THE ORTHOGONALITY AND ENERGY TRANSMITION CHARACTERISTICS OF EULER-BERNOULLI BEAM DYNAMIC MOTION FIELD

Based on analytical solution of undamped Euler-Bernoulli beam's equation of motion, the temporal & spatial average of mechanical energy and power flow's calculation formula are derived. The formula is related to spectral coefficients and based on finite length beam. From the view of functional analysis, the bending motion field, which can be decomposed into evanescent vibration and travelling wave mode, is investigated and the discussion focuses on orthogonality. The result shows that, the evanescent vibration mode is mutual independent of travelling wave mode with regard to energy and power flow functional. In another word, there is no interference between these two modes and the energy superposition principle is satisfied. The important difference between evanescent vibration and wave energy transfer is that the superposition principle is unsatisfied in the evanescent vibration energy transmit mode. That means the interference of two local vibration mode is the reason why the whole vibration field having the capability of energy conduction. The simulation result of a beam with damping at right end and harmonic exciting at middle length is given. The result exhibits that evanescent vibration energy transmit mode shouldn't be neglected in low-frequency range and it is existed that energy exchange between the two modes. But with the increase of frequency, evanescent vibration transmission mode decreases and the total efficiency of energy conducting also falls down.