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| Study on Free Vibration and Bending Deformation of Functional Gradient One-dimensional Hexagonal Quasicrystal Laminated Beam |
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Abstract In this paper, the free vibration and bending problems of one-dimensional(1D) hexagonal quasicrystal(QC) laminated beams with functional gradients are investigated using the pseudo-Stroh formula. The QC laminated simply supported beam is modeled, and the transfer matrix method is used to derive the exact solutions of the natural frequency of free vibration and bending deformation displacement of the beam under the simply supported boundary conditions. The results are compared with the existing ones to verify the accuracy and precision of the model and method. The effects of high span ratio, layer thickness ratio and functional gradient coefficient on the natural frequency and bending deformation of 1D QC laminated simply supported beams under two different stacking sequences are analyzed by numerical examples. The results show that the natural frequency increases with the increase of the functional gradient coefficient, and the phonon displacement decreases while the phason displacement increases with the increase of the functional gradient coefficient under the two stacking sequences. The exact solutions obtained in this paper can provide theoretical references for various numerical methods and experimental results for the study of QC beams.
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Received: 28 April 2024
Published: 27 December 2024
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2024, Vol. 45 
