  In this paper, we consider a vibrating nonlinear Timoshenko system with
thermoelasticity with second sound. We first investigate the strong stability
of this system, then we devote our efforts to obtain the strong lower energy
estimates using Alabau--Boussouira's energy comparison principle introduced in
\cite{2} (see also \cite{alabau}). One of the main advantages of these results
is that they allows us to prove the optimality of the asymptotic results (as
$t\rightarrow \infty$) obtained in \cite{ali}. We also extend to our model the
nice results achieved in \cite{alabau} for the case of nonlinearly damped
Timoshenko system with thermoelasticity. The optimality of our results is also
investigated through some explicit examples of the nonlinear damping term. The
proof of our results relies on the approach in \cite{AB1, AB2}.

Analysis of PDEs