BIFURCATION AND CHAOTIC MOTION OF AN ELASTIC PLATE OF LARGE DEFLECTION UNDER PARAMETRIC EXCITATION

2005 ◽  
Vol 15 (09) ◽  
pp. 2849-2863
Author(s):  
Q. HAN ◽  
L. DAI ◽  
M. DONG
Keyword(s):  
Large Deflection ◽  
Single Mode ◽  
Harmonic Excitation ◽  
Governing Equations ◽  
External Excitation ◽  
Mode Method ◽  
Elastic Rectangular Plate ◽  
The Stability ◽  
Nonlinear Elastic ◽  
Bifurcation Behavior

The dynamic behavior of a nonlinear elastic rectangular plate of large deflection subjected to harmonic excitation is investigated. Using the Galerkin principle, a double mode model is established for the plate. The stability and bifurcation behavior of the plate is studied in detail for various loading conditions and system parameters. A set of autonomous equations is derived with the method of averaging. The bifurcation behavior is examined on the basis of the autonomous equations, and the results of theoretical bifurcation analysis are numerically verified. The chaotic response of the plate to the external excitation is also investigated. The governing equations of single as well as double modes are established and the comparison between the single and double mode models is carried out. The applicable conditions of the single mode method are provided. The results obtained show that the single mode approach usually used may lead to incorrect conclusions under certain conditions.

scholarly journals A Single and Double Mode Approach to Chaotic Vibrations of a Cylindrical Shell with Large Deflection

2004 ◽  
Vol 11 (5-6) ◽  
pp. 533-546 ◽  
Author(s):  
Liming Dai ◽  
Qiang Han ◽  
Mingzhe Dong
Keyword(s):  
Cylindrical Shell ◽  
Large Deflection ◽  
Single Mode ◽  
Order Mode ◽  
Governing Equations ◽  
Chaotic Vibrations ◽  
Nonlinear Dynamic Equations ◽  
Different Types ◽  
Mode Method ◽  
Research Show

The chaotic vibrations of a cylindrical shell of large deflection subjected to two-dimensional exertions are studied in the present research. The dynamic nonlinear governing equations of the cylindrical shell are derived on the basis of single and double mode models established. Two different types of nonlinear dynamic equations are obtained with varying dimensions and loading parameters. The criteria for chaos are determined via Melnikov function for the single mode model. The chaotic motion of the cylindrical shell is investigated and the comparison between the single and double mode models is carried out. Results of the research show that the single mode method usually used may lead to incorrect conclusions under certain conditions. Double mode or higher order mode methods should be used in these cases.

Stick-Slip Vibrations of Layered Structures Undergoing Large Deflection and Dry Friction at the Interface

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Hamid M. Sedighi ◽  
Kourosh H. Shirazi ◽  
Khosro Naderan-Tahan
Keyword(s):  
Dry Friction ◽  
Large Deflection ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Layered Structures ◽  
Order Mode ◽  
Chaotic Motions ◽  
Stick Slip ◽  
Coupled Equations ◽  
Mode Method

The present study focuses on the nonlinear analysis of the dynamical behavior of layered structures, including interfacial friction in the presence of the stick-slip phenomenon and large deformation. To achieve a proper outlook for the two-layer structure's behavior, it is essential to precisely realize the mechanisms of motion. Taking the dry friction into account, coupled equations of the transversal and longitudinal large vibration of two-layers are derived and nondimensionalized. Furthermore, the free and forced vibration of the aforementioned system is investigated. From the results of the numerical simulation, it is observed that there exist quasi-periodic and stick–slip chaotic motions in the system. The results demonstrate that the single mode method usually utilized may lead to incorrect conclusions and, instead, the higher order mode method should be employed. A comparative study with ANSYS is developed to verify the accuracy of the proposed approach.

scholarly journals Dynamics and Stability of a Two Degree of Freedom Oscillator With an Elastic Stop

2005 ◽  
Vol 1 (1) ◽  
pp. 94-102 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Solutions ◽  
Analytical Form ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
External Excitation ◽  
Time Duration ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Two Degree Of Freedom

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

scholarly journals Analytical Investigation of the Dynamics of a Nonlinear Structure With Two Degree of Freedom

2005 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Solutions ◽  
Analytical Form ◽  
Harmonic Excitation ◽  
Analytical Investigation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
External Excitation ◽  
Time Duration ◽  
The Stability ◽  
Two Degree Of Freedom

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes from a finite value to an infinite value. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 2: Nonautonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Autonomous System ◽  
Critical Value ◽  
Harmonic Excitation ◽  
Nonautonomous System ◽  
External Excitation ◽  
Zero Eigenvalue ◽  
Bifurcation And Stability

This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

Analytical and Experimental Flutter Analysis of a Typical Wing Section Carrying a Flexibly Mounted Unbalanced Engine

2019 ◽  
Vol 19 (02) ◽  
pp. 1950013 ◽  
Author(s):  
A. S. Mirabbashi ◽  
A. Mazidi ◽  
M. M. Jalili
Keyword(s):  
Stability Domain ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Wing Section ◽  
Unbalanced Force ◽  
Engine Thrust ◽  
Finite State Model ◽  
Flutter Analysis ◽  
Finite State ◽  
The Stability

In this paper, both experimental and analytical flutter analyses are conducted for a typical 5-degree of freedon (5DOF) wing section carrying a flexibly mounted unbalanced engine. The wing flexibility is simulated by two torsional and longitudinal springs at the wing elastic axis. One flap is attached to the wing section by a torsion spring. Also, the engine is connected to the wing by two elastic joints. Each joint is simulated by a spring and damper unit to bring the model close to reality. Both the torsional and longitudinal motions of the engine are considered in the aeroelastic governing equations derived from the Lagrange equations. Also, Peter’s finite state model is used to simulate the aerodynamic loads on the wing. Effects of various engine parameters such as position, connection stiffness, mass, thrust and unbalanced force on the flutter of the wing are investigated. The results show that the aeroelastic stability region is limited by increasing the engine mass, pylon length, engine thrust and unbalanced force. Furthermore, increasing the damping and stiffness coefficients of the engine connection enlarges the stability domain.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

scholarly journals Speaker Localization Based on Audio-Visual Bimodal Fusion

2021 ◽  
Vol 25 (3) ◽  
pp. 375-382
Author(s):  
Ying-Xin Zhu ◽  
Hao-Ran Jin ◽  
◽  
◽  
Keyword(s):  
Microphone Array ◽  
Single Mode ◽  
Frame Rate ◽  
Multimodal Fusion ◽  
Mode Localization ◽  
Localization Method ◽  
Adaboost Algorithm ◽  
Speaker Localization ◽  
The Stability ◽  
Stability And Accuracy

The demand for fluency in human–computer interaction is on an increase globally; thus, the active localization of the speaker by the machine has become a problem worth exploring. Considering that the stability and accuracy of the single-mode localization method are low, while the multi-mode localization method can utilize the redundancy of information to improve accuracy and anti-interference, a speaker localization method based on voice and image multimodal fusion is proposed. First, the voice localization method based on time differences of arrival (TDOA) in a microphone array and the face detection method based on the AdaBoost algorithm are presented herein. Second, a multimodal fusion method based on spatiotemporal fusion of speech and image is proposed, and it uses a coordinate system converter and frame rate tracker. The proposed method was tested by positioning the speaker stand at 15 different points, and each point was tested 50 times. The experimental results demonstrate that there is a high accuracy when the speaker stands in front of the positioning system within a certain range.

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