The present study develops and validates a high-order spectral finite element framework for the dynamic response analysis of beam-type structures under broadband harmonic excitation. The formulation, based on the Euler–Bernoulli beam theory with \(C^1\) -continuity, employs Gauss–Lobatto nodes with variable polynomial order to enable controlled spectral resolution. The novelty of this work lies in the introduction of the Condition Number Amplification Factor (CNAF) as a quantitative measure linking matrix conditioning to spectral accuracy, the systematic characterization of spectral jumps at high wave numbers and instabilities at low wave numbers across discretization parameters, and the development of a polynomial-order-dependent spectral correction coefficient to compensate for high-frequency spectral errors. Numerical investigations reveal that highly accurate convergence is achieved for modes up to approximately \(n \le \textrm{DoF}/2\) , whereas modes beyond this limit are increasingly affected by conditioning-induced instabilities. The proposed framework is validated through natural frequency analysis of clamped cantilever and simply supported beams. In addition, forced response analysis under distributed excitation across multiple frequency bands demonstrates the capability of the method to capture both low- and high-frequency dynamics. The results provide new insight into the interplay between polynomial order, numerical conditioning, and spectral accuracy in high-order spectral finite element formulations.
