Nonlinear Dynamic Response Analysis Research Articles

Pulse-like near-fault ground motion effects on controlled rocking steel cores

Controlled rocking steel cores (CRSCs) with reliable self-centering capability have been known as a low-damage seismic force-resisting system. The flag-shaped hysteresis response of CRSCs can be provided using unbonded post-tensioning tendons and replaceable energy dissipation devices. This paper examines the seismic performance of CRSCs subjected to a suite of pulse-like near-field and far-field ground motions. Non-linear dynamic response analysis is performed for 3-, 6-, 9-, and 12-story archetypes with single and coupled configurations. Results are quantified for different seismic responses, and the influences of earthquake type and structural configuration are compared from various aspects. The findings indicate remarkable changes in the performance of CRSCs due to modeling and ground motion properties. The outcomes reveal that rocking-core archetypes are efficient for mitigating residual damage and restricting peak displacements under both far- and near-field motions.

Longitudinal damage of cable-stayed bridges subjected to near-fault ground motion pulses

This paper investigated the nonlinear seismic performance of an existing cable-stayed bridge longitudinally subjected to a set of simulated near-fault ground motion pulses. An elaborated non-linear finite element model of the bridge was established which particularly considered cable sag effect, material nonlinearity of the tower and the deck. Through non-linear dynamic response analyses, seismic responses of the tower, deck and cables were evaluated at the yield and ultimate state of the structure. In particular, the yield and ultimate state of the structure were defined in the text based on damage levels of the structure and structural integrity requirement. It is revealed that the pulse period (Tp), by determining the relative contribution of multiple modes of the structure, strongly affected the damage process of the structure. As Tp was close to the period of first vertical vibration of the deck, the responses of the deck and cables were largely excited so that the deck might yield prior to yield of the tower, the cables failed prior to the ultimate state of the tower, and the deck suffered most of the damage despite of the yielding of the tower.

Mechanical characteristics and nonlinear dynamic response analysis of rotor-bearing-coupling system

A mathematical model is presented for studying the dynamic properties of rotor-bearing-coupling system under the effects of varying compliance, radial clearance, rotor-stator rubbing, raceway defects and surface waviness. Nonlinearity of bearings, localized and distributed defects will elicit abundant nonlinear response, which will directly affect the mechanical characteristics of bearings as well as motion stability of rotor systems. The effects of typical parameters on mechanical characteristics and nonlinear dynamic response of the rotor system are analyzed by means of bifurcation diagrams, speed-amplitude, time-histories, spectrum, phase diagrams, and Poincaré sections. The results provide theoretical support for studying the nonlinear vibration mechanism and the control of rotor-bearing system in practical applications.

Dynamic Response Analysis of Spur Gear System with Backlash

There are few studies on space-driven gear systems in the existing literature. In this paper, a spacedriven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. A nonlinear dynamic response analysis was performed. The backlash was introduced into the dynamic model, and the time-varying stiffness was corrected to make the theoretical model closer to reality. By comparing two kinds of dynamic response curves with and without return difference, it was illustrated that the influence of return difference on dynamic transmission error in a gear system. The results obtained in this paper provide a reference and basis for subsequent research.

Time-varying Response Analysis of Spur Gear System

In this paper, a space-driven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. Considering the high load characteristics of the space drive system and the time-varying stiffness and tooth clearance of the gear system, a nonlinear dynamic response analysis was performed. The characteristics of the vibration acceleration, shock and transmission error of the gear system are studied in this paper. This paper analyzes the relationship between backlash and return difference, and derives the theoretical formula between the two. The time-varying stiffness was corrected to make the theoretical model closer to reality. The research in this paper enriches the study on space drive systems and high load gear systems.

Nonlinear dynamic response analysis of a pressurized carbon nanotube resting on winklerpasternak foundation using multi-dimensional differential transform method

The tremendous strength and light weight properties of Carbon nanotubes (CNTs) have fascinated the interest of researchers and scientists towards using CNTs for thermal, chemical, optical, electrical, structural and mechanical applications. This paper presents analytical solutions to the nonlinear dynamic response, shear force and bending moment of such CNTs. The CNT is modeled via thermal elasticity mechanics and Euler-Bernoulli theories. Without linearization, series expansion or omission of any independent variable, the developed nonlinear model that governs the physics of the behaviour of the CNT when excited by the aforementioned external agents is solved using transient differential transform method (TDTM) and verified with an inbuilt numerical scheme in MAPLE16. The results of the generated close form solution in this work are also compared with those of past works and excellent agreements are achieved. The parametric studies revealed that an increase in pressure term increases CNT deflection for any mode while a corresponding increase in the temperature and foundation parameters have an attenuating impact on deflection. Finally, the dynamic study reveals that locations with maximum bending moments are observed to possess minimum shear forces. It is envisaged that this work will enhance the use of CNTs for structural, electrical and mechanical applications.

Nonlinear dynamic response and deformation analysis of soil under the explosion shock loading

Energy is released during explosions, and this creates shock waves. The dynamic pressure generated from an explosion is transmitted through soil in the form of compression waves. In military engineering and industrial safety protection, soil, a blast-resistant material, is used to achieve blast resistance. This study used the blast pressure and ground acceleration measured in an experimental explosion to verify the results of finite element numerical analysis. A fluid–solid interaction numerical analysis method was employed to simulate a trinitrotoluene explosion on the ground. Through analysis of the dynamic characteristics of soil after an explosion, the relationship between the dynamic stress wave formed by the explosion and the plastic deformation of the soil was studied. The results may provide a reference for the design of blast-resistant protective soil layers.

Nonlinear dynamic response analysis of marine risers under non-uniform combined unsteady flows

Considering the top-end platform surge induced by periodic wave, the encountered flow field of marine risers under the actual marine environment is approximate to a combined sheared and sheared-oscillatory flow, which is non-uniform in both time and spatial domains. A published time domain force-decomposition model is proposed to predict the riser's nonlinear dynamic response under non-uniform combined unsteady flows. A 90 m flexible riser is chosen as the simulated object, and a large amount of the combined flow cases with different oscillation periods and combined ratios are designed. With the fundamental study on a steady sheared flow case, the structural dynamic response characteristics under non-uniform combined flows are investigated systematically. The overall dynamic response presents travel wave pattern, and the high-frequency response is easier to be excited for the riser's top and bottom segments. Some time-sharing response characteristics like amplitude modulation, frequency transition and mode jumps are captured, and they are affected by the flow field parameters significantly. Under the long oscillation period cases, the intermittent dynamic response follows the accordant periodicity with the current velocity. While under the short oscillation period cases, the unstable structural vibration occurs persistently without clear regularity. The combined ratio also influences the RMS displacement, excited frequency bandwidth and travel wave propagation velocity evidently. Associated with VIV mechanism analysis, the individual response characteristics under different flow field parameter combinations are explained reasonably.

A Method of Improving Time Integration Algorithm Accuracy for Long-Term Dynamic Simulation

This paper aims to improve the accuracy of time integration algorithms (TIAs) for long-term simulation of structural dynamics. To this end, a new method of reducing the period elongation (numerical dispersion) was proposed by utilizing the mass scaling matrix. Firstly, the period elongation of explicit Gui-[Formula: see text] algorithm as a representative was analyzed, and the strategy of enhancing the algorithm accuracy was investigated. Subsequently, the period elongation was reduced by introducing a parameter to change the mass matrix, which is weighted by the original mass matrix and stiffness matrix. The bisection method is utilized to determine the parameter according to the formulation of period elongation. Since just the mass matrix of original algorithm is changed slightly, the convergence rate of original TIA remains unchanged and the proposed mass scaling method imposes little influence on the stability condition of original algorithm. Moreover, this method has few modifications to the computer program of TIA and is easy to implement. Finally, both linear and nonlinear long-term dynamic response analyses for multiple-degree-of-freedom systems indicated that the proposed mass scaling method is effective and convenient to reduce the period elongation for several typical TIAs.

Seismic Demand on Acceleration-Sensitive Nonstructural Components in Viscously Damped Braced Frames

AbstractThis paper investigates the seismic demand on acceleration-sensitive nonstructural components in buildings equipped with fluid viscous dampers. Nonlinear dynamic response analyses were cond...

Nonlinear Response of Marine Riser with Large Displacement Excited by Top-End Vessel Motion using Penalty Method

A marine riser operated in a deep-water field could be substantially affected by large amounts of movement of the floating platform, which is more complicated and very challenging to analyze. This paper presents a mathematical model involving nonlinear dynamic response analysis of a marine riser caused by sways and heave motions at the top end, which are treated as the constraint conditions. The nonlinear equation of motion, arising from the nonlinearity of the ocean current and wave loadings, is derived and written in general matrix form using the finite element method. The excitation caused by platform movement is imposed on the riser system through the time-dependent constrained condition using the penalty method. The advantages of this method are that it is easily implemented on the nonlinear equation of motion and it requires no additional unknown variable, and thus consumes less computational time. By this method, the stiffness matrix and the force vector of the system are then modified, enforcing top-end vessel motion. The dynamic responses are evaluated by using numerical time integration based on Newmark’s method with direct iteration. The effects of the oscillation frequency of top-end vessel sway and heave motions on the nonlinear dynamic characteristics of the riser are investigated. The numerical results reveal that the riser responses to the top-end vessel excitation behave like a periodic motion, which is conformable to the characteristics of vessel movements. The increase in the oscillation frequency of the top-end vessel increases the maximum displacement amplitude for both the horizontal and vertical directions. The directional motion of the vessel also significantly influences the response amplitude of the riser.

Nonlinear Dynamic Response and Stability Analysis of a Tensegrity Bridge to Selected Cable Rupture

This paper presents a nonlinear dynamic analysis procedure used for the investigation of the response of a tensegrity bridge to a selected sudden cable rupture. In order to simulate a cable rupture, for the loaded or unloaded geometry of the tensegrity structure, a geometrical nonlinear analysis is performed, and the cable end tensions projected in the global coordinate system are determined. Next, these forces are applied as external nodal forces to the tensegrity structure, from which the selected cable has been omitted (damaged structure). Next, the nonlinear equation of motion of the tensegrity bridge subjected to dynamic loads is discretized and integrated in time using the unconditionally stable Newmark constant-average acceleration method combined with a Newton-Raphson iterative scheme. The dynamic simulation is initiated by cancelling the vector of external forces representing the damaged cable. For each case, the largest tension force in the cables, the largest compression force in the struts as well as the largest average midspan displacement are determined. The maximum tension obtained in all the bridge cables was way below their tension capacities for the unloaded bridge and exceeded them for only one case of the loaded one. However, the maximum compression forces obtained in the struts of the bridge were below their compression capacities. The limit deflection has been exceeded only for of the loaded bridge and for several cases of cable rupture. Nonlinear dynamic instabilities caused by cable slackening were observed in all simulations.

Blast Resistant Structure Using Steel Hollow Sections

The number of terrorist attacks increased in the last few years, so the effect of blast loads on structures become an important matter which should be taken into consideration in the design and planning process. Terrorist attacks are exceptional cases and man-made disasters, so blast loads are calculated carefully just like earthquake and wind loads. The objective of this research is to determine the quality of blast load simulation for non-linear dynamic response analysis of trussed structure subjected to blast loads. Blast resistant structure design theories, the enhancement of building security against the effects of explosives in both architectural and structural design process are discussed in this paper. Steel hollow sections are used as structural members those can undergo large nonlinear deformations to absorb blast energy. Essential techniques for increasing the capacity of a structure to provide protection against blast effects are discussed in this paper both with an architectural and structural approach.

Nonlinear dynamic response and damage analysis of hydraulic arched tunnels subjected to P waves with arbitrary incoming angles

Due to the randomness and uncertainty of the earthquake, the incoming angle of the seismic waves acting on the underground structure is also subject to great uncertainty. Most dynamic response analyses and seismic design for hydraulic tunnels are based on the assumption of vertically incoming seismic waves. This assumption may underestimate the nonlinear response of the hydraulic tunnels. Hence, understanding the nonlinear dynamic response and evaluate the damage of the hydraulic tunnels under obliquely incoming compression waves (P waves) is essential for better analysis and seismic design of hydraulic tunnels. For this purpose, the input method of P waves with arbitrary angle is presented and validated through two examples. In addition, the fluid-structure-rock interaction (FSRI) system is considered based on coupled Eulerian-Lagrangian method, to approximate the environment conditions of the hydraulic arched tunnels when the real earthquake occurs. The numerical results reveals that the incoming angle of P waves have great impact on the displacement peak index and the damage degree of hydraulic arched tunnel. It is recommended that the influence of obliquely incoming P waves should be considered in the seismic design of hydraulic tunnels.

Analysis of nonlinear dynamic response of spatial flexible tether system by Symplectic difference scheme

This paper transforms the discrete Langrangian formulation of spatial flexible tether systems to Hamiltonian formulism. The resulting Hamiltonian canonical equations are solved by Symplectic difference scheme. The application of Symplectic difference method for solution of nonlinear tether dynamic problems ensures conservation of system energy, momentum and volume. Two numerical examples are conducted to validate the proposed method, one is the free swing pendulum system and the other one is the three-dimensional circular towed system. The simulation results are compared with theoretical and the existing numerical results. The comparisons demonstrate the proposed Symplectic difference integrator for the Hamiltonian nodal position finite element method is numerically accurate and efficient to predict the dynamic response of spatial flexible tether systems.

An improved performance-based plastic design method for seismic resilient fused high-rise buildings

The performance-based plastic design (PBPD) method generally relies on the nonlinear response of equivalent elastic-perfectly-plastic single degree of freedom system. It usually cannot achieve the design of three performance objectives simultaneously and may not consider the high mode effect of structure, which is significant for high-rise building. In this paper, a trilinear force-displacement model indicating three prescribed performance objectives at three seismic hazard levels is adopted to improve the PBPD method. The proposed improved PBPD method is derived based on multiple degrees of freedom system, while the high-mode effect and post-yield stiffness of the structure is considered. It can be used for designing seismic resilient fused high-rise buildings. A novel dual system composed of steel energy-dissipative column (EDC) and moment resisting frame (MF) is employed for application of the proposed method. This dual system has its fuse members decoupled from the gravity-resisting system, and the performance-based design of this system is discussed as well as its application for high-rise buildings. To demonstrate the effectiveness of the proposed method, a 20-story EDC-MF structure system is designed using the improved PBPD method. A detailed numerical model of the designed EDC-MF system is then built, and nonlinear dynamic response analyses at different seismic intensities are performed to verify the actual structure performance. Results show that the designed structure can achieve the prescribed yielding mechanism and performance objectives at three seismic hazard levels, and the EDC-MF system can be effectively applied to high-rise building as a seismic resilient fused structure.

Nonlinear dynamic modeling and response analysis of a rotor–blade system with whirling motion

In this paper, we propose a new nonlinear dynamic model of a rotor–blade system with whirling motion, in which a rigid rotor and blades are modeled as a Jeffcott rotor and Euler–Bernoulli beams, respectively. The stiffening effects of the rotating blades are considered using a hybrid set of deformations, which consist of the stretch and chordwise deformations. After the nonlinear partial differential equations of motion are derived using Hamilton’s principle, they are discretized using the Galerkin method. From the discretized equations, the nonlinear dynamic responses are computed using the generalized- $$\upalpha $$ time integration method. Based on the dynamic responses and the frequency spectra, the proposed model is verified both for the case where the blade is considered to be a rigid body and for the case where there is no whirling motion of the rotor. In this study, the nonlinear dynamic responses of the rotor–blade system are analyzed in terms of the natural frequencies for whirling motion and the natural frequencies of the deformation of the rotating beam. In addition, the effects of the supporting stiffness, rotating speed and blade stiffness on the dynamic responses of the radial displacement and stretch/chordwise deformations are also analyzed.

DIMENSION REDUCTION OF FPK EQUATION FOR VELOCITY RESPONSE ANALYSIS OF STRUCTURES SUBJECTED TO ADDITIVE NONSTATIONARY EXCITATIONS1)

The nonlinear response analysis of structures subjected to random excitation is a highly challenging problem. The solution of FPK equation provides exact solutions to these problems. However, for nonlinear multi-degree-of-freedom systems, the direct solutions of the FPK equation is prohibitively difficult. Actually, the numerical solutions are strictly limited by the dimension of the equation, while the analytical solutions are available only for very few specific systems, and most of them are steady-state solution. Therefore, reducing the dimension of the FPK equation is an important way to solve the high-dimensional nonlinear dynamic response analysis problem. In the present paper, for the nonstationary response analysis of multi-degree-of-freedom nonlinear structures subjected to amplitude-modulated additive white noise, the high-dimensional FPK equation in terms of the joint probability density function is reduced in dimension. For the probability density function of velocity response, it is converted to a one-dimensional FPK-like equation through introducing the equivalent drift coefficient. The method of conditional mean function estimate is suggested to construct the equivalent drift coefficient. Afterwards, the numerical results of probability density function of velocity can be obtained by applying the path integration method to solve the dimension-reduced FPK-like equation. The accuracy and efficiency of the proposed method are discussed and verified through the numerical examples, including the non-stationary response analysis of velocity of a single-degree-of-freedom Rayleigh oscillator, a ten-story linear shear frame structure and a nonlinear shear frame structure subjected to amplitude-modulated additive white noise.

Development of fragility functions for natural gas transmission pipelines at anchor block interface

In this paper, fragility functions are developed for natural gas transmission pipelines at anchor block interface under the effect of seismic wave propagation. The fragility functions are developed for three typical pipelines in two types of soils. Seismic response of the pipeline at anchor block interface is evaluated by conducting non-linear dynamic response analysis of the pipeline system. The pipeline system consisting of the pipe, the anchor block, and the surrounding soil is subjected to ground shakings associated with a set of 36 earthquake records to develop the fragility function. The results of analyses indicate that the critical pipeline section is at pipe-anchor block interface where the pipe is susceptible to local buckling failure. The fragility functions are developed using strain limit state associated with local buckling of the pipe. The results of this study indicate that the vulnerability of pipelines to the local buckling failure at pipe-anchor block interface increases with increasing pipe diameter. Also because of the relatively large anchor blocks in soft soils, pipelines are more vulnerable to the local buckling failure in soft soils than in hard soils.

State-of-Health Diagnosis of Lithium-Ion Batteries Using Nonlinear Frequency Response Analysis

Estimation of the State-of-Health (SOH) of Lithium-ion Batteries (LIBs) is commonly conducted using in-situ measurement methods, such as Incremental Capacity Analysis (ICA) and Differential Voltage Analysis (DVA) as well as impedance based techniques. In this study, we present an alternative method for SOH estimation: The nonlinear dynamic measurement method Nonlinear Frequency Response Analysis (NFRA) is shown to be able to estimate capacity fade of LIBs due to loss of active material. Capacity loss correlates with the quotient of the root mean square of the second and the third harmonic response for different excitation amplitudes in the frequency range sensitive to electrochemical reactions at approximately 1 Hz. The results of the experimental cycle-aging study are validated and further analyzed by using a reaction model containing Butler-Volmer kinetics with a dynamic charge balance of the electrode. Simulations show that the NFR quotient and capacity fade due to loss of specific surface area correlate exactly. We identify the NFR quotient as a reliable, easily measurable parameter for the diagnosis of the SOH of LIBs. Therefore, this study reveals a novel approach for SOH estimation of LIBs based on dynamic analysis with NFRA.