Symmetrical Vibration of a Thick Circular Membrane

1967 ◽  
Vol 34 (4) ◽  
pp. 1020-1022
Author(s):  
W. H. Li ◽  
B. M. Tang ◽  
J. A. Mandel
Keyword(s):  
Circular Membrane ◽  
Symmetrical Vibration

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Differential transformation method for circular membrane vibrations

2020 ◽  
Vol 61(12) (2) ◽  
pp. 333-350
Author(s):  
Jaipong Kasemsuwan ◽  
◽  
Sorin Vasile Sabau ◽  
Uraiwan Somboon ◽  
◽  
...  
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Membrane ◽  
Differential Transformation ◽  
Membrane Vibrations

An inflatable circular membrane mirror for space telescopes

2005 ◽  
Author(s):  
Mingwan Soh ◽  
Jun Ho Lee ◽  
Sung-Kie Youn
Keyword(s):  
Circular Membrane ◽  
Space Telescopes

Proper Orthogonal Decomposition Analysis and Braking Control on Hydrodynamic Retarders by Bionic Iris Effective Diameter Regulation

2021 ◽  
Author(s):  
Xiuqi Chen ◽  
Wei Wei ◽  
Tangzhu Liu ◽  
Wenhao Xie ◽  
Yifei Li ◽  
...  
Keyword(s):  
Flow Field ◽  
Rate Control ◽  
Decomposition Analysis ◽  
Middle Layer ◽  
Torque Control ◽  
Effective Diameter ◽  
Circular Membrane ◽  
Nonlinear Controller ◽  
Filling Rate ◽  
Braking Torque

Abstract AIris, a flat circular membrane in the middle layer of human eyeball, is controlled by sympathetic nerve and can automatically adjust pupil size according to light intensity to limit the amount of light entering the eyeball. This paper attempts to introduce the artificial iris diameter changing mechanism into hydrodynamic machinery, that is, to control the hydrodynamic retarder without filling fluid by changing the inner diameter of iris and changing the flow path of retarder. Through the decomposition and reconstruction of the intrinsic flow field, the flow field characteristics of the iris retarder are deeply understood, and the fast prediction of the braking torque is realized. At the same time, the close-loop controller is designed to control the iris opening that realizing the adaptive adjustment of the output torque of the retarder, thus overcoming the difficulty on-line observation of actual filling rate of oil problem and the inaccurate tracking of braking torque on traditional hydrodynamic retarder with filling rate control. Our work prove that the nonlinear controller can achieve fast and accurate torque closed-loop torque control in various braking conditions compared with the hydrodynamic rate control retarder, and the potential of iris mechanism for adaptive control of hydrodynamic retarder is verified.

Research on Active Control for Thermal Deformation of Precise Membrane Reflector With Boundary SMA Actuators

2014 ◽  
Author(s):  
Yi-Fan Lu ◽  
Hong-Hao Yue ◽  
Zong-Quan Deng ◽  
Horn-Sen Tzou
Keyword(s):  
Active Control ◽  
Thermal Load ◽  
Membrane Structure ◽  
Shape Control ◽  
Membrane Surface ◽  
Circular Membrane ◽  
Equilibrium Equations ◽  
Large Space ◽  
Surface Accuracy ◽  
Thermal Disturbance

Along with the rapid development of space exploration, communication and earth observation technology, the large space membrane structure gains its widely application. With poor stiffness and large flexibility, the surface accuracy of membrane structures can be easily interfered by the space environment variety, so precise shape control of in-orbit space membrane reflector becomes the focus in space technology area. As an object for this paper, the active control of the membrane reflector deformation under typical thermal disturbance in space is investigated. Considering of Von-Karman geometrical nonlinearity, the equilibrium equations of a circular membrane are firstly presented based on Hamilton’s Principle and Love’s thin shell theory. As a simplification for equilibrium equations, the nonlinear mathematical model for the circular membrane in a symmetrical temperature field is obtained. In the next place, an FE model for a circular membrane under thermal load is developed in Abaqus as an example. By contrasting the FEM deformation analysis with mathematical modeling solutions of circular membrane reflectors under typical thermal load, it is demonstrated that the theoretical model is capable of predicting the amplitude of membrane surface deformation. At last, a boundary actuation strategy for membrane shape control is proposed, which could effectively decrease the membrane wrinkle induced by thermal disturbance via precisely control to the tension of the SMA wire actuators. The simulation result indicates the effectiveness of boundary active control strategy on improving membrane surface accuracy with different temperature distributions. The conclusions of modeling and analysis in this paper will be an essential theoretical foundation for future research on active flatness control for in-orbit large space membrane structure.

scholarly journals Modeling of the Eigenfield of a Prestressed Hyperelastic Membrane Encapsulating a Liquid

2006 ◽  
Vol 6 (4) ◽  
pp. 367-385 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
M. Hermann ◽  
A. Timokha ◽  
V. Trotsenko
Keyword(s):  
Boundary Problem ◽  
Approximate Method ◽  
Cylindrical Cavity ◽  
Circular Membrane ◽  
Singular Behavior ◽  
Operator Formulation ◽  
Circular Cylindrical Cavity

AbstractA spectral boundary problem on the eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circular cylindrical cavity filled with a liquid, is examined. The paper presents an operator formulation of the problem and proposes a new semi-analytical approximate method. The method captures singular behavior of the solution in the pole and at the fastening contour of the membrane.

scholarly journals Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 126
Author(s):  
Guangwei Zhou ◽  
Changzhao Qian ◽  
Changping Chen
Keyword(s):  
Finite Element ◽  
Fundamental Frequency ◽  
Vibration Frequency ◽  
Structural Characteristics ◽  
Physical Characteristics ◽  
Parameter Analysis ◽  
Lateral Bending ◽  
Bending Vibration ◽  
Main Cable ◽  
Symmetrical Vibration

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.

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