In the literature, we can find many studies that investigate the so-called truncated version of the Timoshenko beam system. In general, the truncated version eliminates the second spectrum of velocity and therefore does not require equal wave velocities to achieve exponential decay. However, the truncated system does not satisfy a Cauchy problem, which makes studying its qualitative properties more challenging. In this article, we present the truncated version of the laminated beam system. Our main results are the well-posedness of the problem using the classical Faedo-Galerkin method combined with a priori estimates and the exponential decay of the energy functional without requiring equal wave velocities.
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