Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Abstract

Abstract This study introduces a semi-analytical New Trigonometric Radial Basis Function (NTRBF) method for solving strongly nonlinear differential equations in vibration problems. The method uses a particular trigonometric function to deal with differential equations in an extraordinary and original approach. It was compared to four different problems, including the Global Residue Harmonic Balance Method (GRHBM) in solving circular sector oscillator problem, the Continuous Piecewise Linearization method (CPLM) in solving strong nonlinear differential equation of a tapered beam, the Differential Transform Method (DTM) to solve centrifugal rotating frame motion, and Akbari-Ganji's Method (AGM) to solve Duffing-type nonlinear oscillator. These problems were solved in different conditions. The plots and tables represent both cumulative and maximum errors between the NTRBF and other methods, which use the numerical 4th-order Runge-Kutta method as a benchmark for accuracy. The outcomes prove the high accuracy and efficiency of the innovative technique and its unique capability in solving various nonlinear vibration problems.