The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods

Aydın Demir

doi:10.17776/csj.789526

EN

The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods

Abstract

The present paper is concerned with the determination of the frequency equation and sensitivity of the eigenfrequencies of a fixed-free longitudinally vibrating rod and transversally vibrating beam carrying a tip mass by using several methods. First, the exact frequency equations of the such systems are established, and then approximate formulas are given for the fundamental frequency using several methods which contain the equivalent system, Rayleigh quotient, Dunkerley’s formula and continuous system model. The applicability and proximity of these methods versus exact solutions reviewed. The results are compared in a wide range of relevant parameters to give a clear idea about the validity of the proposed formulas. These new derived equations can be very useful for a design engineer who is interested in the eigencharacteristics of similar systems and their sensitivity.

Keywords

Axial vibrations, longitudinal vibrations, rod, beam, tip mass

References

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Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Aydın Demir ^*
0000-0002-8514-2301
Türkiye

Publication Date

March 29, 2021

Submission Date

September 2, 2020

Acceptance Date

March 2, 2021

Published in Issue

Year 2021 Volume: 42 Number: 1

DOI

https://doi.org/10.17776/csj.789526

IZ

https://izlik.org/JA83ZB93XW

APA

Demir, A. (2021). The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods. Cumhuriyet Science Journal, 42(1), 209-217. https://doi.org/10.17776/csj.789526

AMA

1.Demir A. The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods. CSJ. 2021;42(1):209-217. doi:10.17776/csj.789526

Chicago

Demir, Aydın. 2021. “The Fundamental Frequencies of Longitudinally Vibrating Rods Carrying Tip Mass and Transversally Vibrating Beams Carrying Tip Mass by Using Several Methods”. Cumhuriyet Science Journal 42 (1): 209-17. https://doi.org/10.17776/csj.789526.

EndNote

Demir A (March 1, 2021) The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods. Cumhuriyet Science Journal 42 1 209–217.

IEEE

[1]A. Demir, “The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods”, CSJ, vol. 42, no. 1, pp. 209–217, Mar. 2021, doi: 10.17776/csj.789526.

ISNAD

Demir, Aydın. “The Fundamental Frequencies of Longitudinally Vibrating Rods Carrying Tip Mass and Transversally Vibrating Beams Carrying Tip Mass by Using Several Methods”. Cumhuriyet Science Journal 42/1 (March 1, 2021): 209-217. https://doi.org/10.17776/csj.789526.

JAMA

1.Demir A. The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods. CSJ. 2021;42:209–217.

MLA

Demir, Aydın. “The Fundamental Frequencies of Longitudinally Vibrating Rods Carrying Tip Mass and Transversally Vibrating Beams Carrying Tip Mass by Using Several Methods”. Cumhuriyet Science Journal, vol. 42, no. 1, Mar. 2021, pp. 209-17, doi:10.17776/csj.789526.

Vancouver

1.Aydın Demir. The fundamental frequencies of longitudinally vibrating rods carrying tip mass and transversally vibrating beams carrying tip mass by using several methods. CSJ. 2021 Mar. 1;42(1):209-17. doi:10.17776/csj.789526

Cited By

Pseudospektral Chebyshev yöntemi ile fonksiyonel dereceli çubukların zorlanmış titreşim analizi

DÜMF Mühendislik Dergisi

https://doi.org/10.24012/dumf.1573732

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