High precise analysis of lateral vibration of quintic nonlinear beam

this article intends to achieve a new formulation of beam vibration with quintic nonlinearity, including exact expressions for the beam curvature. to attain a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode which in turn yields the natural frequency of the system. in this direction, new powerful analytical method called parameter expansion method (pem) is employed to obtain the exact solution of frequency-amplitude relationship. afterwards, it is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of mentioned system. finally, preciseness of the present analytic procedures is evaluated in contrast with numerical calculations methods, giving excellent results.