A NEW FORM OF THE BENDING VIBRATION INTERNAL FORCES FOR EULER-BERNOULLI STRAIGHT BEAMS

The article focuses on the bending vibration problem of Euler Bernoulli straight beams under the harmonic load. A new form of bending internal force is proposed by using d'Alembert principle again after obtaining the response. This solution directly shows the contributions of the harmonic load and the inertial force to the bending internal forces, respectively. It is proved that it is equivalent to the bending internal force obtained by using the differential equation for deflection of beams and the differential relationship between the beam internal force in the textbook based on Fourier series. This provides a comprehensive case for deeply understanding and application of Fourier series, statics theory, d'Alembert principle and beam bending theory. It is expected to improve the teaching effectiveness of basic mechanics.