Nonlinear Dynamic Stability Analysis Research Articles

Directional crystallization with a mushy region. Part 2: nonlinear analysis of dynamic stability

Directional crystallization with a mushy region. Part 2: nonlinear analysis of dynamic stability

Nonlinear dynamic stability analysis of imperfect architected cellular sandwich plate under impact loading

Nonlinear dynamic stability analysis of imperfect architected cellular sandwich plate under impact loading

Voltage monitoring based on ANN-aided nonlinear stability analysis for DC microgrids

Due to the low inertia of the DC microgrid, the DC bus voltage is prone to drop or oscillate under disturbance. It is also challenging to supervise the stability of a DC microgrid since it is a highly nonlinear dynamic system with high dimensionality and randomness. To tackle this problem, this paper proposes a new method using ANN-aided nonlinear dynamic stability analysis for monitoring the DC bus voltage, which is combined with two steps. The first step is to establish six corresponding nonlinear accurate discrete iterative models of six switching modes of the PV-battery-load-based DC microgrid system, based on the Poincaré map theory, in order to judge the stability quantitatively with a promoted stability margin index. The second step is to use artificial neural networks (ANNs) to forecast the operating mode of the system when random changes occur in environmental circumstances and load power; this will aid the first step in being efficient and adaptable while determining stability cases. And the employed ANNs are trained with the datasets, including the circuit data, ambient temperature, irradiance, and load power, which are generated by MATLAB/Simulink simulation. Theoretical and simulation analyses are carried out under different operating conditions to validate the proposed method’s efficacy in judging the DC microgrid’s destabilizing oscillation and stable running.

Nonlinear dynamic stability analysis of axial impact loaded structures via the nonlocal strain gradient theory

In engineering applications, there has been an overwhelming tendency towards portability, miniaturization, and integration in recent years. To link the intrinsic size dependency feature of the small-scale structure with its structural stability, the nonlocal strain gradient theory, which captures the size effect in a more general size-dependent continuum-based model, is introduced to explore the nonlinear dynamic stability behaviour of nanoplates. Four types of axial impact loading configurations, namely, sinusoidal, exponential, rectangular, and damping, are considered. Some practical factors, such as Winkler-Pasternak elastic foundation and damping, are taken into account in the analysis. The equations of motion for the size-dependent initially imperfect plate are derived in the framework of the first-order shear deformation plate theory in conjunction with the Von Kármán nonlinear terms. Then the Airy stress function corresponding to simply supported nanoplate is introduced; then, by applying the Galerkin method, the obtained differential equations are addressed by the fourth-order Runge-Kutta algorithm. Subsequently, the specific value of the critical dynamic buckling load is determined by the Volmir criterion. Organic solar cells (OSCs), a type of emerging solar-to-electrical energy conversion nanodevice, are used as an illustrative example within the existing framework. The effects of size dependency in conjunction with the pulse load configuration, the initial imperfection, the elastic foundation, as well as the damping ratio on the nonlinear dynamic buckling behaviour of the OSC are thoroughly investigated.

Nonlinear dynamic stability analysis of three-dimensional graphene foam-reinforced polymeric composite cylindrical shells subjected to periodic axial loading

Nonlinear dynamic stability analysis of three-dimensional graphene foam-reinforced polymeric composite cylindrical shells subjected to periodic axial loading

Nonlinear analysis of dynamic stability in walking with toe-only rocker sole shoes in elderly

BackgroundElderly subjects are at the risk of falling. One type of shoe intervention used for this group of the subjects is the shoe with rocker. The aim of this study was to investigate the effects of shoes with various degrees of rockers on dynamic stability of elderly subjects while walking. Method15 elderly subjects were recruited in this study. A motion analysis system was used to record the motions of body while walking on a treadmill. The local dynamic stability (LDS) was evaluated based on use of Lyapunov exponent of center of mass (COM) movement. The subjects were asked to walk barefoot, with shoe with no rocker and with shoe with various rockers (10, 20, 30 and 40°). ResultsThe mean values of LDS (λmax-S) in anteroposterior direction were 0.95 ± 0.46, 0.78 ± 0.51 and 0.74 ± 0.54 in bare foot, shoes with no rocker and shoe with 10° rocker, respectively. The mean value of LDS (λmax-S) in vertical direction varied between 1.21 and 1.23. There was no significant difference between LDS of elderly subjects while walking with shoes with various rocker angles. DiscussionUse of shoes with various rocker angles dose not influence on dynamic stability of elderly subjects while walking. Therefore, it is recommended to use this kind of shoe intervention for other trapeutic purposes.

Nonlinear dynamic stability analysis of clamped and simply supported organic solar cells via the third-order shear deformation plate theory

This study presents a semi-analytical framework to explore the nonlinear dynamic buckling characteristics of the imperfect organic solar cell (OSC) with clamped and simply supported restrains grounded on the third-order shear deformation plate theory (TSDT). The exerting axial displacement loading is divided into infinite and finite durations. Moreover, the spatially dependent Winker-Pasternak elastic foundation and damping effect are incorporated in the current analysis. Combining the von Kármán nonlinearity, the governing equations are derived with the aid of the Airy stress function. By applying the Galerkin method and fourth-order Runge–Kutta procedure, the dynamic buckling critical condition of the OSC subjected to these two kinds of loadings is determined by Budiansky–Hutchinson (B-H) criterion. Based on the numerical results, the influence of some critical parameters, including the geometrical dimension, boundary condition, loading configuration, initial imperfection, damping ratio, and elastic foundation coefficient are investigated. Not limited to the solar cell, this method is also suitable to the dynamic buckling behaviours of other laminated plates.

Finite element-based probabilistic stability analysis of rock-fill tailing dam considering regional seismicity

The recent tailing dam failure in Brazil has again emphasized the need of performing robust stability analysis prior to construction. This paper demonstrates the probabilistic dynamic stability analysis of tailing dams considering an existing rock-fill tailing dam in India. The stability analysis was performed using 2D finite element-based package RS2. In the probabilistic analysis, the strength parameters such as cohesion (c) and the friction angle (φ) were considered as random variables. In total, 3000 numbers of samples were generated assuming a normal distribution. Monte Carlo simulation was used to evaluate the probability of failure (PoF) and reliability index. Strength reduction method was used for the finite element analyses. A pseudo-static seismic loading was incorporated in the strength reduction analysis to check the seismic stability of the dam. A factor of safety (FoS) of 1.15 was observed from the deterministic analysis for downstream slope. For the same case, the probabilistic analysis provided a mean FoS of 1.19 with 5.46% probability of failure. The FoS values and the locations of the critical failure surface obtained by the limit equilibrium method and finite element method were compared. The observed FoS values were found to be higher than the values specified in the IS 7894-1975 (reaffirmed in 1997) and ANCOLD (1999). In the case of pseudo-static approach, the maximum displacement of 0.53 m was observed in the slope. Furthermore, nonlinear dynamic stability analysis was performed to simulate a true earthquake event. The permanent deformation of the slope after the earthquake was found to be 0.40 m. The zone of failure observed in both pseudo-static and nonlinear dynamic stability analyses was found to be the same. Overall, the results revealed that the spatial variability of the soil significantly influences the FoS values.

Nonlinear high-order dynamic stability of AL-foam flexible cored sandwich beam with variable mechanical properties and carbon nanotubes-reinforced composite face sheets in thermal environment

In this paper, the nonlinear dynamic stability analysis of sandwich beam including AL-foam flexible core and carbon nanotubes-reinforced composite face sheets subjected to axial periodic load are investigated by using generalized differential quadrature method. The flexible core of sandwich beam is made of Aluminum alloy foam with variable mechanical properties in the thickness direction. With considering the high-order geometrical nonlinearity in the core and face sheets, the high-order sandwich panel theory and modified couple stress theory are employed for AL-foam flexible core and face sheets, respectively. The governing nonlinear partial differential equations of dynamic stability are derived from the Hamilton’s principle and then discretized by using generalized differential quadrature method to convert them into a linear system of Mathieu–Hill equations. These formulations lead to nine partial differential equations which are coupled in axial and transverse deformations. The boundaries of the instability region are achieved by Bolotin’s method and are illustrated in the dimensionless nonlinear excitation frequency (Ω NL) and excitation frequency ratio (Ω NL/Ω L) to load amplitude plane. A parametric study is carried out to investigate the influence of some important parameters such as slenderness ratio, face sheet thickness, temperature rise, carbon nanotube volume fraction, static load factor, coefficients of Pasternak foundation, and end supports on the nonlinear dynamic instability characteristics of AL-foam core sandwich beam. The numerical results show that with temperature increasing, the nonlinear excitation frequency (Ω NL) and width of corresponding unstable zone decrease, but dynamic frequency ratio (Ω NL/Ω L) and associated unstable region increase. With an increase in the application of sandwich structures for compressible core in advanced industries such as spacecraft, high-speed aircraft, naval vessels, transportation, and automobiles, a further interest in the problem-involving dynamic instability of structures has resulted. Because of their applications, sandwich structures are frequently exposed to periodic axial compressive forces and so the dynamic instability has been a very important topic in structural dynamics and is of practical importance in different engineering industries.

Nonlinear dynamic stability analysis of Euler–Bernoulli beam–columns with damping effects under thermal environment

In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted.

Stability and Dynamic Analyses of Transmission Tower-Line Systems Subjected to Conductor Breaking

Ice loads exerted on the transmission line can increase the probability of conductor breaking, which will lead to the stability failure of transmission towers. In this paper, a transmission tower-line system is established for two towers and three span lines. Then the nonlinear static stability analysis and nonlinear dynamic stability analysis induced by the conductor breaking are carried out to obtain the load versus displacement curves, while studying the failure modes of the transmission tower-line system. Moreover, the ice load and initial eccentricity are considered in the numerical simulation. In addition, a parametric analysis is performed to investigate the influence of span, insulator length and initial tension force on the stability failure of the system. The results show that the dynamic instability will occur earlier than the static instability due to the dynamic impact effect and conductor breaking with ice loads can lead to the progressive collapse of the transmission tower-line system. Finally, the span length has the greatest effect on the response of transmission tower caused by conductor breaking.

Nonlinear Dynamic Stability Analysis of Flexibly Supported Finite Oil Journal Bearings with Variable Viscosity Including Bearing Liner Surface Deformation

Nonlinear Dynamic Stability Analysis of Flexibly Supported Finite Oil Journal Bearings with Variable Viscosity Including Bearing Liner Surface Deformation

Stability Analysis of an Underactuated Autonomous Underwater Vehicle Using Extended-Routh’s Stability Method

In this paper, a new approach to stability analysis of nonlinear dynamics of an underactuated autonomous underwater vehicle (AUV) is presented. AUV is a highly nonlinear robotic system whose dynamic model includes coupled terms due to the hydrodynamic damping factors. It is difficult to analyze the stability of a nonlinear dynamical system through Routh's stability approach because it contains nonlinear dynamic parameters owing to hydrodynamic damping coefficients. It is also difficult to analyze the stability of AUVs using Lyapunov's criterion and LaSalle's invariance principle. In this paper, we proposed the extended-Routh's stability approach to verify the stability of such nonlinear dynamic systems. This extended-Routh's stability approach is much easier as compared to the other existing methods. Numerical simulations are presented to demonstrate the efficacy of the proposed stability verification of the nonlinear dynamic systems, e.g., an AUV system dynamics.

Nonlinear analysis of dynamic stability for the thin cylindrical shells of supercavitating vehicles

The dynamic stability of supercavitating vehicles under periodic axial loading is investigated in this article. The supercavitating vehicle is simulated as a long and thin cylindrical shell subjected to periodic axial loading and simply supported boundary conditions. The nonlinear transverse vibration differential equation is obtained in terms of nonlinear geometric equations, physical equations, and balance equations of cylindrical shells. Mathieu equation with periodic coefficients and nonlinear term is derived by employing Galerkin variational method and Bolotin method. The analytical expressions of the steady-state amplitudes of vibrations in the first- and second-order instable regions are obtained by solving nonlinear Mathieu equation derived in this article. Numerical results are presented to analyze the influence of the sailing speed, ratio of loads, the frequency of axial loads, and the mode of vibration on parametric resonance curves and to show the nonlinear parametric resonance curves incline toward the side where it is greater than the excitation frequency, which significantly extends the range of the exciting region. The presented results indicate the enlargement of the exciting region will cause shrinkage of the safe frequency range of external loads and decrease in dynamic stability of supercavitating vehicle.

Nonlinear dynamic stability analysis of the coupled axial-torsional motion of the rotary drilling considering the effect of axial rigid-body dynamics

Dynamic stability of the coupled axial-torsional motion of a drill string is studied in this paper. Considering the drill string as a continuous system, governing equations of axial and torsional motions are derived. The drill string motion is divided into the rigid-body motion and elastic vibrations. Dynamic behavior of axial rigid-body motion is included through an independent equation. Natural vibration mode shapes of a free-free bar and a fixed-free shaft is introduced as trial functions for discretizing axial and torsional equations of elastic vibration, respectively. Due to the presence of state-dependent delay in equations of motion, semi-discretization method is implemented for stability analysis of the delay differential equations. The effect of nominal rotational speed of the drill string (Ω) and nominal weight on bit (W0) are investigated on drilling stability. Stability charts are presented and maximum allowable value of W0 is depicted with respect to Ω. Comparison of the results reveals that considering a constant axial velocity for the top of the drill string which is a common simplifying assumption in the previous researches, affects stability analysis of the drill string dynamics. It is observed that drilling operation is unstable for speeds lower than a threshold value. Based on the stability analysis, the maximum allowable value of W0 shows an increasing and then decreasing behavior with respect to the nominal rotary speed of the drill string. However, by increasing the damping of the system, its behavior changes into a fully decreasing profile with respect to Ω. It can be recognized from the results that both velocity-weakening friction and regenerative cutting have great effect on stability of the system and should be considered in dynamic modeling of the drill string. In this paper effects of several parameters of rock formation and drill string on the stable region are also presented. Finally, variation of steady-state axial speed is depicted with respect to the rotary table angular speed and nominal WOB which can be useful for choosing optimal and safe parameters for drilling.

Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium

In this study, nonlinear dynamic stability analysis of embedded temperature-dependent viscoelastic plates reinforced by single-walled carbon nanotubes (SWCNTs) is investigated. The equivalent material properties of nanocomposite are estimated based on the rule of mixture. For the carbon-nanotube reinforced composite (CNTRC) visco-plate, both cases of uniform distribution (UD) and functionally graded (FG) distribution patterns of SWCNT reinforcements are considered. The surrounding elastic medium is modeled by orthotropic temperature-dependent elastomeric medium. The viscoelastic properties of plate are assumed based on Kelvin–Voigt theory. Based on orthotropic Mindlin plate theory along with von Kármán geometric nonlinearity and Hamilton’s principle, the governing equations are derived. Generalized differential quadrature method (GDQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR) of system. The effects of different parameters such as distribution type of SWCNTs in plate, volume fractions of SWCNTs, elastomeric medium, temperature, boundary condition and viscoelastic properties of plate are discussed on the DIR of the visco-plate. Results indicate that CNT distribution close to top and bottom are more efficient than those distributed nearby the mid-plane for increasing the DIR.

An ANSYS-Based Approach for Nonlinear Dynamic Stability Analysis

Study on dynamic stability of structure is a hot subject in the fields of engineering mechanics, but its basic theory and analytical method still need to be further improved. This paper improved the current method for dynamic stability analysis called “dynamic eigenvalue method”, and the method for nonlinear dynamic stability analysis based on ANSYS platform is proposed. A long column under harmonic loads is taken as the research objective, dynamic eigenvalues affected by the load frequency, load amplitude and damping ratio are studied. Results show that, the increasing of load frequency or dynamic load amplitude will lead to the increase of maximum dynamic eigenvalue and decrease of minimum dynamic eigenvalue, which is not beneficial to dynamic stability of structure. The increasing of damping ratio will lead to the decrease of maximum dynamic eigenvalue and increase of minimum dynamic eigenvalue, this make the dynamic eigenvalue more stable. Therefore, the high damping is beneficial to dynamic stability of structure.

Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading

Abstract This paper presents a simple solution of the dynamic stability of functionally graded shells under periodic axial loading based on large deflection theory. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The equations of motion are solved by Galerkin procedure. Bolotin’s method is then employed to obtain the steady-state vibrations for non-linear Mathieu equations. The effect of the volume fraction of the material constituents and their distribution on the parametric resonance, in particular steady-state vibrations amplitude and also the effect of the length-to-radius and thickness-to-radius ratios of the cylinder are examined and compared. A good agreement is obtained by comparing the present analysis with other available literature.

Nonlinear Dynamic Analysis of Reticulated Space Truss Structures

AbstractIn this paper, a simpler formulation for the nonlinear motion analysis of reticulated space truss structures is developed by applying a new concept of computational mechanics, named the vector form intrinsic finite element (VFIFE or V-5) method. The V-5 method models the analyzed domain to be composed by finite particles and the Newton's second law is applied to describe each particle's motion. By tracing the motions of all the mass particles in the space, it can simulate the large geometrical and material nonlinear changes during the motion of structure without using geometrical stiffness matrix and iterations. The analysis procedure is vastly simple, accurate, and versatile. The formulation of VFIFE type space truss element includes a new description of the kinematics that can handle large rotation and large deformation, and includes a set of deformation coordinates for each time increment used to describe the shape functions and internal nodal forces. A convected material frame and an explicit time integration scheme for the solution procedures are also adopted. Numerical examples are presented to demonstrate capabilities and accuracy of the V-5 method on the nonlinear dynamic stability analysis of space truss structures.

Nonlinear Analysis of Dynamic Stability and the Prediction of Wing Rock

Nonlinear analysis of dynamic stability for a delta wing in rolling motion at high angles of attack is presented based on a modeled differential equation for wing rolling motion. A method for determining the aerodynamic coefe cients up to third-order approximation in the modeled equation, which are functions of the amplitude of wing rolling oscillation at a e xed high angle of attack, is proposed by use of the Fourier expansion approach. Using the modeled equations of motion combined with the aerodynamic coefe cients determined by the conical Eulerian computations of supersonic e ow past a forced rolling delta wing, we predicted the rock motion of a delta wing that was set into a free-to-roll motion. The results were compared with those obtained by direct coupling calculations based on solving the unsteady e ow equations and the wing motion equations simultaneously, which proved to be in fairly good agreement with each other. A numerical investigation of active control technique of the wing rock was also performed by use of the present method.