Harmonic excitation of bolted joints
Bolted joints provide one of the most common means of joining two structural
components together. The joints themselves use friction to transmit force, torque and
motion across a common interface from one component to another. In many cases a
pretensioned bolt, running through a common hole at the joint interface, provides the
The friction force at a joint interface is highly nonlinear. This makes the analysis
of dynamic systelTIS with joints unrealistic with conventional linear techniques. It has also
been shown that the contact pressure at a joint interface is not necessarily uniform. A
variable contact pressure results in a variable limiting friction load. Where the contact
pressure can be shown to be smallest on an interface, local microslip can take place
whilst the joint maintains its sticking contact elsewhere. Microslip is responsible for the
dissipation of energy from within bolted joints that otherwise maintain their integrity.
The level of energy dissipation caused by microslip can be significantly larger
than that provided by other dissipative mechanisms within a structure. This provides an
incentive to be able to describe and predict the energy losses and overall joint behaviour
accurately. Difficulties arise when considering 3-Dimensional contact, changing contact
conditions during dynamic loading and the nonlinear nature of friction phenomena.
To investigate microslip behaviour in bolted joints a detailed finite element model
of an isolated lap joint interface was constructed. The joint interface was subjected to a
variety of preloads and applied torque. Output from the joint is in the form of hysteresis
loops that reveal information about the energy dissipated and overall joint stiffness during
a loading cycle.
Representative models are presented that reduce the complexity of the joint, yet
still maintain the defining characteristics of the hysteretic behaviour. The first
representative model uses Jenkins elements that match the physical response of the joint at a number of discrete points during the loading cycle. Good agreement between the
finite element model and the Jenkins element model is illustrated. The Jenkins element
model is also capable of predicting the response of the finite element model when
different magnitudes of preload and applied torque are applied.
The second representative model is the Bouc-Wen representation of hysteresis.
This model offers significant gains in efficiency when approximating the smooth
transition from a fully sticking interface to the onset of joint failure. All of the hysteresis
can be described using just four parameters, and matching with the finite element model
To demonstrate microslip behaviour physically an individual joint was
experimentally analysed. A cantilever beam with a single lap joint near the clamped end
is resonated to generate the dynamic joint hysteresis. The joint behaviour is monitored by
local time domain measurements at a number of different preloads and excitation
amplitudes. Microslip is demonstrated in the joint when the preload is reduced from a
maximum "rigid" clamping value. Notably at low preloads the spectral content of the
response reveals a large contribution from the superharmonics of the excitation
frequency. Both the Jenkins element model and the Bouc-Wen model are successfully
matched to the hysteresis output of the experimental joint.