The author is to be commended for his new approach to the important problem of calculation of natural frequencies for anisotropic plates. However, two comments are in order.
First, the paper lists only three classical boundary conditions: simply supported, clamped, and free. Actually, there is a fourth one: guided or sliding (Bert and Malik 1). For this boundary condition, the effective shear force and the bending slope are both zero. Exact natural frequency results were given for a variety of such cases of isotropic plates in 1.
The second comment is that, although the Ritz method is an upper bound solution, it converges rather slowly in the case of anisotropic plates. For design purposes, a lower bound to a frequency is often more important than an upper bound. The convergence of the Ritz method, a Fourier series method (Whitney 2), and the differential quadrature method were studied by Bert et al. 3 for free vibration of simply supported plates of highly anisotropic material ( compared to 15.4 in the present paper). The latter two methods provided lower bounds.