In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach

Abstract Firstly, the Chebyshev-Ritz method is applied to the free in-plane vibration of arbitrary shaped laminated triangular plates with elastic boundary conditions. In order to facilitate the calculation of energy, the arbitrary shaped triangular laminated plate is mapped into a square plate by the coordinate transformation. The constitutive equation of laminated materials is constructed by the equivalent monolayer theory. The displacement functions of the square plate after transformation are generally expressed as two-dimensional Chebyshev polynomials multiplied by coefficients. By means of artificial virtual spring technology, the arbitrary elastic boundary conditions of the plate can be obtained by changing the stiffness values of each spring. The in-plane free vibration characteristics of the triangular laminated plate under different boundary conditions are calculated and the accuracy of this method is verified by comparing with finite element results and experimental results. In this paper, modal experiments of three different triangular plates with free boundary and cantilever support boundary are carried out. The comparison results show that the present method has good convergence, high efficiency and satisfactory actuarial accuracy. Finally, novelty numerical analysis is carried out, the influence of geometrical properties, material parameters and boundary conditions on in-plane modal characteristics of laminated triangular plates are studied in detail.