Some aspects of analysis of transverse free vibrations of uniform beams loaded with axial force

Majstorović  Dijana; Aleksandar Borkovic; Prokić  Aleksandar; Vukomanović  Radovan

doi:10.5937/grmk1802035m

Some aspects of analysis of transverse free vibrations of uniform beams loaded with axial force

Majstorović Dijana, Aleksandar Borkovic, Prokić Aleksandar, Vukomanović Radovan

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

U radu se analizira uticaj konstantne aksijalne sile pritiska na slobodne poprečne vibracije prizmatičnih greda. Primijenjene su tri tehničke gredne teorije za dobijanje odgovarajućih analitičkih rješenja. Hamiltonov varijacioni princip koristi se za izvođenje dobro poznatih diferencijalnih jednačina kretanja Timošenkove grede, dok se Bernuli-Ojlerova teorija i Rejlijeva teorija dobijaju kao specijalni slučajevi. Za numeričku analizu, koristi se jednostavan dvodimenzionalni konačni element za ravno stanje napona s drilling stepenom slobode. Odgovarajući programski kod razvijen je i verifikovan poređenjem s komercijalnim softverom Abakus, kao i sa odgovarajućim analitičkim rezultatima. Potom, izvršena je parametarska analiza uticaja aksijalne sile na modalne karakteristike greda, o kojoj je detaljno diskutovano.

Originalsprache	englisch
Seiten (von - bis)	35-55
Seitenumfang	21
Fachzeitschrift	Gradjevinski materijali i konstrukcije
Jahrgang	61
Ausgabenummer	2
DOIs	https://doi.org/10.5937/grmk1802035m
Publikationsstatus	Veröffentlicht - 2018
Extern publiziert	Ja

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http://dx.doi.org/10.5937/grmk1802035m

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abstract = "Influence of constant compressive axial force on free transverse vibrations of uniform beams is considered. Three technical beam theories are applied and appropriate analytical solutions are obtained. Hamilton's variation principle is utilized for derivation of well -known differential equations of motion of Timoshenko beam, while Bernoulli-Euler and Rayleigh theories are considered as special cases. Furthermore, simple two-dimensional plane stress finite element with drilling degree of freedom is employed for numerical analysis. Appropriate code is developed and verified via comparison with commercial finite element software Abaqus, as well as with analytical results. Parametric analysis of influence of the axial force on the modal characteristics of considered beams is performed and discussed in detail.",

author = "Majstorovi{\'c} Dijana and Aleksandar Borkovic and Proki{\'c} Aleksandar and Vukomanovi{\'c} Radovan",

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AU - Radovan, Vukomanović

PY - 2018

Y1 - 2018

N2 - Influence of constant compressive axial force on free transverse vibrations of uniform beams is considered. Three technical beam theories are applied and appropriate analytical solutions are obtained. Hamilton's variation principle is utilized for derivation of well -known differential equations of motion of Timoshenko beam, while Bernoulli-Euler and Rayleigh theories are considered as special cases. Furthermore, simple two-dimensional plane stress finite element with drilling degree of freedom is employed for numerical analysis. Appropriate code is developed and verified via comparison with commercial finite element software Abaqus, as well as with analytical results. Parametric analysis of influence of the axial force on the modal characteristics of considered beams is performed and discussed in detail.

AB - Influence of constant compressive axial force on free transverse vibrations of uniform beams is considered. Three technical beam theories are applied and appropriate analytical solutions are obtained. Hamilton's variation principle is utilized for derivation of well -known differential equations of motion of Timoshenko beam, while Bernoulli-Euler and Rayleigh theories are considered as special cases. Furthermore, simple two-dimensional plane stress finite element with drilling degree of freedom is employed for numerical analysis. Appropriate code is developed and verified via comparison with commercial finite element software Abaqus, as well as with analytical results. Parametric analysis of influence of the axial force on the modal characteristics of considered beams is performed and discussed in detail.

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