• Selection of structural materials corresponding to high inherent energy dissipation or damping depends on three factors
• Material properties are connected with the system parameters as follows:
• Damping capacity of structural materials may depend on the following mechanisms
Stress Dependence of Energy Dissipation
The stress-strain plot of a structural material (metals and metallic alloys are considered here) under harmonic loading and low stress level may be plotted as
Figure 9.1: Stress strain plot
• The energy dissipated per unit volume of a structural material per unit cycle is given by the area of the hysteresis loop (also known as mechanical hysteresis loop).
• This is generally denoted as Dm (dissipated energy per m3 per cycle)
• The energy dissipated per unit volume per cycle, Dm is related to the applied stress as
where J is the damping constant and n the damping index.
• At a very low stress level, n=2 and the stress diagram becomes elliptic instead of showing pointed tip
Figure 9.2 : Energy dissipation at different stress level
Generally n varies from 2 to 3. For, higher values of n a modified relationship is used as follows
whereJ1, J2 are the damping constants.
For multi axial loading of a structural member, The Dm is given by
Note that the uniaxial stress σ is replaced by equivalent stress, .
is denoted as
s1, s2, s3 are the principal stress amplitudes. λ1, usually is very small.
The material loss factor ηm could be expressed in terms of Dm as
The total loss factor of a composite specimen ηs can be obtained as
bi - width of the i-th layer
ti - thickness of i-th layer
Table below shows the list of density, Young's modulus, and the order of loss factor of a few common structural materials.
Table 9.1: Mechanical properties of important structural materials