This thesis contributes to the understanding of one dimensional mechanical lattice
structures. Structures formed from freely pin jointed rigid links with either vertical or
torsional springs at the pivots, or both, are studied under the in
uence of an axial load.
These studies fall into three parts: static behaviour of a `simple' mechanical system with
only vertical springs, dynamic behaviour of this `simple' system, and static behaviour
of a compound mechanical lattice with both vertical and torsional springs.
The �rst part uses ideas from the �eld of discrete mechanics to derive several discrete
boundary value problems that model the static equilibrium states of the `simple' mechanical
lattice. This application of discrete mechanics allows us to better understand
the relationships between the mechanical system and the discrete boundary value problem
used to model it. The resulting discrete boundary value problem is studied in detail
and interesting complex behaviour is observed.
The study of the dynamic behaviour of the `simple' mechanical lattice concentrates on
the existence and stability of time periodic spatially localised solutions called discrete
breathers. Discrete breathers are found to exist and to be stable. Also, related solutions
called phonobreathers are found to exist and, although the exact phonobreather
solutions are unstable, interesting nonlinear dynamic behaviour is observed close to the
Finally, the static behaviour of a new compound mechanical lattice, a discrete version
of the strut on a linear foundation, is studied in Chapter 6. We see how the behaviour of
two simpler mechanical lattices is manifested in this compound lattice, before presenting
analytic and numerical results on the primary, static, bifurcations of this compound
lattice. The localised behaviour of the most physically relevant static equilibrium states
is also investigated. Extensions to the discrete boundary value problem methods of the
earlier chapters are also discussed.
|Date of Award||1 Jun 2009|
|Supervisor||Chris Budd (Supervisor) & Giles Hunt (Supervisor)|