Abstract:The Timoshenko beam model was used as the flexural wave propagation model in a single, fully-embedded pile. Based on the differential equation of transverse vibration of single, fully-embedded piles in a frequency domain, combined with the force balance and displacement compatibility equations of nodes and the dual transformation of the internal forces and displacements in two local dual coordinate systems, the orthogonality conditions of transverse vibration modes of a single, fully-embedded pile were derived. By virtue of the reverberation-ray matrix method, the natural frequencies, attenuation coefficients, and modes corresponding to different natural frequencies for a single, fully-embedded pile were solved. A specific case study is proposed to verify the correctness of the orthogonality conditions of modes.