spur gear systems considering friction under localized tooth breakage

Localized tooth breakage is one of the common failures of spur gears, which affects the smooth and safe operation of spur gear transmission systems. The tooth collision cannot be neglected, and it is especially important to reveal the meshing-impacting dynamic characteristics of the gear system under localized tooth breakage to improve the safe and stable operation of the gear system. Based on the gear meshing principle and the dissipative collision contact force model, the drive-side tooth meshing model and back-side tooth impacting model are established with considering the transient nature of tooth back-side contact. The tooth surface meshing model and tooth back collision model under partial breakage are established. According to the contact state and force environment of the gear pair, the multi-state meshing-impacting behaviour under local breakage is classified, and the discrete meshing-impact dynamics model of an involute spur gear system under local breakage is established to explore the influence of local breakage on the meshing stiffness and load distribution. The mechanism of contact force under partial tooth breakage is revealed, and the influence of load coefficient and meshing frequency on the nonlinear dynamics is studied by defining two Poincaré maps. It is found that local tooth breakage affects the contact force of single-and double-tooth meshes and reduces gear load carrying capacity. Larger loads inhibit back-side impact, and smaller loads induce the coexistence behaviour and back-side impact. Larger or smaller meshing frequency induce back-side impact behaviour. The coexistence of chaotic and periodic motions induces back-side impact behaviour, and localized tooth breakage affects the coexistence phenomenon and aggravates the complexity of the dynamic behaviour. The dynamic model of gear system considering energy dissipation and nonlinear vibration under the presence of local tooth breakage of the pinion is explored, and the conditions of back-side impact are studied. This research provides new methods and ideas for nonlinear dynamic modelling and analysis of faulty gear systems.

Mechanical and Thermal Analysis of a Rocker Arm Shaft Support Based on Finite Element Method

Abstract The Finite Element Method (FEM) is a powerful numerical technique for solving complex physical problems involving differential equations and partial derivatives. This study presents the mechanical and thermal analysis of a rocker arm shaft support using FEM. Employing the ADINA (Automatic Dynamic Incremental Nonlinear Analysis) software, the behavior of the shaft support has been modelled, leveraging ADINA’s extensive material libraries, diverse loading conditions, and customizable behavioral properties. The analysis focuses on determining deformations, stresses, and displacements, particularly in the median plane section at the point of maximum stress. Both treated and untreated material conditions are evaluated to assess stress transmission in the transition zone between surface-hardened and base materials. A 2D analysis is conducted, given the geometry of the rocker arm spindle support, to ensure fidelity to real structural behavior while optimizing computational efficiency. The validated model provides insights into design constraints for new materials, supporting industrial applications.

Nonlinear dynamic analysis of a cylindrical panel with a discontinuous unilateral elastic base

Nonlinear dynamic analysis of a cylindrical panel with a discontinuous unilateral elastic base

Non-linear dynamic analysis of Collapsed grandstand

Non-linear dynamic analysis of Collapsed grandstand

Confinement effects within the seismic design of reinforced concrete frames: reliability assessment and comparison

The current Italian code “NTC2018” and Eurocode “EC8” provide specific design requirements in terms of flexural overstrength factors for reinforced concrete (RC) buildings in seismic areas. This study proposes to improve the design methodology by including explicitly the confinement effects within the seismic design of a new regular RC frame due to their influence on the capacity design principles (at structural and member level). Specifically, the seismic performance of a RC frame designed according to codes is compared, in reliability terms, with the one of the same frame designed including the concrete confinement effects. Moreover, a comparison between three constitutive models for confined concrete is performed. Selecting L’Aquila (Italy) as reference site, the two design methodologies combined with the three confinement models are numerically implemented. Scaling 30 non-frequent natural ground motions to increasing seismic intensity measures, according to the site seismic hazard, non-linear incremental dynamic analyses (IDAs) have been developed. Assuming the interstory drift indices as engineering demand parameters, the peak responses have been fitted through log-normal distributions to define IDA curves. Subsequently, appropriate limit state thresholds have been adopted to define the seismic fragility curves. Finally, through the convolution integral and Poisson model, the seismic reliability curves have been derived showing the importance of the proposed design methodology. In fact, for the frame under investigation, the seismic performance strongly improves in terms of ductility respecting all the reliability objective levels if the confinement effects are explicitly considered in the seismic design. Furthermore, the different confinement models provide similar results when the proposed seismic design is adopted, implying a reduction of the model uncertainty.

Evaluation of Pylon Shape and Cable Layout Interaction on the Seismic Behavior of Cable-stayed Bridges

Nowadays, cable-stayed bridges are among the most widely used bridges. In these bridges, the seismic behavior is critical due to the nonlinear behavior of the cables and the high seismic weight. In recent years, some research has been done on measuring the seismic behavior of cable-stayed bridges. Most of them have evaluated the seismic behavior of the pylon shape or cable layout separately. Nevertheless, it seems very unlikely that these two elements’ reactions do not affect each other. Therefore, this article has tried to consider the mutual effect of these variables in a wide range of span lengths using spectral nonlinear dynamic analysis. On the other hand, the connection angle of the cables to the bridge deck has also been investigated as another variable. The results show that the response of the bridge may change entirely according to the combination of pylon shape and cable layout. For example, in A and diamond-shaped pylons, using a Harp configuration of cables reduces the period of free vibration of the bridge and, as a result, provides the greatest stiffness. On the other hand, the Fan configuration creates more stiffness in the H-shaped and single pylons.

Nonlinear dynamic analysis of parked large wind turbine blade considering parametric excitation

In this study, the nonlinear dynamics of parked large wind turbine blades are investigated, with a focus on the consideration of parametric excitations induced by the combined effect of wind and support motion. A continuum mathematical model for the blade is adopted. The time-varying damping terms that may induce parametric excitation are derived in this study. Nonlinear dynamic responses of NREL 5-MW wind turbine blade are numerically investigated using the multiple-scale method. Results show that the primary resonance of the first flapwise mode can induce the super-harmonic resonance of the first edgewise mode, with considering parametric excitation. Notably, when the ratio between the first flapwise to first edgewise modal eigenfrequencies is tuned to 1:2, the super-harmonic resonance leads to internal resonance between the two modes. In this case, the effects of incident wind speed, excitation direction and amplitude on the blade response are discussed. Quasi-periodic motions can also be induced because of the Neimark-Snack bifurcation in the case of large excitation amplitude.

Structural and dynamic evaluation of a test bench for mechanical vibrations using finite elements

This numerical study was conducted to assess the experimental bench structure’s adequacy for measuring mechanical vibrations. The bench allows for three types of tests: dynamic imbalance of a single flywheel, dynamic imbalance of dual flywheels, and dynamic imbalance due to defective gears. A CAD (Computer-Aided Design) model of the vibration bench was developed in three distinct configurations. We then conducted structural (static) and dynamic (non-linear) analyses to assess the structural integrity of the bench, its components, and the expected vibration amplitudes during testing. Additionally, the structure’s natural frequencies were determined, and their compatibility with the expected excitation frequencies was confirmed. These assessments were executed using finite element models within the Solidworks Simulation™ framework. The findings indicate that, when designing such machinery, it is crucial to ensure that the vibration modes do not coincide with the excitation frequencies, as this can compromise the experimental results. Consequently, we have proposed and accessed two redesigned versions of the bench to ensure structural integrity and prevent resonance during experimental procedures. The redesigns aim to mitigate the risk of resonance by altering the bench’s structural parameters to shift the natural frequencies away from the range of excitation frequencies. This proactive approach is based on the idea that a big difference between the natural and excitation frequencies lowers the chance of resonance, which makes the results of the experiment more reliable. The enhanced designs were subjected to a series of rigorous simulations to validate their performance, ensuring that they meet the stringent requirements for educational and research applications.

Seismic hazard study for the duration of ground-motions triggered by intraslab earthquakes

This paper presents a probabilistic seismic hazard analysis for the duration of ground motions in Mexico City caused by intraslab earthquakes. The study implies establishing criteria to measure the duration of ground motions and developing predictive equations (GMPEs) for its estimation. Focus is placed on the relative significant duration, DSr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{Sr}$$\\end{document}, which is based on the accumulation of energy of ground motions. The study extends to the development of hazard curves that allow estimating the annual probability of exceedance of said parameter. The scope is limited to ground motions caused by intraslab earthquakes occurring in Mexico and that engineeringly affect its capital, Mexico City, which is in a geographical region where the effects of soil-dynamic amplification are manifested considerably. A strong-motion database that includes 1517 horizontal accelerograms, with peak ground acceleration, PGA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PGA$$\\end{document}, greater than or equal to 3 cm/s2, recorded during 21 earthquakes from 1994 to 2023 were used to develop the GMPEs. The quantitative description of the time, size, and spatial distribution of the seismic-activity occurrence was defined using a catalog of 46 earthquakes that occurred from 1900 to 2023. The earthquakes have moment magnitude, Mw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{w}$$\\end{document}, greater than or equal to 6. With the tools developed, amplitude- and duration-based hazard-consistent accelerograms can be simulated and used in nonlinear dynamic analyses (NDAs) of structures. This study includes an application example where three sites in Mexico City are selected to compute inelastic response spectra. Hysteretic-energy demands up to 5 times higher are found after a comparison between the inelastic-response spectra from hazard-consistent accelerograms and those provided by current Mexican regulations.

Probabilistic assessment of seismic performance of slopes considering the sensitivity of sliding surface to input motion

Seismic fragility assessments that predicts the exceedance probabilities of predefined limit states of a structure subjected to earthquakes are widely used to reduce economic losses and casualties. This paper presents a probabilistic assessment of slopes based on the permanent displacements calculated from a suite of two-dimensional (2D) nonlinear dynamic analyses. The slopes are categorized into four groups based on static factor of safety (FSstatic). The centrifuge test measurements of a slope composed of granular soil are utilized to validate the 2D finite element numerical model. The Newmark displacements are calculated by integrating the stresses imposed on the sliding surface. The sliding surface is determined from the maximum accumulated strain contours, thereby accounting for the slope and input motion characteristics. The Newmark displacement is correlated with various earthquake intensity measures (IMs). The optimal IMs are selected based on the goodness of fit, efficiency, practicality, and proficiency. The fragility curves are developed using selected optimal IMs for three sliding displacement-based damage levels, which are minor, moderate, and severe. The results show that FSstatic, which contains information on both the slope geometry and the shear strength of soil, is an effective parameter to estimate the Newmark displacement. In addition, a suite of seismic fragility surfaces are developed using dual IMs.

Innovative hysteretic device for seismic retrofit of single-story RC precast buildings

In the last decades, many efforts have been made by the scientific community and technicians in order to develop effective and practical retrofit approaches for industrial RC precast buildings. Given the aftermath of recent earthquakes, which identified structural and non-structural dry joints as the highest source of seismic vulnerability, the majority of the retrofit techniques involves interventions at the connections level. The primary function of creating an adequate constraint is nowadays frequently associated to energy dissipation, allowing to both remove the major building weakness and decreasing the seismic demand in terms of elements’ stresses and deformations. In the following, a novel metallic hysteretic device intended for beam-to-column connection retrofit is presented. An existing one-story RC precast building with friction beam-to-column joints is considered as case-study structure; mechanical properties of the device are calibrated, and its effectiveness validated though nonlinear dynamic analyses. The proposed device demonstrates its ability in both restrain the relative displacement between structural elements and dissipate an adequate amount of input energy coming from ground motions, preventing structural damage. A comparison with the same device without hysteretic properties, i.e., a non-dissipative device, is also carried out, highlighting the benefits in using the hysteretic version.