It has been a challenge to reduce unwanted vibration in rotating equipment. The impact of this vibration can range from premature failure of the machine to consumer’s perception of poor product quality. Many designers and product engineers from all industries have been working diligently to solve noise and vibration problems in their products.
One of the most effective methods to solve noise and vibration problems is to dampen the system. Damping, can be divided into two types: active and passive damping. Active damping requires external means to dissipate energy such as electronically controlled actuator. Passive damping requires add-on solutions such as shock absorber, isolator, structural member’s internal damping, etc to dissipate energy. Internal damping itself can be divided into two categories: material and system damping. Material damping is related to diffusion of atoms or molecules or internal friction of the material. System damping is related to energy dissipation in the total structure, which includes material damping and energy dissipation due to joints, interfaces, and fasteners. We will focus on material damping of viscoelastic material in this article.
Viscoelastic material is characterized by possessing both viscous and elastic behavior. A purely elastic material is material which stores all the energy during loading and returns it when the load is removed (unloading). So there is no energy loss during loading and unloading for purely elastic material. Let’s take an example of a slab of concrete with a thickness of T and cross section area A. When it is subjected to cyclic loading, F(t), the concrete will expand and contract, given by displacement function x(t). The stress is given by dividing the load by the cross section area; the corresponding strain on the material can be found by dividing the displacement by the thickness. For elastic material, Hooke’s law is obeyed; the modulus, E can be related to stress σ(t) and strain ε(t) as:
σ(t) = E ε(t)
A purely viscous material does not return any of the energy stored during loading. All energy is lost once the load is removed. In this case, the stress is proportional to the rate of the strain, and the ratio of stress to strain is known as viscosity, η. In most cases, linear (Newtonian) viscosity is considered to be the principal form of energy dissipation. These materials have only damping component.
Viscoelastic materials (e.g. rubbers, plastics) resemble the pure viscous and elastic materials. Some of the energy stored in a viscoelastic material is recovered upon removal of the load, and the reminder is dissipated in the form of heat.
The stress-strain relationships of viscoelastic material is presented by:
σ(t) = E ε(t) + η d ε
The equation above contains elastic and viscous components; where viscous component contains viscosity of material, η multiplied by time derivative of strain. This term is related to material damping; the ability of material to dissipate energy or absorb vibration.