In this thesis a method is derived and presented, for the efficient analysis of the steady
state response of dynamic systems with time variant propenies. The method is especially
attractive for the simulation of the steady state response of lightly damped systems with
low numbers of degree of freedom which are forced by a periodic excitation. A major
feature of the method is that the system non-linearities can be successfully modelled as
time variant propenies.
An ideal application for this approach is the calculation of the dynamic response of a modal
model for progressive valve springs in the frequency domain. The solution method is
explained and derived using this example. The differences, drawbacks, and advantages
are assessed by comparison with both a linear modal model and a discrete time-domain
model; correlation with actual measurement is also shown.
The extreme efficiency of the method allows its application in a more general study of the
dynamic propenies of valve springs. This analysis is initially discussed and examined
using statistical methods. Then the frequency domain solution method is employed to
perform an automatic optimization of the spring frequency characteristic for a 16 valve
prototype engine application.
The spring design obtained from this study has been manufactured and the resulting
hardware is discussed. The measured response of this hardware is compared with
simulation results for the same configuration, verifying the fmdings from the statistical
investigation and the optimization.
Finally open issues and further envisaged work in the area of damping mechanisms in
valve springs and manufacturing issues are diScussed and an approach for the next steps
to take is outlined.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.