scholarly journals Dynamic Response of Non-linear Beam Structures in Deterministic and Chaos Perspective

2019 ◽  
Vol 30 (2) ◽  
pp. 14-19
Author(s):  
Anwar Dolu ◽  
Amrinsyah Nasution
Keyword(s):  
Phase Plane ◽  
Initial Conditions ◽  
Time History ◽  
Type Equation ◽  
Poincaré Mapping ◽  
Beam Structures ◽  
Nonlinear Beam ◽  
Axial Forces ◽  
Poincare Mapping ◽  
Non Linear

The behavior of large deformation beam structures can be modeled based on non-linear geometry due to geometricnonlinearity mid-plane stretching in the presence of axial forces, which is a form a nonlinear beam differential equationof Duffing equation type. Identification of dynamic systems from nonlinear beam differential equations fordeterministic and chaotic responses based on time history, phase plane and Poincare mapping. Chaotic response basedon time history is very sensitive to initial conditions, where small changes to initial terms leads to significant change inthe system, which in this case are displacement x (t) and velocity x’(t) as time increases (t). Based on the phase plane, itshows irregular and non-stationary trajectories, this can also be seen in Poincare mapping which shows strange attractorand produces a fractal pattern. The solution to this Duffing type equation uses the Runge-Kutta numerical method withMAPLE software application.

Stability analysis of an electrically actuated microbeam using the Melnikov theorem and Poincaré mapping

2010 ◽  
Vol 225 (2) ◽  
pp. 488-497 ◽  
Author(s):  
M Zamanian ◽  
S E Khadem
Keyword(s):  
Phase Plane ◽  
Chaotic Behaviour ◽  
Damping Factor ◽  
Poincaré Mapping ◽  
System A ◽  
Poincare Mapping ◽  
Electrically Actuated ◽  
Electric Actuation ◽  
The Stability ◽  
Parameter Values

In this article, the stability of a microbeam under an electric actuation is studied. The electric actuation is induced by applying a voltage between the microbeam and an electrode plate that lies at the opposite side of the microbeam. In microswitches, the electric actuation is applied as a DC voltage, and in microresonators it is applied as a combination of AC—DC voltages. It is assumed that the midplane of the microbeam is stretched when it is deflected. It is also shown that by the altering DC electric actuation as a control parameter in a microswitch system, a stable and an unstable branches of equilibrium solution is observed, which meet each other at a saddle-node bifurcation point. The stability of a microresonator is studied using the phase plane diagram and Poincaré mapping. It is shown that depending on the value of damping factor, AC and DC electric voltages, and other parameters of the microresonator, a periodic solution, a quasi periodic, or a pull-in instability may be realized. The prediction of possible chaotic behaviour for microresonator is studied using the Melnikov theorem. It is shown that although for selected domain of system parameters the Melnikov function is satisfied for occurrence of chaotic behaviour, for theses parameter values the pull-in instability occurs before going into the chaotic behaviour. Briefly, the system does not realize any chaotic behaviour.

PERILAKU STRUKTUR BAJA TIPE MRF DENGAN BEBAN LATERAL BERDASARKAN SNI 1726-2012 DAN METODE PERFORMANCE BASED PLASTIC DESIGN (PBPD)

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Nidiasari Jati Sunaryati Eem Ikhsan
Keyword(s):  
Pushover Analysis ◽  
Time History ◽  
Time History Analysis ◽  
Plastic Design ◽  
History Analysis ◽  
Non Linear ◽  
Static Pushover Analysis

Struktur rangka baja pemikul momen merupakan jenis struktur baja tahan gempa yang populer digunakan. Daktilitas struktur yang tinggi merupakan salah satu keunggulan struktur ini, sehingga mampu menahan deformasi inelastik yang besar. Dalam desain, penggunaan metode desain elastis berupa evaluasi non-linear static (Pushover analysis) maupun evaluasi non-linear analisis (Time History Analysis) masih digunakan sebagai dasar perencanaan meskipun perilaku struktur sebenarnya saat kondisi inelastik tidak dapat digambarkan dengan baik. Metode Performance-Based Plastic Design (PBPD) berkembang untuk melihat perilaku struktur sebenarnya dengan cara menetapkan terlebih dahulu simpangan dan mekanisme leleh struktur sehingga gaya geser dasar yang digunakan adalah sama dengan usaha yang dibutuhkan untuk mendorong struktur hingga tercapai simpangan yang telah direncanakan. Studi dilakukan terhadap struktur baja 5 lantai yang diberi beban gempa berdasarkan SNI 1726, 2012 dan berdasarkan metode PBPD. Hasil analisa menunjukkan bahwa struktur yang diberi gaya gempa berdasarkan metode PBPD mencapai simpangan maksimum sesuai simpangan rencana dan kinerja struktur yang dihasilkan lebih baik .

scholarly journals Record-to-record variability and code-compatible seismic safety-checking with limited number of records

2021 ◽  
Author(s):  
Fatemeh Jalayer ◽  
Hossein Ebrahimian ◽  
Andrea Miano
Keyword(s):  
Seismic Hazard ◽  
Linear Time ◽  
Time History ◽  
Time History Analysis ◽  
Seismic Safety ◽  
Hazard Curve ◽  
History Analysis ◽  
Non Linear ◽  
Seismic Hazard Curve ◽  
Cloud Analysis

AbstractThe Italian code requires spectrum compatibility with mean spectrum for a suite of accelerograms selected for time-history analysis. Although these requirements define minimum acceptability criteria, it is likely that code-based non-linear dynamic analysis is going to be done based on limited number of records. Performance-based safety-checking provides formal basis for addressing the record-to-record variability and the epistemic uncertainties due to limited number of records and in the estimation of the seismic hazard curve. “Cloud Analysis” is a non-linear time-history analysis procedure that employs the structural response to un-scaled ground motion records and can be directly implemented in performance-based safety-checking. This paper interprets the code-based provisions in a performance-based key and applies further restrictions to spectrum-compatible record selection aiming to implement Cloud Analysis. It is shown that, by multiplying a closed-form coefficient, code-based safety ratio could be transformed into simplified performance-based safety ratio. It is shown that, as a proof of concept, if the partial safety factors in the code are set to unity, this coefficient is going to be on average slightly larger than unity. The paper provides the basis for propagating the epistemic uncertainties due to limited sample size and in the seismic hazard curve to the performance-based safety ratio both in a rigorous and simplified manner. If epistemic uncertainties are considered, the average code-based safety checking could end up being unconservative with respect to performance-based procedures when the number of records is small. However, it is shown that performance-based safety checking is possible with no extra structural analyses.

Non-Linear Vibration Technique for Crack Detection in Beam Structures Using Frequency Mixing

2010 ◽  
Vol 96 (5) ◽  
pp. 977-980 ◽  
Author(s):  
E. Douka ◽  
K. A. Zacharias ◽  
L. J. Hadjileontiadis ◽  
A. Trochidis
Keyword(s):  
Crack Detection ◽  
Linear Vibration ◽  
Beam Structures ◽  
Vibration Technique ◽  
Non Linear ◽  
Frequency Mixing

scholarly journals Entanglement and geometric phase of the coherent field interacting with a three two-level atoms in the presence of non-linear terms

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 237-245
Author(s):  
Eman Hilal ◽  
Sadah Alkhateeb ◽  
Sayed Abel-Khalek ◽  
Eied Khalil ◽  
Amjaad Almowalled
Keyword(s):  
Coherent State ◽  
Geometric Phase ◽  
Initial Conditions ◽  
Von Neumann Entropy ◽  
Field Mode ◽  
Von Neumann ◽  
Coherent Field ◽  
Non Linear ◽  
Atomic States ◽  
The Impact

We study the interaction of a three two-level atoms with a one-mode optical coherent field in coherent state in the presence of non-linear Kerr medim. The three atoms are initially prepared in upper and entangled states while the field mode is in a coherent state. The constants of motion, three two-level atoms and field density matrix are obtained. The analytic results are employed to perform some investigations of the temporal evolution of the von Neumann entropy as measure of the degree of entanglement between the three two-level atoms and optical coherent field. The effect of the detuning and the initial atomic states on the evolution of geometric phase and entanglement is analyzed. Also, we demonstrate the link between the geometric phase and non-classical properties during the evolution time. Additionally the effect of detuning and initial conditions on the Mandel parameter is studied. The obtained results are emphasize the impact of the detuning and the initial atomic states of the feature of the entanglement, geometric phase and photon statistics of the optical coherent field.

A non-linear disturbance observer-based cooperative adaptive cruise control for real traffic scenarios

2021 ◽  
pp. 095440702110518
Author(s):  
Jaswandi Sawant ◽  
Uttam Chaskar
Keyword(s):  
Disturbance Observer ◽  
Adaptive Cruise Control ◽  
Initial Conditions ◽  
Control Input ◽  
Highway Traffic ◽  
Cruise Control ◽  
Cooperative Adaptive Cruise Control ◽  
Non Linear ◽  
Linear Disturbance ◽  
Real Traffic

Cooperative adaptive cruise control (CACC) has a strong potential to improvise highway traffic capacity and ease traffic disturbances. Extensive exploration is not carried out in the area of CACC for a cut-in maneuver. Contemporary control strategies proposed for CACC cannot regulate the peaking of control input and thus the acceleration/deceleration of following vehicles when applied for various real traffic scenarios. This paper aims to develop a non-linear disturbance observer-based sliding mode control to control a CACC system for various traffic scenarios. The proposed observer estimates the uncertainty present in the actuator dynamics and the preceding vehicle’s acceleration as the lumped disturbance at the same time, it adjusts the observer gain to alleviate the peaking of control input. The stability of individual vehicles and the string stability of vehicle platoon are derived The performance of the proposed scheme is validated with various traffic scenarios, that is, cut-in maneuver, cut-out maneuver, and non-zero initial conditions. The effectiveness of the proposed scheme is demonstrated by comparing it with a linear disturbance observer-based control.

Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator

1993 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Initial Conditions ◽  
Numerical Algorithms ◽  
Time History ◽  
Coupled System ◽  
Interaction Force ◽  
Forced Response ◽  
Linear Oscillator ◽  
Response Analysis ◽  
History Of ◽  
Axially Moving

Abstract The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed between two supports with a damped linear oscillator attached to it, is predicted for arbitrary initial conditions, external forces and boundary excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when transverse waves propagating along the string interact with the oscillator. The discontinuities are treated using the theory of distributions. Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integral-differential equation are developed. Response analysis shows a discontinuous velocity history of the payload attachment point. Special conditions leading to absence of the discontinuities above are given.

scholarly journals An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yu Wang ◽  
Heng Cao ◽  
JinLin Jiang
Keyword(s):  
Domain Of Attraction ◽  
Mapping Method ◽  
Simple Cell ◽  
Iteration Algorithm ◽  
Poincaré Mapping ◽  
Cell Mapping ◽  
Improved Method ◽  
Stable Domain ◽  
Simple Cell Mapping ◽  
Poincare Mapping

An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.

scholarly journals Study on Clearance-Rubbing Dynamic Behavior of 2-DOF Supporting System of Magnetic-Liquid Double Suspension Bearing

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 973
Author(s):  
Jianhua Zhao ◽  
Weidong Yan ◽  
Ziqi Wang ◽  
Dianrong Gao ◽  
Guojun Du
Keyword(s):  
Stable Operation ◽  
Poincaré Mapping ◽  
Eccentricity Ratio ◽  
Magnetic Liquid ◽  
Rotating Speed ◽  
Single Period ◽  
Operating Stability ◽  
Poincare Mapping ◽  
Assembly Error ◽  
Mapping Point

As a new type of suspension bearing, Magnetic-Liquid Double Suspension Bearing (MLDSB) is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting. Its bearing capacity and stiffness can be greatly improved. Because of the small liquid film thickness (it is smaller 10 times than air gap), the eccentricity, crack, bending of the rotor, and the assembly error, it is easy to cause a clearance-rubbing fault between the rotor and stator. The coating can be worn and peeled, the operating stability can be reduced, and then it is one of the key problems of restricting the development and application of MLDSB. Therefore, the clearance-rubbing dynamic equation of 2-DOF system of MLDSB is established and converted into Taylor Series form and the nonlinear components are retained. Dimensionless treatment is carried out by dimensional normalization method. Finally, the rotor displacement response under different rotor eccentricity ratio and rotating speeds is numerically simulated. The studies show that the trajectory of the rotor is periodic elliptic without clearance-rubbing phenomenon when the eccentricity ratio is less than 0.2, while the rotor is greatly affected by the rotation speed and a variety of motions, such as single-period, quasi-period, double-period and chaos, are presented when greater than 0.3. Within the largest range of rotating speed and eccentricity ratio, the rotor presents the single-period trajectory, and then the number of Poincare mapping point is 1, without a clearance-rubbing fault. When the rotational speed is in the scope of (9, 13) krpm and the eccentricity ratio is in the scope of (0.27, 0.4), the number of Poincare mapping point is more than one, the maximum dimensionless rubbing force is −5.7, and then clearance-rubbing fault occurs. The research can provide a theoretical basis for the safe and stable operation of MLDSB.

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