Spline finite point method for calculation natural frequency of arch structures

A spline finite point method is presented for studying on the dynamic behavior of arch structures. The displacement mode shape function of the free vibration of arch structures is simulated with a linear combination of the cubic B spline functions. Based on the curved bar deformation theory, the free vibration frequency equation of arch structures is derived according to principle of minimum potential energy. The calculation program was compiled with MATLAB language. The spline finite point method, verified by examples, is proved to be efficient, accurate, and simple in form. Moreover, the affection of the arch span and the radius thickness ration to the natural frequency coefficient is analyzed. The calculation curves of the smallest longitudinal and the lateral vibration frequency are obtained through which the axial deformation of the arch is suggested to consider and meanwhile its application scope is pointed out.