The Small Motion at the Nodes of a Vibrating String

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

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Optimal control for a vibrating string with variable axial load and damping gain

IFAC Proceedings Volumes ◽

10.3182/20140313-3-in-3024.00087 ◽

2014 ◽

Vol 47 (1) ◽

pp. 75-81

Author(s):

Ramdas B. Sonawane ◽

Anil Kumar ◽

S.B. Nimse

Keyword(s):

Optimal Control ◽

Axial Load ◽

Vibrating String

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Flatness-based control without prediction: example of a vibrating string

PAMM ◽

10.1002/pamm.201010307 ◽

2010 ◽

Vol 10 (1) ◽

pp. 629-630 ◽

Cited By ~ 5

Author(s):

Joachim Rudolph ◽

Frank Woittennek

Keyword(s):

Vibrating String

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Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification ◽

10.1115/detc1995-0646 ◽

1995 ◽

Author(s):

Ebrahim Esmailzadeh ◽

Gholamreza Nakhaie-Jazar ◽

Bahman Mehri

Keyword(s):

Periodic Solution ◽

Fixed Point ◽

Nonlinear Function ◽

Axial Direction ◽

Equation Of Motion ◽

The Other ◽

Sufficient Condition ◽

Vibrating String ◽

The Stability ◽

Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

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The Vibrating String

The Physics of Music and Color ◽

10.1007/978-3-030-19219-8_2 ◽

2019 ◽

pp. 15-51

Author(s):

Leon Gunther

Keyword(s):

Vibrating String

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Strain Measuring Techniques of the Geogrid

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.578-579.1306 ◽

2014 ◽

Vol 578-579 ◽

pp. 1306-1310

Author(s):

Xiao Jing Feng ◽

Zhong Yi Zuo ◽

Wei Tong

Keyword(s):

Strain Measurement ◽

Preventive Measures ◽

Effective Interaction ◽

High Strength ◽

Relative Displacement ◽

Corrosion Resistant ◽

Pullout Tests ◽

Inductive Type ◽

Measuring Techniques ◽

Vibrating String

The strain measurement is a most important and absolutely necessary task on the probing into the constitution of the materials. The ways of strain measurement are theoretically divided as the mechanical type, vibrating-string type, inductive type and bonded resistance type, and the last one is widely used for its high precision and convenience. The geogrid, which has been widespread in the reinforcement structures, is more and more popular for its high strength, good toughness, corrosion resistant, anti-fatigue and effective interaction with soil. The geogrid is made of polymer, its ultimate strain can reach above 10%, and it is sensitive to the time, furthermore it usually has significant relative displacement with soil in the tests. Then some measures have to be taken to make the measuring range wider and make the all gauges achieving synchronization, measures also should be conducted to prevent the strain gauges separated from the geogrid when it has slightly bending, prevent the wires break when the gauges going forward and reduce the influences from the forward preventing measures. Some researchers have showed their techniques to avoiding part of the above problems. Based on a series of pullout tests of geogrid, this paper gives the contrast and analysis on those techniques above, and lists the relative measures that used in these tests, especially for the gauge sticking techniques and preventive measures.

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