Upper and lower bounds for the frequencies of clamped orthotropic plates

Upper and lower bounds are given for the three lowest frequencies of vibration of clamped rectangular orthotropic plates. The bounds were obtained by using a recently developed method which gives estimates for the vibrational frequencies in terms of easily evaluated integrals of trial functions. Important features of the method are that rigorous, improvable upper and lower bounds on the frequencies are obtained and that the trial functions need not satisfy any boundary conditions.