Technical Report: Vibration Damping Materials and Their Performance Measurement 1

"Vibration damping" is a technique that converts the vibration energy of a solid surface into thermal energy, thereby reducing the vibration of the solid surface. In contrast, "vibration isolation" is a technique that reduces vibration by decreasing the vibration transmission rate between the vibration source and the vibrated source. It is necessary to clearly distinguish between vibration damping and vibration isolation. Vibration damping can not only reduce vibrations of a solid surface but also reduce solid-borne sound radiated from the solid surface. It is particularly effective in reducing vibrations near the resonance point of the vibrating surface. This vibration damping technology has been studied for a long time as a vibration countermeasure technology, but recently it has attracted the most attention and research has progressed as an application to noise reduction technology, and the development of vibration damping materials has also become active.

Vibration damping materials are made by bonding a vibration damping material made of viscoelastic materials such as resin-based, rubber-based, asphalt-based, or metal-based materials (viscoelastic materials are materials that possess both the properties of "viscosity," which indicates the fluidity of a fluid, and "elasticity," which indicates the restorative properties of a solid) to a base material (steel, wood, concrete, plastic, etc.). Depending on the bonding method, they are divided into "unconstrained type (base material + vibration damping material)" and "constrained type (base material + vibration damping material + constraint material)." Unconstrained type vibration damping materials are commercially available as standalone products (some with double-sided tape attached). A typical example of a constrained type is vibration damping steel plate, which is also commercially available.

The loss coefficient η is one of the evaluation indicators for the damping characteristics of damping materials. The original meaning of the loss coefficient is that when there is damping in a vibration response system, its stress-strain diagram (or load-displacement diagram) draws a hysteresis curve as shown in Figure 1. From this hysteresis curve, the force f = _K1χ at the maximum displacement χ and the force f = _K2χ at zero displacement are measured, and the loss coefficient η is calculated from η = _K2 / _K1. In the representation method shown in Figure 2, where _K1 is represented by a real part and _K2 by an imaginary part, K' is called the complex modulus of elasticity, _K1 is called the storage modulus of elasticity, and _K2 is called the loss modulus of elasticity.

There are various quantities that represent vibration damping performance, and the quantities used differ depending on the specialized field, such as electrical engineering, mechanical engineering, and physics. However, there are simple relationships between these quantities. These relationships are shown in Table 1.

Table 1

ζ: Damping ratio, the ratio of the viscosity coefficient C to the critical viscous damping constant = 2√km.
η: Loss coefficient, representing the loss when the elastic term, including the spring and viscous resistance, is expressed as k(1+iη) in complex form.
K: Damping constant, vibration damping
Δ: Logarithmic decay rate; when amplitude decays, it is the natural logarithm of the ratio of adjacent amplitudes.
D: Damping degree, the amount of damping per second expressed in dB for damped oscillations.
The reverberation time (the time it takes for a signal to decay by 60 dB) can be calculated as T = 60 / D.
Δf: Full width at half maximum, plotted by varying the frequency near resonance.
The frequency range that shows 1/√2 of the maximum value of the resonance curve.
Q: Q: When a vibrating system resonates, the sharpness of this resonance is a quantity that represents the energy of the vibrating system and 2π times the energy per cycle supplied externally to sustain the vibration.
ψ: Natural damping capacitance, the ratio of the energy lost per cycle in an oscillating system to the energy stored in the system.

The most common indicator of vibration damping performance is the loss coefficient η. Typical methods for measuring the loss coefficient include the half-width method, the damping rate method, and the mechanical impedance method. While all of these methods are resonance methods measured near the resonant frequency, non-resonant methods also exist, although they are less common. The following is a summary of the measurement methods.