  This paper investigates a predictive model that considers the impact of
stretch on the dynamic response of laminar premixed conical and V- flames; the
flame stretch consists of two components: the flame curvature and flow strain.
The steady and perturbed flame fronts are determined via the linearized
$G$-equation associated with the flame stretch model. Parameter analyses of the
effects of Markstein length $\mathcal{L}$, flame radius $R$ and unstretched
flame aspect ratio $\beta$ are also conducted. Results show that the flame
stretch reduces the steady flame height, with this effect being more
significant for larger Markstein lengths and smaller flame sizes. The effects
of flame stretch on perturbed flames are evaluated by comparing the flame
transfer function (FTF) considering the flame stretch and not. For flames of
different sizes, the impact of flame stretch on FTF gain can be divided into
three regions. When both $\beta$ and $R$ are relatively small, due to the
decrease in steady flame height and the impact of flow strain, the FTF gain
increases. As $\beta$ and $R$ gradually increase, the FTF gain of the conical
flame oscillates periodically while the FTF gain of the V-flame decreases,
primarily due to the flame curvature enhancing the flame front disturbance and
the wrinkle counteracting effect. When $\beta$ and $R$ are large, a disruption
in wrinkle counteracting effect ensues, leading to a significant increase in
FTF gain. Furthermore, as the actual flame height is reduced, the flame stretch
also reduces the FTF phase lag which is related to the disturbance propagation
time from the flame root to the tip.
