Exact Vibration Solutions for a Class of Nonuniform Beams

New exact vibration solutions are presented for a class of nonuniform beams where their density and the flexural rigidity vary along the longitudinal axis. The vibration solutions for this class of beams take the form of power functions instead of the Bessel functions of Kirchhoff and other researchers. The exact solutions are useful as reference benchmarks for assessing the validity, convergence, and accuracy of numerical and infinite series methods. (C) 2013 American Society of Civil Engineers.