Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section

ŠTUBŇA, Igor ;TRNÍK, Anton .
Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 51, n.2, p. 90-94, august 2017. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/>. Date accessed: 23 jan. 2026. 
doi:http://dx.doi.org/.

Štubňa, I., & Trník, A.
(2005).
Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section.
Strojniški vestnik - Journal of Mechanical Engineering, 51(2), 90-94.
doi:http://dx.doi.org/

@article{.,
	author = {Igor  Štubňa and Anton  Trník},
	title = {Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {51},
	number = {2},
	year = {2005},
	keywords = {flexural vibration; partial differential equation; Timoshenko’s equation; bending moments; },
	abstract = {A short review of the known equations of flexural vibration used for determining the Young’s modulus and sound velocity is presented, as well as a new equation that accounts for the rotary inertia and the influence of the shear forces with the term, where iz is the radius of gyration of the cross-section, m is Poisson’s ratio, and k is the shape coefficient introduced by Timoshenko. The dispersion curves show a very good fit between the commonly accepted Timoshenko’s equation and the new equation derived by Štubna and Majerník.},
	issn = {0039-2480},	pages = {90-94},	doi = {},
	url = {https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/}
}

Štubňa, I.,Trník, A.
2005 August 51. Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 51:2

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%A Trník, Anton 
%D 2005
%T Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section
%B 2005
%9 flexural vibration; partial differential equation; Timoshenko’s equation; bending moments; 
%! Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section
%K flexural vibration; partial differential equation; Timoshenko’s equation; bending moments; 
%X A short review of the known equations of flexural vibration used for determining the Young’s modulus and sound velocity is presented, as well as a new equation that accounts for the rotary inertia and the influence of the shear forces with the term, where iz is the radius of gyration of the cross-section, m is Poisson’s ratio, and k is the shape coefficient introduced by Timoshenko. The dispersion curves show a very good fit between the commonly accepted Timoshenko’s equation and the new equation derived by Štubna and Majerník.
%U https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/
%0 Journal Article
%R 
%& 90
%P 5
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 51
%N 2
%@ 0039-2480
%8 2017-08-18
%7 2017-08-18

Štubňa, Igor, & Anton  Trník.
"Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section." Strojniški vestnik - Journal of Mechanical Engineering [Online], 51.2 (2005): 90-94. Web.  23 Jan. 2026

TY  - JOUR
AU  - Štubňa, Igor 
AU  - Trník, Anton 
PY  - 2005
TI  - Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - flexural vibration; partial differential equation; Timoshenko’s equation; bending moments; 
N2  - A short review of the known equations of flexural vibration used for determining the Young’s modulus and sound velocity is presented, as well as a new equation that accounts for the rotary inertia and the influence of the shear forces with the term, where iz is the radius of gyration of the cross-section, m is Poisson’s ratio, and k is the shape coefficient introduced by Timoshenko. The dispersion curves show a very good fit between the commonly accepted Timoshenko’s equation and the new equation derived by Štubna and Majerník.
UR  - https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/

@article{{}{.},
	author = {Štubňa, I., Trník, A.},
	title = {Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {51},
	number = {2},
	year = {2005},
	doi = {},
	url = {https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/}
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TY  - JOUR
AU  - Štubňa, Igor 
AU  - Trník, Anton 
PY  - 2017/08/18
TI  - Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 51, No 2 (2005): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 
KW  - flexural vibration, partial differential equation, Timoshenko’s equation, bending moments, 
N2  - A short review of the known equations of flexural vibration used for determining the Young’s modulus and sound velocity is presented, as well as a new equation that accounts for the rotary inertia and the influence of the shear forces with the term, where iz is the radius of gyration of the cross-section, m is Poisson’s ratio, and k is the shape coefficient introduced by Timoshenko. The dispersion curves show a very good fit between the commonly accepted Timoshenko’s equation and the new equation derived by Štubna and Majerník.
UR  - https://www.sv-jme.eu/sl/article/equations-for-the-flexural-vibration-of-a-sample-with-a-uniform-cross-section/

Štubňa, Igor, AND Trník, Anton.
"Equations for the Flexural Vibration of a Sample with a Uniform Cross-Section" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 51 Number 2 (18 August 2017)