Frequency response of skew and trapezoidal shaped mono-layer graphene sheets via discrete singular convolution

In the present study, the frequency response of skew and trapezoidal shaped single layer graphene sheets are studied via Kirchho plate theory. A four node Discrete Singular Convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral graphene. The straight-sided skew and trapezoidal graphene is mapped into a square graphene in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the graphene are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew and trapezoidal shaped graphene sheets are presented. New results for skew and trapezoidal shaped graphene have been presented, which can serve as benchmark solutions for future investigations.