Exact free vibration analysis of Timoshenko stepped shaft carrying elastically supported eccentric masses with application on SWRO mechanical system

T. A. El-Sayed; S. H. Farghaly

doi:10.1016/j.desal.2016.02.010

Exact free vibration analysis of Timoshenko stepped shaft carrying elastically supported eccentric masses with application on SWRO mechanical system

T. A. El-Sayed^*, S. H. Farghaly

^*Corresponding author for this work

Engineering

Helwan University

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

The aim of the study is to investigate the exact natural frequencies and their associated modal shapes for an axially loaded Timoshenko steppedmulti-span shaft or beamsystem. Each span is carrying an elastically supported eccentric mass and resting on Pasternak elastic foundation. The end and intermediate conditions governing the lateral deflections and slope due to bending of the system have been formulated. Application models have been chosen to verify the reliability of the generalized system frequency equation. Some results of previous works are validated using the present analysis. Real application example of a combined shaft assembly for high pressure boosting device for sea water reverse osmosis (SWRO) desalination plant is investigated. Experimental tests for extended real shaft are carried out. The comparison between the analytical results and the experimental ones, for the first twomodes of vibration, shows good agreementwithminimal errors. These errors do not exceed 5%. In addition, the results of the proposed shaftmodel can be easily obtained for any number of spans and attachments. The present model and analysis is important for industrial applications, such as mechanical, civil, naval and for wider range of sea water desalination machinery.

Original language	English
Pages (from-to)	194-206
Number of pages	13
Journal	Desalination
Volume	385
Early online date	1 Mar 2016
DOIs	https://doi.org/10.1016/j.desal.2016.02.010
Publication status	Published - 2 May 2016

Bibliographical note

Acknowledgments
The authors would like to deeply thank the reviewers of this manuscript for their valuable comments. The supporting and funding of this work, by the Science and Technology Development Fund, STDF, grant No. 3965, Egypt, is gratefully acknowledged. The authors are thankful to Prof. A. M. A. El-Butch, PI of this project for his support and encouragement. Many thanks for the assistants, Eng. Magdy, Mrs. Amal and Mrs. Gamalat for their well contributions.

Keywords

Eccentric mass
Exact solution
Free vibration
High pressure boosting device
Pasternak foundation
Timoshenko stepped shaft

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title = "Exact free vibration analysis of Timoshenko stepped shaft carrying elastically supported eccentric masses with application on SWRO mechanical system",

abstract = "The aim of the study is to investigate the exact natural frequencies and their associated modal shapes for an axially loaded Timoshenko steppedmulti-span shaft or beamsystem. Each span is carrying an elastically supported eccentric mass and resting on Pasternak elastic foundation. The end and intermediate conditions governing the lateral deflections and slope due to bending of the system have been formulated. Application models have been chosen to verify the reliability of the generalized system frequency equation. Some results of previous works are validated using the present analysis. Real application example of a combined shaft assembly for high pressure boosting device for sea water reverse osmosis (SWRO) desalination plant is investigated. Experimental tests for extended real shaft are carried out. The comparison between the analytical results and the experimental ones, for the first twomodes of vibration, shows good agreementwithminimal errors. These errors do not exceed 5%. In addition, the results of the proposed shaftmodel can be easily obtained for any number of spans and attachments. The present model and analysis is important for industrial applications, such as mechanical, civil, naval and for wider range of sea water desalination machinery.",

keywords = "Eccentric mass, Exact solution, Free vibration, High pressure boosting device, Pasternak foundation, Timoshenko stepped shaft",

author = "El-Sayed, {T. A.} and Farghaly, {S. H.}",

note = "Acknowledgments The authors would like to deeply thank the reviewers of this manuscript for their valuable comments. The supporting and funding of this work, by the Science and Technology Development Fund, STDF, grant No. 3965, Egypt, is gratefully acknowledged. The authors are thankful to Prof. A. M. A. El-Butch, PI of this project for his support and encouragement. Many thanks for the assistants, Eng. Magdy, Mrs. Amal and Mrs. Gamalat for their well contributions.",

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AU - El-Sayed, T. A.

AU - Farghaly, S. H.

N1 - Acknowledgments The authors would like to deeply thank the reviewers of this manuscript for their valuable comments. The supporting and funding of this work, by the Science and Technology Development Fund, STDF, grant No. 3965, Egypt, is gratefully acknowledged. The authors are thankful to Prof. A. M. A. El-Butch, PI of this project for his support and encouragement. Many thanks for the assistants, Eng. Magdy, Mrs. Amal and Mrs. Gamalat for their well contributions.

PY - 2016/5/2

Y1 - 2016/5/2

N2 - The aim of the study is to investigate the exact natural frequencies and their associated modal shapes for an axially loaded Timoshenko steppedmulti-span shaft or beamsystem. Each span is carrying an elastically supported eccentric mass and resting on Pasternak elastic foundation. The end and intermediate conditions governing the lateral deflections and slope due to bending of the system have been formulated. Application models have been chosen to verify the reliability of the generalized system frequency equation. Some results of previous works are validated using the present analysis. Real application example of a combined shaft assembly for high pressure boosting device for sea water reverse osmosis (SWRO) desalination plant is investigated. Experimental tests for extended real shaft are carried out. The comparison between the analytical results and the experimental ones, for the first twomodes of vibration, shows good agreementwithminimal errors. These errors do not exceed 5%. In addition, the results of the proposed shaftmodel can be easily obtained for any number of spans and attachments. The present model and analysis is important for industrial applications, such as mechanical, civil, naval and for wider range of sea water desalination machinery.

AB - The aim of the study is to investigate the exact natural frequencies and their associated modal shapes for an axially loaded Timoshenko steppedmulti-span shaft or beamsystem. Each span is carrying an elastically supported eccentric mass and resting on Pasternak elastic foundation. The end and intermediate conditions governing the lateral deflections and slope due to bending of the system have been formulated. Application models have been chosen to verify the reliability of the generalized system frequency equation. Some results of previous works are validated using the present analysis. Real application example of a combined shaft assembly for high pressure boosting device for sea water reverse osmosis (SWRO) desalination plant is investigated. Experimental tests for extended real shaft are carried out. The comparison between the analytical results and the experimental ones, for the first twomodes of vibration, shows good agreementwithminimal errors. These errors do not exceed 5%. In addition, the results of the proposed shaftmodel can be easily obtained for any number of spans and attachments. The present model and analysis is important for industrial applications, such as mechanical, civil, naval and for wider range of sea water desalination machinery.

KW - Eccentric mass

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KW - High pressure boosting device

KW - Pasternak foundation

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ER -

Exact free vibration analysis of Timoshenko stepped shaft carrying elastically supported eccentric masses with application on SWRO mechanical system

Abstract

Bibliographical note

Keywords

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