Numerical study of vibration damping, energy and energy flow in a beam–plate system

A full analytical model of a beam–plate system has been produced in order to study the distribution of vibration energy and energy flow in beams and rods under simple but realistic excitation conditions. Axial and flexural vibrations are only analysed. Using the developed model as well as energy formulae presented in a companion paper some characteristic features of energy distribution in thin beams/rods have been identified which can be considered as universally applicable. It has been found that axial vibrations, often neglected, may be of the same importance with respect to energy and energy flow as flexural vibrations. Moreover, axial beam vibrations may provide an efficient mechanism of energy transfer to the adjacent sub-systems. Realistic boundary conditions may result in wave conversion which in turn may reverse the flow of energy of either axial or flexural vibration toward the source. The frequency-averaged net power consumed by the beam sub-system was found to depend largely on damping, contrary to the total input power to the system which stays fairly insensitive to it. The energy sharing between the beam and the connected plate was found to depend little on the amount and distribution of damping within the system providing the coupling between the two is strong. Finally, simulation of measurements of energy flow as well as of absorption/reflection/transmission energy coefficients of incorporated joints was shown to be affected to a large degree by beam damping which is often disregarded in experimental work.