Fourier Series Based on the Deflection EquationExpansion of Simple Beam

Beginning with the differential equation of deflection curve for the beam, Fourier series based on the deflection equation expansion of the simple beam carrying the uniform load is given, and the deflection equation of the simple beam is generalized, Results of a series of infinite series sums structured by the reciprocals of the odd numbers are obtained, It is found that the results are related to Bernoulli numbers. The relationships between the coefficients of the beam, Berno-ulli numbers and Euler numbers are then found, and the relevant calculation formulas are given.