Application of modified generalized trigonometric functions in identification of human tooth vibration properties

Highlights

• Modified generalized trigonometric function is solutions of nonlinear oscillators.

• New Modified Krylov Bogolubov method is developed.

• The tooth-support motion is modelled as a strong nonlinear oscillator.

• Analytical and experimental results for tooth motion are in good agreement.

Summary

In this paper the generalized trigonometric functions are modified for solving of the ordinary differential equation describing the motion of the strong nonlinear oscillator. The generalized trigonometric functions related to the p-Laplacian, which is the nonlinear differential operator, are modified for solving equations with nonlinearity of any rational order. Based on the modified generalized trigonometric function (MGTF) and the known Krilov-Bogoliubov method (KBM) the new, so called, MGTF – KBM method is developed. The method is applied for solving perturbed second order equations of oscillatory motion. As an example the oscillatory tooth motion excited with initial impulse force is considered. The tooth-support system is modeled as a strong nonlinear oscillator. The analytically obtained vibration properties of the tooth are compared with experimentally obtained one and show a good agreement.