Free vibration of generally layered composite beams using symbolic computations

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case, i.e. the stepped beam are calculated and finally, free vibrations of a symmetric and non-symmetric LCB are compared with each others.

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Use of trigonometric series functions in free vibration analysis of laminated composite beams

Challenge Journal of Structural Mechanics ◽

10.20528/cjsmec.2020.02.002 ◽

2020 ◽

Vol 6 (2) ◽

pp. 61

Author(s):

Muhittin Turan ◽

Volkan Kahya

Keyword(s):

Free Vibration ◽

Trigonometric Series ◽

Vibration Analysis ◽

Natural Frequencies ◽

Laminated Composite ◽

Free Vibration Analysis ◽

Beam Theory ◽

Composite Beams ◽

Layered Composite ◽

End Conditions

In this study, free vibration analysis of layered composite beams is performed by using an analytical method based on trigonometric series. Based on the first-order shear deformation beam theory, the governing equations are derived from the Lagrange’s equations. Appropriate trigonometric series functions are selected to satisfy the end conditions of the beam. Navier-type solution is used to obtain natural frequencies. Natural frequencies are calculated for different end conditions and lamina stacking. It was seen that the slenderness, E11/E22 and fiber angle have a significant effect on natural frequency. The results of the study are quite compatible with the literature.

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Assessment of Thermal Effects on the Free Vibration Characteristics of Composite Beams

Materials Testing ◽

10.3139/120.110525 ◽

2014 ◽

Vol 56 (1) ◽

pp. 59-64 ◽

Cited By ~ 5

Author(s):

Emin Ergun ◽

Veysel Alkan

Keyword(s):

Free Vibration ◽

Thermal Effects ◽

Composite Beams ◽

Vibration Characteristics

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Vibration of Beams with a Single Delamination under Axial Loading

Materials Science Forum ◽

10.4028/www.scientific.net/msf.675-677.477 ◽

2011 ◽

Vol 675-677 ◽

pp. 477-480

Author(s):

Dong Wei Shu

Keyword(s):

Free Vibration ◽

Natural Frequency ◽

Analytical Solutions ◽

Axial Load ◽

Natural Frequencies ◽

Axial Loading ◽

Composite Beams ◽

Mode Shapes ◽

Equilibrium Conditions ◽

Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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