Nonlinear Dynamic Response Analysis Research Articles

Time Domain Nonlinear Dynamic Analysis of Vertically Loaded Tapered Pile in Layered Soils

A simplified model is proposed for predicting the nonlinear dynamic response of vertically loaded tapered piles in the time domain, in which the tapered pile is divided into several frustum segments and the four-spring is used for the simulation of the soil–pile interaction. The differential equations for the tapered pile are given and solved by the finite difference method. The vertical dynamic response of a typical tapered pile is investigated, and the consistency of the computational results compared with the finite element results convincingly verifies the reliability of the proposed simplified model. Then, recommended segment numbers, considering the computational efficiency and accuracy requirements for the dynamic analysis of tapered piles, are given. And parametric studies are also carried out to investigate the effect of soil and pile parameters on the nonlinear dynamic response of the tapered pile. The results show that soil nonlinearity significantly affects the vertical dynamic characteristics of the tapered pile. And the tapered pile shows better dynamic characteristics than the cylindrical pile with the same volume and pile length. In addition, the properties of the soil along the upper part of the tapered pile have a more considerable effect on the dynamic response of the tapered pile. These results help to further improve the theory of nonlinear dynamic response analysis of tapered piles and promote its widespread application in engineering practice.

Nonlinear dynamic response analysis of a hybrid concrete‐filled steel tubular truss lightweight bridge under strong earthquakes

AbstractConcrete‐filled steel tubular (CFST) trusses have seen recent development and application in bridges found in mountainous regions with deep valleys, and especially in seismic zones. In this study, a hybrid CFST truss lightweight bridge was selected as the research object. This bridge is composited of CFST composite truss girders (superstructure) and CFST lattice piers (substructure). Two different finite element models (FEM) for nonlinear seismic response analysis, one is detailed model and the other is simplified model, were established. By comparing with the detailed model, the results of the shaking table test as well as the real bridge test, the simplified model was found to be accurate. Considering the CFST columns' edge strain, the most unfavorable input direction of horizontal ground motion was perpendicular to the connection line of the bearings at both ends of the main girder. Also, the simultaneous influence of vertical ground motion and horizontal ground motion needs to be taken into consideration. By increasing the intensity of input ground motion, the yielding order of CFST lattice piers and its effect on the seismic response were also discussed. Results indicated that the bridge was in the elastic stage for the designed seismic ground motion. After the CFST lattice piers reached the plastic stage, the displacement and in‐plane bending moment had larger amplification coefficients compared to the increase coefficient of the input ground motion, while had a much smaller axial force amplification coefficient. Moreover, the in‐plane bending moment had a larger amplification coefficient in high piers compared to short piers.

Theoretical analysis of non-linear dynamic response of a bridge pier under two-phase flow excitation

Theoretical analysis of non-linear dynamic response of a bridge pier under two-phase flow excitation

Short-time frequency-domain method for truly nonlinear dynamic ground response analysis: The equivalent-nonlinear approach

Evaluating soil nonlinearity during cyclic loading is one of the most significant challenges in ground response analysis, especially when dealing with the inverse problem of deconvolution. Different schemes have already been developed for dynamic ground response analysis, both in the time and the frequency domain. The most accurate method to account for soil nonlinearity is the nonlinear dynamic analysis in the time domain. This approach is based on nonlinear constitutive models capable of accurately simulating highly nonlinear problems like soil liquefaction. However, the time-domain analysis is suitable only for the convolution analysis to define the ground motion at the free surface of a soil deposit from the bedrock motion. The frequency-domain analysis is the most common solution for the inverse problem called deconvolution, which is used to define the bedrock motion from the free surface ground motion. A well-known approach developed in the frequency domain for ground response analysis is the equivalent-linear method (EQL). This approach adopts an iterative procedure to define elastic shear modulus and damping ratio compatible with the induced strain level. Still, it presents some limitations, especially for highly nonlinear soil response, due to the use of strain-compatible but constant soil properties. This article presents a new scheme to conduct truly nonlinear dynamic analysis in the frequency domain based on the new concept of the short-time transfer function. Unlike the EQL method, which uses a constant transfer function, the proposed approach, called the “Equivalent-Nonlinear” method (EQNL), defines a soil transfer function evolving in time, depending on the shear stress and strain demands. The EQNL method approximates the response of a nonlinear system as an incrementally changing viscoelastic system and could represent a valuable tool for nonlinear deconvolution. This article shows the analytical formulation and the first set of validations of the EQNL approach, with detailed comparisons with the EQL and NL methods and vertical array data. These comparisons show the potentialities of the EQNL approach to reproduce the results of the nonlinear dynamic analysis. The EQNL approach has been implemented in MATLAB, and the source code is provided as supplementary material for this article. A more comprehensive validation is underway, aiming to better characterize the limitations and the capabilities of the method.

Rapid damage assessment of regional beam bridges after earthquake based on simplified models and different seismic inputs

As the hub of the traffic network, the rapid damage assessment of bridges after earthquake is of great significance for post-disaster rescue. Traditional vulnerability-based method can only provide the probability of different damage states of structures under different earthquake intensity indicators, which confuses the selection of post-disaster rescue routes. Therefore, this paper proposes a post earthquake damage assessment technique for regional bridges based on nonlinear dynamic time-history response analysis. First, a simplified mechanical model for a single pier was established for a large number of beam bridges in the region, achieving standardized and batch rapid finite element model establishment. Secondly, using Kriging interpolation method and continuous wavelet transform technology, the surface seismic response of geological drilling points is calculated to obtain the seismic motion history of any bridge site in the region. Finally, using parallel computing technology, nonlinear dynamic time-history response analysis was conducted on the simplified beam bridge model, and the bridge damage status was quantitatively evaluated based on the calculation results. Eighty-five bridges in a specific area are considered as an example to verify the proposed method. The results show that the proposed method has high calculation efficiency and can consider the site characteristics and structural design parameters. Also, the calculation results can better reflect the actual earthquake damage distribution, providing strong technical support for post-disaster rescue.

Nonlinear dynamic response and stability analysis of the stapes reconstruction in human middle ear

Nonlinear dynamic response and stability analysis of the stapes reconstruction in human middle ear

Dynamic analysis of offshore triceratops supporting wind turbine: Preliminary studies

Offshore triceratops, the recent innovation in deep water compliant platforms, is primarily designed to withstand lateral forces through its geometric shape. The uniqueness of the platform is the presence of the ball joints between the legs and deck, which partially restrain the transfer of rotations from the legs to the deck and vice-versa. However, displacements such as surge, sway, and heave motions are transferred, ensuring a rigid connection between the legs and the deck. Efficient operations of offshore wind turbines are more dependent on the support systems on which they are mounted. Increased stability and reduction in stress concentration in rigid connections are desirable. Nonlinear dynamic response analysis is carried out in FAST by coupling the frequency response of the platform obtained in ANSYS AQWA with that of the HydroDyn module of FAST. The current study investigates a fully coupled three-dimensional hydro-aerodynamic model of triceratops mounted with a horizontal axis wind turbine. Unsteady Blade Element Momentum theory (BEM) is used to estimate the aerodynamic loads, which encompasses the effect of wind shear using a power law and spatially coherent turbulence. In contrast, Morison equations are used to estimate the hydrodynamic loads on the platform. After the preliminary proportioning of the platform, Response Amplitude Operator (RAO) plots are drawn to illustrate the partial motion transfer between the deck and the buoyant legs. Based on the preliminary studies, it is seen that the environmental loads do not impose instability, reinforcing the dynamic stability of the platform. Frequency responses for operating and parked conditions illustrate the coupling between the degrees of freedom and the influence of the rotor motion of the wind turbine on the platform deck. Tether tension variation is assessed in all three legs for the operational sea states to check the safety standards for a compliant system to avoid tether pull-out. The presented study is prima facie to encourage the suitability of triceratops as floaters to support the wind turbine under moderate sea states. Highlights This study is focused on new-generation offshore triceratops as support system for wind turbine Prelimiary dynamic anlaysis of coupled action of the supprting system and wind turbine are presented Use of ball joints help partial isolation of the deck and restrain transfer of moment from the turbine shaft to the supporting system, which is a novelty Infleunce of rotor motion of the triceratops is illustarted to highlight the advantage of complinacy of trirceratops This study disucsses only the performance assessment and not the design perspectives

Hazard‐consistent simulated earthquake ground motions for PBEE applications on stiff soil and rock sites

AbstractGround motion record selection is a standard step in state‐of‐the‐art performance‐based earthquake engineering (PBEE) applications. It links the structural response to seismic hazard of the site of interest. In this process, suites of hazard‐consistent ground motion recordings of a wide range of intensity levels are selected (and often scaled) from a database of ground motions to be used as input to nonlinear dynamic response analysis. The ideal practice would be to select ground motions from a database of recorded accelerograms in such a way that they are consistent with the seismic hazard at as many intensity measure (IM) levels as possible and for all important causative scenarios. However, the available databases are not heavily populated, especially for the large‐magnitude short‐distance scenarios. Therefore, synthetic ground motions are the natural candidates to enlarge the database of recordings for scenarios that are important to the site hazard but lack, completely or partially, recorded accelerograms. The usage of such recordings, however, can be recommended only after they are proven to be “realistic” through a battery of seismological and statistical tests. In this study, we propose and implement a multi‐fold testing framework for such an evaluation. We first generate a ground motion database of simulated ground motions (SDB) whose values of the parameters of the causative earthquakes are, to the extent possible, the same of those that caused the ground motions in a mirror database of recorded ground motions (RDB). We then utilize the conditional spectrum (CS) approach computed for a hypothetical rock site in Perugia, Italy, to select hazard consistent records separately from the RDB and SDB databases. A comprehensive set of comparisons of distributions of several IMs, computed from the selected sets, and of distributions of engineering demand parameters (EDPs), that such record sets induce on simple SDoF structures suggests the adequacy of using the proposed simulated ground motions for structural response analyses of structures on stiff and rock sites.

The two-level probabilistic description of the compressive constitutive parameters of concrete

The constitutive model of concrete is the critical basis for the nonlinear analyses of concrete structures. Due to the fact that the mechanical behavior of concrete exhibits remarkable randomness, the probabilistic modeling of the key parameters of the concrete constitutive model is of paramount significance. In the present study, a two-level probabilistic model is proposed to describe the dependent random constitutive parameters based on the compressive test results of several batches of concrete specimens of different strength grades. Both the local probabilistic dependence, i.e., the dependence of the parameters of intra-batch specimens, and the global probabilistic dependence, i.e., the dependence of the parameters of inter-batch specimens, are captured by the proposed method. To this end, the constitutive parameters of concrete are first standardized by their means and coefficients of variation (COVs). In this way, the local dependence can be represented by the same copula model for the concrete of different strength grades. The global dependence is expressed as the empirical formulae in terms of the means and COVs of the parameters. The full probabilistic model can then be obtained by synthesizing the local and global dependence models. The effectiveness of the proposed approach is demonstrated by comparing the generated samples with the test results. To illustrate the effect of the probabilistic dependence of the compressive constitutive parameters on the structural evaluation result, the nonlinear stochastic dynamic response analysis of a reinforced concrete frame is carried out. The results indicate that the probabilistic dependence of the constitutive parameters of concrete has a non-negligible effect on the structural response and reliability, and should be reasonably considered in practice.

SECTION OPTIMIZATION OF RIGID STEEL FRAMES USING RESPONSE SURFACE MODELS

The increase of combination number according to the increase of variables is a serious problem in using section optimization for steel structures. Response Surface Method (RSM) which uses approximate functions made by sampling data was proofed as one of effective optimization methods. This paper shows features of the proposed method that combined with genetic algorithm by applying it to allowable stress design of a middle rise steel structure and changing the setting of RSM which are a response surface algorithm and a space filler algorithm. In addition, the feature of the optimized structures is analyzed by nonlinear dynamic response analysis.

Nonlinear dynamic mechanical response analysis of dual-segment single-span rotor-bearing system under normal condition and misalignment fault

Nonlinear dynamic mechanical response analysis of dual-segment single-span rotor-bearing system under normal condition and misalignment fault

Nonlinear stochastic seismic dynamic response analysis of submerged floating tunnel subjected to non-stationary ground motion

Owing to the randomness of seismic excitations, the submerged floating tunnel (SFT), which is a new structure subjected to the combined action of self-weight, buoyancy, and anchorage under seismic excitation, is a nonlinear stochastic dynamic system and the evaluation of its dynamic performance is an issue that must be addressed. In this study, the nonlinear dynamic differential equation of an SFT subjected to seismic dynamic action was systematically derived by considering the wave–structure dynamic coupling interaction, and its numerical solution was obtained based on the Newmark-β integration algorithm. Furthermore, based on the theoretical framework of nonlinear stochastic dynamics and the stochastic seismic model reflecting the characteristics of the site-specific response spectrum, the probability density function (PDF) of the nonlinear seismic dynamic response of the SFT was analyzed, and its seismic dynamic performance was evaluated based on dynamic reliability. Thus, it was found that the randomness of ground motion propagates, fluctuates, evolves, and dissipates in the SFT, and finally reaches the nonlinear seismic dynamic response of the SFT. Additionally, the nonlinear dynamic response of the underwater suspension tunnel is highly sensitive to earthquake excitations. The proposed evaluation framework is an effective tool for evaluating the seismic performance of underwater tunnels.

Nonlinear dynamic response of sea-crossing bridges to 3D correlated wind and wave loads

Long span sea-crossing bridges are often slender and sensitive to wind and wave loads. Nonlinear dynamic response analysis of the bridges under three-dimensional (3D) correlated wind and wave loads is performed in this study in consideration of both geometric and aerodynamic nonlinearities. An optimized C-vine copula is first used to construct a 3D joint probability distribution and environmental contour of mean wind speed, significant wave height and peak wave period. Multi-point fluctuating wind loads with Davenport coherence function and random wave loads with pile group effect are then determined using wind and wave spectra respectively. The nonlinear wind-wave-bridge system considering geometric and aerodynamic nonlinearities is solved by the Newmark-β method with the 3D correlated wind and wave parameters as an input. The proposed approach is finally applied to a real sea-crossing cable-stayed bridge with the measured wind and wave data. The results show that the nonlinear response of the bridge is higher than its linear response with the same input. The bridge response is significantly reduced if the 3D correlated wind and wave loads other than conventional uncorrelated wind and wave loads are considered.

Nonlinear Dynamic Response Analysis of a Three-Stage Gear Train Based on Lightweight Calculation for Edge Equipment.

Bevel gears are widely used in aerospace transmission systems as well as modern mechanical equipment. In order to meet the needs and development of aerospace, high-speed dynamic vehicles, and various defense special equipment, higher and higher requirements are made for the high precision and stability of gear transmission systems, as well as the prediction and control of noise and vibration. Considering the nonlinear factors such as comprehensive gear error and tooth side clearance, a dynamic model of the three-stage gear transmission system is established. The relevant physical parameters, geometric parameters, and load parameters in the gear system are considered random variables to obtain the stochastic vibration model. When the random part of the random parameters is much smaller than the deterministic part, the vibration differential equation is expanded into a first-order term at the mean of the random parameter vector according to the Taylor series expansion theorem, and the ordering equation is solved numerically. Based on the improved stochastic regression method, the nonlinear dynamic response analysis of the three-stage gear train is carried out. This results in a relatively stable system when the dimensionless excitation frequency is in the range of 0.716 to 0.86 and the magnitude of the dimensionless integral meshing error is < 1.089.

Experimental Verification and Nonlinear Dynamic Response Analysis of a Rolling Element Bearing with Localized Defects

In this paper, the dynamic behavior of rolling element bearings with localized faults on the inner and outer rings is investigated. A nonlinear mathematical model is developed with five degrees of freedom considering rotor unbalance. In this bearing model, the nonlinearity is caused by the Hertzian contact forces and the radial internal clearance. The fourth-order Runge–Kutta technique is used to solve the coupled nonlinear equations of motion numerically. Nonlinear vibration response of the rotor and bearing housing can be obtained in both time and frequency domains. An experimental verification of the numerical model is presented where experimental measurements for defective ball bearings are compared with the numerical results. Envelope spectra of the numerical results show similar behavior to that of the measured experimental signals. A parametric analysis is conducted to investigate the effect of system parameters on the nonlinear dynamic response using time waveforms, orbit plots, frequency spectra and bifurcation diagrams. The presented results demonstrate that the dynamic response shows periodic, quasi-periodic and chaotic motions because of varying rotational speeds and defect width. The proposed model contributes toward improved design and better health monitoring of bearings in practice.

An improved dynamic formulation for nonlinear response analysis of thin soft silicone plates with large deflection

This present paper develops an absolute nodal coordinate formulation (ANCF) improved lower-order plate element (ILOPE) for nonlinear dynamic response analysis of thin soft silicone plates with large deflection. Different from a common linear metallic plate which is modeled by combining linear constitutive model with original lower-order plate element (OLOPE), both material nonlinearity and geometric nonlinearity should be taken into account for this type of silicone plate. An improved dynamic formulation is developed for modeling and analyzing the soft deformable silicone plate based on Yeoh nonlinear constitutive model combined with ILOPE, meanwhile the stiffening effect problem is circumvented smoothly. By bringing in penalty function, and the elastic force and its derivative matrices of Yeoh model are deduced, and then a dynamic equations of motion for the silicone plate is founded in the frame of ANCF. The second order differential dynamic equation is solved by uniting Newton–Raphson iterative approach with Newmark numerical integral method. Dynamic free-falling motion process of a half-cantilevered silicone plate and a spherical hinge silicone plate only under the influence of gravitational force are simulated by adopting OLOPE and ILOPE, respectively. The comparison of the simulation results calculated by ILOPE with those obtained by the previously proposed reduced-order plate element and commercial software ANSYS demonstrates that the improved dynamic formulation is feasible and effective. Finally, the displacement nephograms of middle surface of two types of silicone plates are elaborated in terms of displacements and configuration variations, and the law of conservation of energy is elucidated from perspective of different energy variations.

Nonlinear Steady State and Dynamic Response Analysis of Focused Ultrasound Actuated Smart Biomaterials

The nonlinear steady state and dynamic response analysis of focused ultrasound smart biomaterials is presented in this paper. The increasing demand in scientific research to develop robust governing nonlinear model with adequate boundary conditions for proper understanding of the dynamics of smart biomaterials by applying focused ultrasound excitations is of great concern particularly in remote biomedical applications. Hence, in this study, a model which describes the nonlinear steady state and dynamic response of the materials for focused ultrasound actuator which is a nonlinear partial differential equation has been developed. The Galerkin Decomposition and the Differential Transform Methods are applied to obtain the solution of the governing equations. The solutions were validated with the numerical Runge-Kutta method of fourth order and verified with results obtained in recent studies and good agreement is established among them. The effects attenuating coefficient, modal number, and damping term on the steady state response of the smart biomaterials are investigated. From the results, it is observed that the steady state deflection of the system as indicated by the attenuating coefficient is lowest for clamped-clamped boundary condition and highest for clamped-free or cantilever condition. In addition, an increase in modal number and magnitude of the damping term results in an increase in the number of nodes and anti-nodes and a decrease in the amplitude of vibration over time respectively. Hence, this study establishes the practical applications of attenuating coefficient and boundary conditions as controlling factors in the design of smart biomaterials.

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

AbstractThe current article is devoted to the nonlinear dynamic and impact response analyses of rectangular incompressible neo‐Hookean hyperelastic plates with uniform/nonuniform transverse distributions of stiff elastic reinforcing particles. The nonlinear finite element governing equations are derived by using the principle of minimum total potential energy and solved by an updating scheme that uses the Runge‐Kutta time integration and penalty methods. The impact energy expressions are written for the integrated plate‐indenter system. The novelties of the article are: (i) realistic modeling the energy absorption of a particle‐reinforced nonlinear hyperelastic matrix based on the volume fractions of the constituent phases instead of using wrong Voigt‐type models or impractical predefined gradation coefficients, (ii) considering non‐uniform distributions of the reinforcing particles, (iii) using a highly accurate asymmetric (all the available theories are symmetric) infinite‐order plate theory, (iv) including the inherent hyperelastic nature of the material in the definition of the parameters of the plate theory, (v) considering the thickness changes of the plate, (vi) including von Karman's kinematic nonlinearity, (vii) analyzing both the dynamic and impact behaviors, (viii) proposing an adaptive algorithm to match the description of the displacement field with the load/stress variations, (ix) updating not only the stiffness but also the mass matrix within the time steps, (x) incorporation of the nonlinear boundary conditions by the penalty method, and (xi) performing time‐dependent analyses instead of the natural frequency analyses. Results reveal the drastic effects of the volume fraction of the reinforcing particles on the dynamic responses and report the impact responses of the FG hyperelastic plates, for the first time.

Bending-torsional-axial-pendular nonlinear dynamic modeling and frequency response analysis of a marine double-helical gear drive system considering backlash

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

Nonlinear dynamic response analysis of buildings for wind loads. A new frontier in the structural wind engineering

The structural engineering practitioners often deal with natural hazards that generate a structural response that is dynamic in nature. The wind loads are long duration load types and their induced effects, especially for severe events, need to be predicted through analysis by efficient numerical nonlinear solvers. In this paper the nonlinear wind-induced effects on structures are predicted using a non-commercial software based on the 3D Force Analogy Method (3D-FAM). The wind loads consist of time-histories of pressure coefficients recorded at a large number of taps in the wind tunnel test for a model corresponding to an 80 m high prototype building. A considerable number of dynamic nonlinear analyses are performed for different mean hourly wind speeds and wind blowing directions. For each case, the inelastic behavior of building is monitored through and efficient complementary energy balance-based analysis and quantified in time-domain by damage indices at each section, element, story and structural level.