Efficient characterization of the vibration spectrum of long Timoshenko beams on elastic foundations is computationally challenging because of increasing modal density and the numerical instability associated with exponentially growing modal terms. This study investigates the spectral characteristics and dynamic response of free-free Timoshenko beams on elastic foundation using the semi-analytical framework introduced and validated in [1]. A key computational innovation of this framework is the bounded exponential basis, which prevents numerical overflow associated with conventional exponentially growing modal terms and enables stable eigenfrequency extraction even for very long systems. The governing differential equation leads to three transition frequencies that partition the vibration spectrum into spectral regions defined by different types of characteristic roots and the corresponding modal-shape functions. The spectral analysis reveals a pronounced concentration of eigenfrequencies within the second spectral region, where the number of modes grows asymptotically linearly with system length and at a substantially higher rate than in adjacent frequency intervals. This identifies a new modal-clustering behavior that has not previously been reported for Timoshenko beams on elastic foundations. The modal shapes also exhibit distinct nodal behavior: within the third spectral region, the number of nodes increases linearly with the mode number, independently of system length, whereas within the second spectral region it generally decreases, reaching zero for the rigid-body mode. Forced-vibration analyses under transverse base motion show that these spectral characteristics influence modal participation and resonance behavior. The results provide a numerically stable and physically interpretable spectral characterization of long Timoshenko beams on elastic foundations and offer new insights into the mechanisms governing modal clustering and dynamic amplification. REFERENCES [1] G. Banushi. Dynamic analysis of free-free Timoshenko beams on elastic foundation under transverse transient ground deformation. Engineering Structures, 352, 122080, 2026.