Using D'Alembert principle and generalized Galerkin's method the temporal equation of this system can be given by [Pratiher and Dwivedy]
.......................................(5.1.1)

which is same as the equation(2.6.12) derived in module2. The coefficients used in this equation are described below.

The natural frequency ( ) of the lateral vibration of an elastic beam

....................................................(5.1.2)
Damping ratio ( ζ ) , ....................................................................................(5.1.3)

Coefficient of the nonlinear geometric term

= ....................................................................................(5.1.4)

Coefficient of the nonlinear inertia term

= , .........................................................(5.1.5)

Coefficient of the nonlinear inertia term

= ....................................................................................(5.1.6)

Coefficient of the term

= ................................................................................. (5.1.7)