Analytical and finite element modellings of guided waves in multilayered quasicrystal nanoplates with imperfect interfaces and nonlocal effect

• The analytical integration method for expanding boundary conditions using Legendre polynomial is developed. • The finite element method for guided waves in multilayered quasicrystal nanoplates with imperfect interfaces is proposed. • The imperfect interfaces decrease the wave velocities and cut-off frequencies, but increase the amplitude peaks of stresses. • Quasicrystals can increase the overall stiffness and wave velocity of multilayered structures. An analytical integration method for expanding boundary conditions using the Legendre polynomial is developed, which requires that both the control equations and boundary conditions are polynomially expanded to establish a characteristic system. This method can overcome the shortcomings of the available Legendre polynomial method in solving complexity and low efficiency for multilayered structures. Furthermore, a finite element model for Lamb waves in multilayered quasicrystal nanoplates with imperfect interfaces is developed. and then the excitation methods for phonon and phason modes are investigated. The numerical cases reveal that the imperfect interfaces lead to a notable decrease in wave velocities and cut-off frequencies, but increase the amplitude peaks of stresses and displacements. As the frequency increases, the influence of the imperfect interface effect on the nonlocal effect is first enhanced and then suppressed. The research results can provide theoretical references for the guided wave experiments of quasicrystals and the design of quasicrystal composite materials and acoustic devices with high-performance.