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 shapedsingle layer graphene sheets are studied via kirchho plate theory. a four node discretesingular convolution (dsc) method is developed for free vibration analysis of arbitrarystraight-sided quadrilateral graphene. the straight-sided skew and trapezoidal grapheneis mapped into a square graphene in the computational space using a four-node element.by using the geometric transformation, the governing equations and boundary conditionsof the graphene are transformed from the physical domain into a square computationaldomain. numerical examples illustrating the accuracy and convergence of the dsc methodfor skew and trapezoidal shaped graphene sheets are presented. new results for skew andtrapezoidal shaped graphene have been presented, which can serve as benchmark solutionsfor future investigations.