## Exploiting Nonlinear Behaviour in Structural Dynamics

September 13, 2010 — September 17, 2010

Coordinators:

• David J. Wagg (University of Bristol, Great Britain)
• Lawrence Virgin (Duke University, Duham, NC, USA)

In many cases there are clear advantages in deliberately including nonlinear
effects into the design of a structure. An obvious example is structural dampers. The most effective dampers contain highly nonlinear processes such as friction, fluids and most recently magneto-rheological fluids. Understanding and modelling the behaviour of these nonlinear effects is not a trivial process. However, there has been a dramatic increase in our understanding of nonlinear systems in the past 20 years, which has led to the realisation that beyond just modelling nonlinear effects, engineers can also use them to their advantage.

There are many physical phenomena which lead to nonlinear vibration problems. In some cases nonlinearities either cannot be avoided, or add some benefit, which leads to designing in the face of nonlinearity. For example, if minimal mass in a vibration absorber is required, then large amplitude responses would be expected, so designing in this case necessitates consideration of nonlinear behaviour. This important form of nonlinearity is called geometric nonlinearity. In addition to large deformations, this also includes the effects of combined stretching/compressing with vibration and nonlinear alignment of structural elements. Geometric nonlinearity can be used, for example, to design high performing spring elements such as bi-stable structures with snap-through behaviour.

Increasingly applications are found at the nano or micro scale. For example, for a typical nano-scale resonator at room temperature, the system dynamic range requires that it be driven into nonlinear regimes in order to get the response above the thermal noise floor. In such situations one must deal with nonlinear behaviour, and can often utilize it to good effect. Nonlinearity can also be caused by external forces acting on a linear system, such as fluid or magnetic forces. Nonlinear behaviour can be induced from constraints in the system, such as freeplay, backlash, impact and friction. Friction in bolted structural joints can also be used as a source of increased damping for some structures.

Control forces can be added to a structural system in order to control the behaviour in some way and make it an adaptive structure. For example to reduce unwanted vibrations, detect damage, harvest energy or to shape change (morph) the structure. However, to create adaptive structures, the structure needs to have some awareness of its condition and/or the environment it is in. This is achieved by having a series of measurement sensors mounted on (or integrated into) the structure. Information from the sensors is then used by the global control system. This is where the smart (or intelligent) behaviour is generated.

The course will focus on how nonlinear effects can be exploited by the geometric and material design of structures. Introducing actuators and sensors to the structure to create adaptive capability will also be studied. The course is addressed to doctoral and postdoctoral researchers in aerospace, civil and mechanical engineering, applied mathematics, academic and industrial researchers.

Keywords: Vibrations of Solids and Structures, Systems and Control Applications, Structures, Continuum Mechanics