### Abstract

A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.

Original language | English |
---|---|

Pages (from-to) | 177-195 |

Number of pages | 19 |

Journal | Shock and Vibration |

Volume | 12 |

Issue number | 3 |

Publication status | Published - 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- Axial vibration
- Buckling
- Material and geometric properties
- Vibration confinement

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Condensed Matter Physics
- Geotechnical Engineering and Engineering Geology
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Shock and Vibration*,

*12*(3), 177-195.

**Axial vibration confinement in nonhomogenous rods.** / Choura, S.; El-Borgi, Sami; Nayfeh, A. H.

Research output: Contribution to journal › Article

*Shock and Vibration*, vol. 12, no. 3, pp. 177-195.

}

TY - JOUR

T1 - Axial vibration confinement in nonhomogenous rods

AU - Choura, S.

AU - El-Borgi, Sami

AU - Nayfeh, A. H.

PY - 2005

Y1 - 2005

N2 - A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.

AB - A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.

KW - Axial vibration

KW - Buckling

KW - Material and geometric properties

KW - Vibration confinement

UR - http://www.scopus.com/inward/record.url?scp=24044495246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24044495246&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24044495246

VL - 12

SP - 177

EP - 195

JO - Shock and Vibration

JF - Shock and Vibration

SN - 1070-9622

IS - 3

ER -