The role of damping on energy and power in vibrating systems

Abstract The role of damping with respect to energy and energy flow in vibrating mechanical systems was examined with the aim of establishing some general relationships. The link between the energy flow and the system energy is considered from both the local and global points of view. Locally, the mean intensity divergence is shown to be strictly proportional to the product of internal damping and potential energy density at a given point, while the imaginary value of complex divergence is proportional to the mean Lagrangian energy density. Globally, the mean value of the total vibratory power input to a structure is proportional to the volume integral of the product between the loss factor and the potential energy density. If the damping is uniformly distributed within a structure, this integral reduces to the product between the (constant) loss factor and the total potential energy. The global potential and kinetic energies can be obtained from the known complex input power to the structure and the known loss factor. In the case of non-uniform damping, the simple power–energy relationships are shown to hold fairly well where potential energy is involved, but could break down if kinetic energy is used instead. Several examples are given to illustrate the theoretical findings.

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