Exceptional-point conjugate symmetry and migration in fluid-loaded elastic waveguides: restructuring the physical dispersion spectrum

Abstract

The dispersion spectrum of a fluid-loaded elastic waveguide is a non-Hermitian system with eigenmodes on a two-sheeted Riemann manifold. Although exceptional points (EPs) organize avoided crossings, the topological rules by which fluid loading restructures the observable spectrum (both physically admissible modes and their connectivity) remain unknown, and conventional solvers fail to recover complete branches. Here we establish these rules. We prove that, for real elastic moduli and real fluid parameters, EPs obey a conjugate-pair symmetry, and that a pair on the physical sheet enforces an avoided crossing of real wavenumbers between the two modes it controls, yielding a topological criterion for mode identification. We then identify two independent reconstruction mechanisms. First, the physical observation space expands continuously: a mode observable above its vacuum cut-off can extend downward to the sound line, admitting solutions in a frequency band empty in vacuum; vacuum-anchored seeds above cut-offs continued downward capture such branches systematically. Second, EP migration rewires mode connectivity: as fluid density increases, conjugate pairs leaving the physical sheet (signaled by a sign reversal of the imaginary part of either the in-plane or the vertical wavenumber) leave the two previously coupled physical branch segments unconnected by any EP within the observation space; they become independent curves that may intersect freely on the real frequency axis, with the narrowest veerings losing their topological protection first. Mirror-symmetry breaking births additional EPs generically in the trapped regime but only conditionally in the leaky regime. Numerical computations on symmetric and asymmetric composite laminates under single- and double-sided water loading validate the framework, recovering multiple leaky branches missed by standard solvers.