Finite element analysis of dynamic stability of skeletal structures under periodic loading

This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose. The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C++ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of nu-merical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark’s method to verify the results.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

ANALYSIS OF DYNAMIC STABILITY OF SUBMERGED STRUCTURE

The submerged structure is basically a large three-dimensional structure of few statically redundant members. The structure is subjected to vertical dead and live loads in addition to the wave forces. An analysis of dynamic stability of the submerged structure without damping has been made by J. Thomas and Abbas (1980). In this paper the analyses of dynamic stability of the sumberged structure with damping are conducted. The case structure with damping is more complicated 'than the case without it. According to the principle of perturbation, a new model for dynamic stability calculation in consideration of damping effect is developed. In this paper, the formulas are deduced, the computational program is compiled, the practical examples are analysed, and this problem is solved very satisfactorily. The computational results show that the shape and value of the regions of dynamic instability can be changed significantly by damping. So only by considering damping can the property of dynamic stability of the submerged structure be reflected correctly.

A Preliminary of Dynamic Stability Analysis

On account of the traditional method in hybrid stability analysis being too rough, a new method of taking dual or single mode was put forward for 4 typical levers in the hybrid stability analysis respectively and transited to the dynamic analysis smoothly. After verifying the superiority of the method through examples, the broad application prospect would be given in the end.

Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Assessing the seismic behavior of steel moment frames equipped by elliptical brace through incremental dynamic analysis(IDA)

Incremental dynamic analysis and nonlinear static pushover analysis are carried out on a performance-based design to determine the seismic demands and capacities of an elliptic braced moment resisting frame(ELBRF).The objective is to assess ductility,overstrength and response modification factors in a modern steel-braced structural system based on incremental dynamic analysis.This integrated system is connected to a beam and column with an appropriate length while providing enough architectural space to allow for an opening without having the common problems associated with architectural spaces in braced systems.Several different classes of buildings are considered on soil type II.Linear dynamic analysis,nonlinear static pushover analysis and incremental nonlinear dynamic analysis related to 12 records from past earthquakes are carried out using OpenSees software.The factors of ductility,overstrength and response modification are calculated for this system.The values of 9.5 and 6.5 are found and suggested only for the response modification factor for ELBRF systems in allowable stress and ultimate limit state methods,respectively.The fragility curves are plotted for the first time for this type of bracing,which contributes to the assessment of building seismic damage.

Equating incremental dynamic analysis with static nonlinear analysis at near-field excitation

In an incremental dynamic analysis(IDA) using a set of ground motion records,nonlinear time history analysis needs to be performed on structures.It is well recognized that IDA calls for high computational efforts and the results are highly sensitive to selected ground motions.As a result,alternative static methods are needed.This study aims to introduce a new double-stage(N1- N2) static method to estimate capacity curves of MR frames.The technique is regulated to resemble IDA results with specific emphasis on near-field ground motions.Using an ensemble of 56 near-field earthquake records,required ID As have been carried out for SAC-Los Angeles 3-,9- and 20-story buildings and an additional 15-story building.The results of the proposed static method are compared with those from IDA,displacement-based adaptive procedure(DAP),and multimodal procedure(MMP).The results indicate that in addition to enhanced accuracy,very little time is required in the case of N1-N2 method.Thus,for the 3-story structure,the time required is less than 1 minute.The proposed N1-N2 method shows the best accuracy in terms of lateral mechanisms for the 15-story frame while for the other cases,the first mode load pattern leads to the best accuracy.

Multi-timescale Modeling and Dynamic Stability Analysis for Sustainable Microgrids:State-of-the-art and Perspectives

The increasing trend for integrating renewable energy sources into the grid to achieve a cleaner energy system is one of the main reasons for the development of sustainable microgrid(MG)technologies.As typical power-electronized power systems,MGs make extensive use of power electronics converters,which are highly controllable and flexible but lead to a profound impact on the dynamic performance of the whole system.Compared with traditional large-capacity power systems,MGs are less resistant to perturbations,and various dynamic variables are coupled with each other on multiple timescales,resulting in a more complex system instability mechanism.To meet the technical and economic challenges,such as active and reactive power-sharing,voltage,and frequency deviations,and imbalances between power supply and demand,the concept of hierarchical control has been introduced into MGs,allowing systems to control and manage the high capacity of renewable energy sources and loads.However,as the capacity and scale of the MG system increase,along with a multi-timescale control loop design,the multi-timescale interactions in the system may become more significant,posing a serious threat to its safe and stable operation.To investigate the multi-timescale behaviors and instability mechanisms under dynamic inter-actions for AC MGs,existing coordinated control strategies are discussed,and the dynamic stability of the system is defined and classified in this paper.Then,the modeling and assessment methods for the stability analysis of multi-timescale systems are also summarized.Finally,an outlook and discussion of future research directions for AC MGs are also presented.

CFD Based Determination of Dynamic Stability Derivatives in Yaw for a Bird

Dynamic yaw stability derivatives of a gull bird are determined using Computational Fluid Dynamics（CFD） method. Two kinds of motions are applied for calculating the dynamic yaw stability derivatives CNr and CNβ. The first one relates to a lateral translation and, separately, to a yaw rotation. The second one consists of a combined translational and rotational motion. To determine dynamic yaw stability derivatives, the simulation of an unsteady flow with a bird model showing a harmonic motion is performed. The flow solution for each time step is obtained by solving unsteady Euler equations based on a finite volume approach for a small reduced frequency. Then, an evaluation of unsteady forces and moments for one cycle is conducted using harmonic Fourier analysis. The results of the dynamic yaw stability derivatives for both simulations of the model show a good agreement.

Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal, North Western Himalayas

The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

Research on the Stability Analysis Method of DC Microgrid Based on Bifurcation and Strobe Theory

During the operation of a DC microgrid,the nonlinearity and low damping characteristics of the DC bus make it prone to oscillatory instability.In this paper,we first establish a discrete nonlinear system dynamic model of a DC microgrid,study the effects of the converter sag coefficient,input voltage,and load resistance on the microgrid stability,and reveal the oscillation mechanism of a DC microgrid caused by a single source.Then,a DC microgrid stability analysis method based on the combination of bifurcation and strobe is used to analyze how the aforementioned parameters influence the oscillation characteristics of the system.Finally,the stability region of the system is obtained by the Jacobi matrix eigenvalue method.Grid simulation verifies the feasibility and effectiveness of the proposed method.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

Incremental dynamic analysis of concrete gravity dams including base and lift joints

The growth in computer processing power has made it possible to use time-consuming analysis methods such as incremental dynamic analysis（IDA） with higher accuracy in less time.In an IDA study,a series of earthquake records are applied to a structure at successively increasing intensity levels,which causes the structure to shift from the elastic state into the inelastic state and finally into collapse.In this way,the limit-states and capacity of a structure can be determined.In the present research,the IDA of a concrete gravity dam considering a nonlinear concrete behavior,and sliding planes within the dam body and at the dam-foundation interface,is performed.The influence of the friction angle and lift joint slope on the response parameters are investigated and the various limit-states of the dam are recognized.It is observed that by introducing a lift joint,the tensile damage can be avoided for the dam structure.The lift joint sliding is essentially independent of the base joint friction angle and the upper ligament over the inclined lift joint slides into the upstream direction in strong earthquakes.

Stability analysis for flow past a cylinder via lattice Boltzmann method and dynamic mode decomposition

A combination of the lattice Boltzmann method and the most recently developed dynamic mode decomposition is proposed for stability analysis. The simulations are performed on a graphical processing unit. Stability of the flow past a cylinder at supercritical state, Re = 50, is studied by the combination for both the exponential growing and the limit cycle regimes. The Ritz values, energy spectrum, and modes for both regimes are presented and compared with the Koopman eigenvalues. For harmonic-like periodic flow in the limit cycle, global analysis from the combination gives the same results as those from the Koopman analysis. For transient flow as in the exponential growth regime, the combination can provide more reasonable results. It is demonstrated that the combination of the lattice Boltzmann method and the dynamic mode decomposition is powerful and can be used for stability analysis for more complex flows.

Dynamic Modeling, Testing, and Stability Analysis of an Ornithoptic Blimp

In order to study omithopter flight and to improve a dynamic model of flapping propulsion, a series 0f tests are conducted on a flapping-wing blimp. The blimp is designed and constructed from mylar plastic and balsa wood as a test platform for aerodynamics and flight dynamics. The blimp, 2.3 meters long and 420 gram mass, is propelled by its flapping wings. Due to buoyancy the wings have no lift requirement so that the distinction between lift and propulsion can be analyzed in a flight platform at low flight speeds. The blimp is tested using a Vicon motion tracking system and various initial conditions are tested including accelerating flight from standstill, decelerating from an initial speed higher than its steady state, and from its steady-state speed but disturbed in pitch angle. Test results are used to estimate parameters in a coupled quasi-steady aerodynamics/Newtonian flight dynamics model. This model is then analyzed using Floquet theory to determine local dynamic modes and stability. It is concluded that the dynamic model adequately describes the vehicle＇s nonlinear behavior near the steady-state velocity and that the vehicle＇s linearized modes are akin to those of a fixed-wing aircraft.

Assessment of pipeline stability in the Gulf of Mexico during hurricanes using dynamic analysis

Pipelines are the critical link between major offshore oil and gas developments and the mainland. Any inadequate on-bottom stability design could result in disruption and failure, having a devastating impact on the economy and environment. Predicting the stability behavior of offshore pipelines in hurricanes is therefore vital to the assessment of both new design and existing assets. The Gulf of Mexico has a very dense network of pipeline systems constructed on the seabed. During the last two decades, the Gulf of Mexico has experienced a series of strong hurricanes, which have destroyed, disrupted and destabilized many pipelines. This paper first reviews some of these engineering cases. Following that, three case studies are retrospectively simulated using an in-house developed program. The study utilizes the offshore pipeline and hurricane details to conduct a Dynamic Lateral Stability analysis, with the results providing evidence as to the accuracy of the modeling techniques developed.

Stability and dispersion analysis of reproducing kernel collocation method for transient dynamics

A reproducing kernel collocation method based on strong formulation is introduced for transient dynamics. To study the stability property of this method, an algorithm based on the von Neumann hypothesis is proposed to predict the critical time step. A numerical test is conducted to validate the algorithm. The numerical critical time step and the predicted critical time step are in good agreement. The results are compared with those obtained based on the radial basis collocation method, and they axe in good agreement. Several important conclusions for choosing a proper support size of the reproducing kernel shape function are given to improve the stability condition.

Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems

Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.

Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region

In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.

Thermal instability and dynamic response analysis of a tensioned carbon nanotube under moving uniformly distributed external pressure

Single-walled carbon nanotubes(SWCNTs)are receiving immense research attention due to their tremendous thermal,electrical,structural and mechanical properties.In this paper,an exact solution of the dynamic response of SWCNT with a moving uniformly distributed load is presented.The SWCNT is modelled via the theories of Bernoulli-Euler-thermal elasticity mechanics and solved using Integral transforms.The developed closed-form solution in the present work is compared with existing results and excellent agreements are established.The parametric studies show that as the magnitude of the pressure distribution at the surface increases,the deflection associated with the single walled nanotube increases at any mode whilst a corresponding increase in temperature and foundation parameter have an attenuating effect on deflection.Moreover,an increase in the Winkler parameter,as well as a decrease in the SWCNT mass increases its frequency of vibration.Furthermore,an increase in the speed of the external agent decreases the total external pressure as a result of the removal of dead loads.The present work is envisaged to improve the application of SWCNT as nanodevices for structural,electrical and mechanical systems.