ESDU 09005:2009

INTRODUCTION

This Item is intended to provide introductory and background
information to a series of Items that consider some aspects of
damping in more detail. For example, ESDU 07011 (Reference 43) is
concerned with radiation damping and ESDU 09006 (Reference 44)
presents a description of material damping. Future Items will deal
with the damping of composites and the provision of a compendium of
damping for built-up structures. In this Item concepts related to
different measures applied to damping in materials, as well as to
damping in mechanical systems, are introduced. Every structure in
vibration can be approximated by a dynamically equivalent
mechanical system with a finite number of degrees of freedom. The
degrees of freedom refer to the number of independent coordinates
necessary to describe the motion of the system. In particular
situations a single degree of freedom system can be an adequate
model for the real structure. Although the majority of structures
cannot be treated as SDOF systems, the measures specifying damping
can be defined using a SDOF model without compromising the
generality of the definitions.

Damping in structures may be categorised as either intrinsic,
i.e., within the material of the structure, or as the damping which
depends upon other dissipative factors, such as friction in rivets
or bolts, or from lubrication (Reference 22). Damping also occurs
in a structure which is radiating sound, as vibrational energy is
lost in the surrounding medium rather than by dissipation in the
structure. Material and radiation damping can be estimated
theoretically more easily than other types of damping; in the case
of material damping prediction is based on the material properties
and for radiation damping from the geometrical and material
properties of the structure. When the damping of a structure is
measured in most practical tests, it is the damping of all kinds
which is determined, including the material damping and, provided
there is a surrounding fluid medium, radiation damping.

The measures of damping which are most often used in dynamic
analysis are: the viscous damping ratio (?), the specific damping
capacity (?), the loss factor (?), the inverse quality factor
(Q–¹), the logarithmic decrement (d) and, in the case of
material damping, the tangent of the phase lag (?). and the ratio
of the loss modulus to the Young's modulus. Definitions of the
measures are introduced in the Item using examples of linear
mechanical models, such as Kelvin-Voigt (with viscous damper) and
hysteretic damping model (with hysteretic damper), especially
applicable to material damping. In ESDU Items information on
damping is mostly provided in terms of the viscous damping ratio.
For example, in Data Item No. 72005, ‘The estimation of r.m.s.
stress in stiffened skin panels subjected to random acoustic
loading' (Reference 20), nomographs are used which are based on a
viscous damping ratio of 0.017, a value regarded as typical for
aerospace structures, and, if a different value is used, a
correction factor is applied. The relationships between the
different measures of damping are summarised in the Appendix A.