Forced vibration assessment of moderately thick carbon nanotube-reinforced composite plates

Abstract

Carbon nanotubes, distributed in composite sheets with various arrangements, can lead to the development of materials with functionally graded properties. In the present study, the method of spectral components was used to investigate the free vibration frequencies and dynamic responses of single-layer sheets reinforced with carbon nanotubes. The spectral component method offers significant advantages for high-frequency dynamic problems, as it requires fewer fine elements to solve boundary conditions. Based on the first-order shear theory, the governing equations of sheet vibration are derived. The discrete Fourier transform is applied to convert the differential equations from the time domain to the frequency domain. Using dynamic shape functions obtained from the exact solutions, the stiffness matrix of the spectral element is constructed. Dynamic frequency responses are then derived, and time-domain responses are obtained using the inverse Fourier transform. The study extracted the exact natural frequencies of functionally graded sheets and verified them with results from the literature, showing high accuracy with a minimal number of elements. The spectral finite element method of fundamental natural frequencies for different ratios of modulus of elasticity and width-to-thickness ratios obtained were investigated and compared with the results of research. The forced vibration was addressed, demonstrating that the method efficiently captures dynamic responses under different carbon nanotube distributions, with spectral displacements verified through numerical comparison. These findings demonstrate the capability and efficiency of the spectral finite element method for analyzing carbon nanotube-reinforced composite plates.