Free transverse vibration analysis of laminated composite beams with arbitrary number of concentrated masses

In this study, a new closed-form solution for transverse free vibration analysis of laminated composite beams (LCBs) with arbitrary number of concentrated masses is developed. The LCB is modeled based on the Euler–Bernoulli beam theory and concentrated masses are simulated considering Dirac delta fu...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) 2021-06, Vol.91 (6), p.2393-2402
Main Authors: Ghasemi, Ahmad Reza, Heidari-Rarani, Mohammad, Heidari-Sheibani, Bijan, Tabatabaeian, Ali
Format: Article
Language:English
Subjects:
Beam theory (structures)
Boundary conditions
Cantilever beams
Classical Mechanics
Closed form solutions
Composite beams
Delta function
Engineering
Euler-Bernoulli beams
Exact solutions
Free vibration
Laminar composites
Mathematical analysis
Resonant frequencies
Service life assessment
Technical Notes
Theoretical and Applied Mechanics
Transverse oscillation
Vibration analysis
Vibration response
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Summary:In this study, a new closed-form solution for transverse free vibration analysis of laminated composite beams (LCBs) with arbitrary number of concentrated masses is developed. The LCB is modeled based on the Euler–Bernoulli beam theory and concentrated masses are simulated considering Dirac delta function. Obtained governing equations are, then, solved semianalytically, while the frequency equation and mode shapes are extracted for two different boundary conditions, i.e., clamped-free and simply supported. In order to verify the closed-form solution, the represented model is simplified for a beam without concentrated mass and outcomes are compared with available results in the literature. Finally, the effects of mass as well as location and number of concentrated masses on the free vibration response of the beam are investigated in detail. The results highlight that with increase in the value of point masses, the natural frequencies decrease. Also, it was revealed that the number of point masses influences on the vibration of cantilever beam more than the simply supported one. These outcomes would practically be used to minimize detrimental effects of vibrational noises, leading to increase in the structural components’ lifetime.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-021-01924-2