๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

VIBRATION OF AN AXIALLY MOVING STRING WITH GEOMETRIC NON-LINEARITY AND TRANSLATING ACCELERATION

โœ Scribed by J. CHUNG; C.S. HAN; K. YI

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
182 KB
Volume
240
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

โœฆ Synopsis

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von Karman strain theory, the equations of motion are derived considering the longitudinal and transverse de#ections. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse de#ections. These equations are discretized by the Galerkin method after they are transformed into the variational equations, i.e., the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse de#ections respectively. With the discretized equations, the natural frequencies, the time histories of the de#ections, and the distributions of the de#ection and stress are investigated. In addition, comparisons between the results of linear and non-linear theories are provided.

2001 Academic Press

*x !EA * *x *u *x *v *x "p (10) AXIALLY MOVING STRING * * . (40)

๐Ÿ“œ SIMILAR VOLUMES

Non-Linear Vibration and Instabilities o
Non-Linear Vibration and Instabilities of Elastically Supported Beams With Axial Restraints
โœ D.G. Fertis; C.T. Lee ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 363 KB

The research reported here deals with the non-linear vibration and the static and flutter instabilities of a uniform beam that is elastically supported by a horizontal and vertical spring at each of the two ends of the member. The beam is also subjected to axial and transverse restraints. The axial

A GEOMETRICALLY NON-LINEAR MODEL OF ROTA
A GEOMETRICALLY NON-LINEAR MODEL OF ROTATING SHAFTS WITH INTERNAL RESONANCE AND SELF-EXCITED VIBRATION
โœ J. ลUCZKO ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 352 KB

A geometrically non-linear model of the rotating shaft is introduced, which includes KaH rman non-linearity, non-linear curvature e!ects, large displacements and rotations as well as gyroscopic e!ects. Through applying Timoshenko-type assumptions, the shear e!ects are also included in the model. Con

NON-LINEAR VIBRATION AND THERMAL BUCKLIN
NON-LINEAR VIBRATION AND THERMAL BUCKLING OF AN ORTHOTROPIC ANNULAR PLATE WITH A CENTRIC RIGID MASS
โœ S.-R LI; Y.-H ZHOU; X SONG ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 223 KB

A computational analysis of the non-linear vibration and thermal post-buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge. First, based on von Karman's plate theory and Hamil