Higher-order approximate solutions for nonlinear vibration of a constant-tension string

A new harmonic balance approach for solving the large amplitude nonlinear vibration of a constant-tension string is introduced. The coupling of Newton's method with harmonic balancing takes the advantage of reducing the deficiency and complexity of the classical harmonic balance method in dealing with the nonlinear systems. The solutions are directly induced from a set of linear algebraic equations instead of a set of complicated, coupled nonlinear algebraic equations. Illustrative examples are selected and compared to some published data to verify the accuracy of the higher-order solutions.