Transverse and longitudinal mode coupling in a free vibrating soft string

Kurmyshev, Evguenii V.

doi:10.1016/s0375-9601(03)00264-0

Cited by 18 publications

(17 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Galerkin method could be used to transform (16) and (18) into a set of ordinary differential equations by separating the transverse displacement as…”

Section: Dynamic Modelmentioning

confidence: 99%

“…. , ), and integrating (16) and (18) over the interval of 0 and 1, ordinary differential equations can be obtained as ( lon , tr ), and ( lon , tr ) are the mass, damping, stiffness matrices, and the force vector, respectively, and ( lon , tr ) is the coupled term. Entries of these matrices are formulated as…”

Section: Dynamic Modelmentioning

confidence: 99%

“…where ( , ) and ( , ) are the quasistatic and vibratory axial forces at the particle with the coordinate at time , respectively, and ( , ) is the strain in spatial position at time which can be approximated as [18] ( , ) = ( , ) + 0.5 2 ( , ) + 0.5 2 ( , ) .…”

Section: Dynamic Modelmentioning

confidence: 99%

See 2 more Smart Citations

Effect of Hoisting Load on Transverse Vibrations of Hoisting Catenaries in Floor Type Multirope Friction Mine Hoists

Yao

Xiao

2016

Shock and Vibration

View full text Add to dashboard Cite

The effect of hoisting load on transverse vibrations of hoisting catenaries during lifting in coal mines was investigated in this study. Firstly, dynamic analyses of the vertical hoisting rope were performed. The results show that transverse vibration plays the dominating role in the coupled dynamics of the vertical rope subjected to external excitation induced by axial fluctuations of head sheave, and the rope tension can be approximated by the quasistatic tension. Secondly, employing dynamic simulations, the effect of hoisting load on the transverse vibrations of hoisting catenaries was discussed. The results show that, under the second-order excitation frequency, a discrepant large transverse amplitude will be excited when the hoisting load ranges from 0 to 5000 kg, leading to collision between the two adjacent catenaries and accelerating the rupture of rope. To solve this problem, according to simulation curves, the self-weight of conveyance (preload) can be optimized from 39500 kg to 49500 kg. Eventually, on-site measurements were performed on the studied machine, validating the accuracy of the effect of hoisting load on transverse vibrations of hoisting catenaries. This investigation will greatly support facility maintenance, machine design, and even engineering optimization for floor type multirope friction mine hoists.

show abstract

“…Galerkin method could be used to transform (16) and (18) into a set of ordinary differential equations by separating the transverse displacement as…”

Section: Dynamic Modelmentioning

confidence: 99%

Section: Dynamic Modelmentioning

confidence: 99%

See 1 more Smart Citation

Effect of Hoisting Load on Transverse Vibrations of Hoisting Catenaries in Floor Type Multirope Friction Mine Hoists

Yao

Xiao

2016

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…15 The inertial effects of longitudinal modes have been considered in the case of rubberlike strings by Leamy and Gottlieb 16 and by Kurmyshev. 17 However, the results of these earlier papers [7][8][9][10][11]16,17 cannot be directly applied for the present purposes. This is because the present problem is more complex in the sense that not only the first few but 50 to 100 transverse modes have to be taken into account in the case of a struck piano string.…”

Section: Introductionmentioning

confidence: 96%

Generation of longitudinal vibrations in piano strings: From physics to sound synthesis

Bank

Sujbert

2005

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

Longitudinal vibration of piano strings greatly contributes to the distinctive character of low piano notes. In this paper a simplified modal model is developed, which describes the generation of phantom partials and longitudinal free modes jointly. The model is based on the simplification that the coupling from the transverse vibration to the longitudinal polarization is unidirectional. The modal formulation makes it possible to predict the prominent components of longitudinal vibration as a function of transverse modal frequencies. This provides a qualitative insight into the generation of longitudinal vibration, while the model is still capable of explaining the empirical results of earlier works. The semi-quantitative agreement with measurement results implies that the main source of phantom partials is the transverse to longitudinal coupling, while the string termination and the longitudinal to transverse coupling have only small influence. The results suggest that the longitudinal component of the tone can be treated as a quasi-harmonic spectrum with formantlike peaks at the longitudinal modal frequencies. The model is further simplified and applied for the real-time synthesis of piano sound with convincing sonic results.

show abstract

“…Most previous studies have focused on the vibration performance of strings or cables. Kurmyshev (2003) addressed the parametric generation of a second transverse spatial mode caused by transverse and longitudinal mode coupling by strictly following Hooke's law. Bank and Sujbert (2005) derived differential equations of string vibrations through investigating the generation mechanism of longitudinal vibration in piano strings.…”

Section: Introductionmentioning

confidence: 99%

On the behavior and force transmissibility of a cable network isolator

Chen

Zhang

2019

Journal of Vibration and Control

View full text Add to dashboard Cite

The cable network is being paid increased attention and has found application in practice as a new type of vibration isolator. Modal properties and isolation performance are important considerations for the widespread use of network isolators. In contrast with previous experiments on structural synthesis methods, this paper presents an analytical method to obtain the characteristic equation of a network structure. This method is extended to investigate the modal properties, forced vibration and vibration transmissibility of a network isolation system. In addition, the validity of these analytical modal solutions is verified by an independent finite element method. Modal properties and forced vibrations of cable networks with different configurations are examined. The important system parameters are identified and their effect on the system behavior is discussed.

show abstract

Transverse and longitudinal mode coupling in a free vibrating soft string

Cited by 18 publications

References 16 publications

Effect of Hoisting Load on Transverse Vibrations of Hoisting Catenaries in Floor Type Multirope Friction Mine Hoists

Effect of Hoisting Load on Transverse Vibrations of Hoisting Catenaries in Floor Type Multirope Friction Mine Hoists

Generation of longitudinal vibrations in piano strings: From physics to sound synthesis

On the behavior and force transmissibility of a cable network isolator

Contact Info

Product

Resources

About