Stability of Transverse Waves in a Spinning Membrane Disk

1973 ◽  
Vol 40 (1) ◽  
pp. 133-136 ◽  
Author(s):  
P. Z. Bulkeley
Keyword(s):  
Exact Solutions ◽  
Nonlinear Vibration ◽  
Nonlinear Equations ◽  
Transverse Waves ◽  
Disk Rotation ◽  
The Stability ◽  
Direction Opposite ◽  
Membrane Disk

The stability of three known exact solutions to the nonlinear equations governing free transverse motions of spinning membrane disks is investigated for a particular choice of perturbations. A wave which travels circumferentially in the disk in the direction opposite to its rotation is shown to be infinitesimally unstable. A wave traveling in the direction of disk rotation and a nonlinear vibration are not shown to be unstable.

scholarly journals ON NONLINEARITY OF p-BRANE DYNAMICS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261017 ◽  
Author(s):  
A. A. ZHELTUKHIN
Keyword(s):  
Exact Solutions ◽  
Minkowski Space ◽  
Nonlinear Equations ◽  
New Exact Solutions ◽  
Dimensional Minkowski Space

Nonlinear equations of p-branes in D = (2p + 1)-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning p-branes with the Abelian symmetries U(1) × U(1) × ⋯ ×U(1) of their shapes.

scholarly journals Further Results about Seeking for the Exact Solutions of the Nonlinear 2 + 1 -Dimensional Jaulent-Miodek Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jingsen Hu ◽  
Jianming Qi
Keyword(s):  
Nonlinear Equation ◽  
Exact Solutions ◽  
Nonlinear Equations ◽  
Natural Science ◽  
Expansion Method ◽  
Advantages And Disadvantages ◽  
Modern Natural ◽  
Modern Natural Science ◽  
Nonlinear Science ◽  
Formula Method

Nonlinear science is a great revolution of modern natural science. As a result of its rise, the various branches of subjects characterized by nonlinearity have been developed vigorously. In particular, more attention to acquiring the exact solutions of a wide variety of nonlinear equations has been paid by people. In this paper, three methods for solving the exact solutions of the nonlinear 2 + 1 -dimensional Jaulent-Miodek equation are introduced in detail. First of all, the exact solutions of this nonlinear equation are obtained by using the exp − ϕ z -expansion method, tanh method, and sine-cosine method. Secondly, the relevant results are verified and simulated by using Maple software. Finally, the advantages and disadvantages of the above three methods listed in the paper are analyzed, and the conclusion was drawn by us. These methods are straightforward and concise in very easier ways.

scholarly journals Corrigendum

1979 ◽  
Vol 22 (3) ◽  
pp. 571-572
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Large Amplitude ◽  
Plasma Waves ◽  
Relativistic Plasma ◽  
Small Perturbations ◽  
Transverse Waves ◽  
The Stability

In this note we investigate the stability of large-amplitude longitudinal relativistic plasma waves. We find that they are secularly stable, that is, small perturbations grow in time proportional to time but not exponentially with time. Similar results have recently been obtained for transverse waves by Romeiras (1978)

scholarly journals Smartphone-Based Whole-Cell Biosensor Platform Utilizing an Immobilization Approach on a Filter Membrane Disk for the Monitoring of Water Toxicants

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5486
Author(s):  
Junning Ma ◽  
Dorin Harpaz ◽  
Yang Liu ◽  
Evgeni Eltzov
Keyword(s):  
Low Cost ◽  
Environmental Water ◽  
Medical Diagnostics ◽  
Whole Cell ◽  
Filter Membrane ◽  
Sensing Applications ◽  
Bacterial Immobilization ◽  
The Stability ◽  
Whole Cell Biosensor ◽  
Membrane Disk

Bioluminescent bacteria whole-cell biosensors (WCBs) have been widely used in a range of sensing applications in environmental monitoring and medical diagnostics. However, most of them use planktonic bacteria cells that require complicated signal measurement processes and therefore limit the portability of the biosensor device. In this study, a simple and low-cost immobilization method was examined. The bioluminescent bioreporter bacteria was absorbed on a filter membrane disk. Further optimization of the immobilization process was conducted by comparing different surface materials (polyester and parafilm) or by adding glucose and ampicillin. The filter membrane disks with immobilized bacteria cells were stored at −20 °C for three weeks without a compromise in the stability of its biosensing functionality for water toxicants monitoring. Also, the bacterial immobilized disks were integrated with smartphones-based signal detection. Then, they were exposed to water samples with ethanol, chloroform, and H2O2, as common toxicants. The sensitivity of the smartphone-based WCB for the detection of ethanol, chloroform, and H2O2 was 1% (v/v), 0.02% (v/v), and 0.0006% (v/v), respectively. To conclude, this bacterial immobilization approach demonstrated higher sensitivity, portability, and improved storability than the planktonic counterpart. The developed smartphone-based WCB establishes a model for future applications in the detection of environmental water toxicants.

scholarly journals The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Y. H. Qian ◽  
J. L. Pan ◽  
S. P. Chen ◽  
M. H. Yao
Keyword(s):  
Exact Solutions ◽  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Time History ◽  
Approximate Solutions ◽  
Balance Method ◽  
Lumped Mass ◽  
Strongly Nonlinear

The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.

scholarly journals Nonlinear dynamical behaviors of a moving membrane under external excitation

2018 ◽  
Vol 37 (4) ◽  
pp. 774-788
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Shudi Ying
Keyword(s):  
Nonlinear Vibration ◽  
Plate Theory ◽  
State Equation ◽  
Vibration Characteristics ◽  
The State ◽  
External Excitation ◽  
Nonlinear Dynamical ◽  
Runge Kutta Method ◽  
Time Histories ◽  
The Stability

In this paper, the nonlinear vibration characteristics of a moving printing membrane under external excitation are studied. Based on the Von Karman nonlinear plate theory, the nonlinear vibration equation of the axial motion membrane under the external excitation is deduced. The Galerkin’s method is used to discretize the vibration differential equations of the membrane, and then the state equation of the system is obtained. The state equation of the system is numerically solved by the fourth-order Runge–Kutta method. The relationship between the nonlinear vibration characteristics and the amplitude of external excitation, damping coefficient, and aspect ratio of the printing membrane is analyzed by using the time histories, phase-plane portraits, Poincare maps, and bifurcation diagrams. Chaotic intervals and the stable working range of the moving membrane are obtained. This study provides a theoretical basis for predicting and controlling the stability of the membrane.

Stability of shock wave structures in nonlinear elastic media

2019 ◽  
Vol 24 (11) ◽  
pp. 3456-3471 ◽  
Author(s):  
A.P. Chugainova ◽  
A.T. Il’ichev ◽  
V.A. Shargatov
Keyword(s):  
Hyperbolic Equations ◽  
Saddle Points ◽  
Structure Stability ◽  
Nonlinear Hyperbolic Equations ◽  
Discontinuous Solutions ◽  
Transverse Waves ◽  
Stationary Structure ◽  
The Stability ◽  
The Right ◽  
Nonlinear Elastic

The stationary structure stability of discontinuous solutions to nonlinear hyperbolic equations describing the propagation of quasi-transverse waves with velocities close to characteristic ones are studied. A procedure to analyze spectral (linear) stability of these solutions is described. The main focus is the stability analysis of special discontinuities, the stationary structure of which is represented by the integral curve connecting two saddle points corresponding to the states in front of and behind the discontinuity. This analysis is done using the properties of the Evans function, an analytic function on the right complex half-plane, which has zeros in this domain if and only if there exist unstable modes of linearization around a solution representing a special discontinuity with the structure.

Vibration stability analysis of dual motor harmonic synchronous excitation nonlinear vibration conveyer

2018 ◽  
Vol 42 (4) ◽  
pp. 419-426 ◽  
Author(s):  
Xiaohao Li ◽  
Yuanyuan Sun ◽  
Tao Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear Vibration ◽  
Vibration Machine ◽  
Nonlinear Dynamical ◽  
Motion Stability ◽  
Practical Applications ◽  
Nonlinear Force ◽  
The Stability ◽  
Parameter Perturbation Method ◽  
Compensation Function

To enhance the stability of a harmonic vibration synchronous conveyer, this paper establishes a nonlinear dynamical model for this kind of vibration machine, and the effects and compensation function on the stability produced by the nonlinearity of a master vibration spring have been analyzed. A small parameter perturbation method has been used to analyze the effects of a nonlinear force on the conveyer when a fluctuating impact was loaded onto the machine. The reaction between motion stability of the vibration conveyer and the synchronization of the two motors was also investigated. The results of experiments and practical applications demonstrated the correctness of the motion stability analysis of this nonlinear vibration conveyer and its application validity. In conclusion, significant reference values for design, dynamic analysis, testing, and application of the nonlinear vibration conveyer, with harmonic synchronous vibration, actuated by two motors have been achieved.

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