The Vibrating String

2019 ◽  
pp. 15-51
Author(s):  
Leon Gunther
Keyword(s):  
Vibrating String

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

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.

scholarly journals The Small Motion at the Nodes of a Vibrating String

Nature ◽  
1909 ◽  
Vol 82 (2088) ◽  
pp. 9-9 ◽  
Author(s):  
C. V. RAMAN
Keyword(s):  
Small Motion ◽  
Vibrating String

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

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

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

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 629-630 ◽  
Author(s):  
Joachim Rudolph ◽  
Frank Woittennek
Keyword(s):  
Vibrating String

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

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.

Strain Measuring Techniques of the Geogrid

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.

scholarly journals The Effect of String Tension Variation on the Perceived Pitch of a Classical Guitar

2014 ◽  
Vol 2 (1) ◽  
pp. 53-81
Author(s):  
Wanda Jadwiga Lewis ◽  
James Raphael Smith ◽  
Wanda J. Lewis ◽  
James R. Smith
Keyword(s):  
Classical Theory ◽  
Fundamental Mode ◽  
String Tension ◽  
Classical Guitar ◽  
Sound Waves ◽  
Single Wave ◽  
Geometric Stiffness ◽  
Vibrating String ◽  
Novel Method ◽  
Method Of Assessment

Actual motion of a vibrating guitar string is a superposition of many possible shapes (modes) in which it could vibrate. Each of these modes has a corresponding frequency, and the lowest frequency is associated with a shape idealised as a single wave, referred to as the fundamental mode. The other contributing modes, each with their own progressively higher frequency, are referred to as overtones, or harmonics. By attaching a string to a medium (a soundboard) capable of a response to the vibrating string, sound waves are generated. The sound heard is dominated by the fundamental mode, ‘coloured’ by contributions from the overtones, as explained by the classical theory of vibration. The classical theory, however, assumes that the string tension remains constant during vibration, and this cannot be strictly true; when considering just the fundamental mode, string tension will reach two maximum changes, as it oscillates up and down. These changes, occurring twice during the fundamental period match the frequency of the octave higher, 1st overtone. It is therefore plausible to think that the changing tension effect, through increased force on the bridge and, therefore, greater soundboard deflection, could be amplifying the colouring effect of (at least) the 1st overtone.In this paper, we examine the possible influence of string tension variation on tonal response of a classical guitar. We use a perturbation model based on the classical result for a string in general vibration in conjunction with a novel method of assessment of plucking force that incorporates the engineering concept of geometric stiffness, to assess the magnitude of the normal force exerted by the string on the bridge. The results of our model show that the effect of tension variation is significantly smaller than that due to the installed initial static tension, and affects predominantly the force contribution arising from the fundamental mode. We, therefore, conclude that string tension variation does not contribute significantly to tonal response. Photo credit: By Biblola (Own work) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons

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