Abstract
An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.
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