Abstract This article investigates the bandgap characteristics, localized defect states, and multidimensional polarization features of a one-dimensional diatomic gyroscopic periodic structure. A unified mathematical framework is established by introducing binary structural operators, enabling a systematic analysis of the Hamiltonian perturbation mechanisms and wave-manipulation capabilities of perfect, defect-spring, and defect-gyroscope configurations. The results indicate that intrinsic Coriolis coupling breaks the time-reversal symmetry of the system, lifts band degeneracy, and modulates the Bragg bandgap. The defect-spring configuration produces an elastic-potential perturbation, whereas the defect-gyroscope configuration simultaneously modifies the local inertia and velocity-dependent Coriolis coupling, thereby providing multiple independent dynamic tuning channels and facilitating a fixed-frequency, active-background decoupling mechanism. A multi-parameter robustness analysis demonstrates that their relative frequency sensitivities depend on the defect strength: the defect-gyroscope configuration becomes more sensitive in the strong-defect regime, while the defect-spring configuration exhibits stronger spatial confinement over the investigated parameter range. Wave-propagation analysis further shows the preservation of linear polarization within overlapping passbands and chirality-selective filtering of circularly polarized waves within isolated passbands. Moreover, the localized defect-gyroscope state produces an isolated orientation-angle reversal, providing a localized polarization-phase tuning mechanism. These findings clarify the distinct roles of defect-site amplification, spatial confinement, and frequency tunability, and provide theoretical guidance for programmable vector vibration controllers, reconfigurable waveguides, and phononic defect sensors.
Abstract The equilibrium positions of edge dislocations in a bicrystal are determined under the combined influence of a grain boundary, interdislocation interactions, and misfitting elliptical precipitates. The grain boundary is represented by a disclination dipole, and the elliptical precipitates are modeled as Eshelby inclusions. The superposition principle of linear elasticity is utilized to calculate the total stress field and equilibrium states are obtained from minima of the total elastic energy using the Peach–Koehler framework. Two precipitate configurations are considered: coquadrant and opposite quadrant. In the coquadrant configuration, the equilibrium lies in the far-field due to precipitate attraction, with a near-field local minimum state arising only within a limited, misorientation-dependent range of eigenstrain. In the opposite-quadrant configuration, the equilibrium shifts toward the precipitate and the near-field equilibrium is suppressed. The misorientation angle governs initial local minima states, while dislocation offset and precipitate size modify the transition conditions. When the precipitate lies close to the dislocation, its stress field dominates the equilibrium.
Abstract The number of modes of a mechanical system is generally assumed to equal its number of degrees of freedom. In this work, a simple nonclassically damped system is shown to possess fewer modes than degrees of freedom unless a restrictive condition is met. When this condition is met, while there is a full set of modes, they are not orthogonal. These results hold for vanishingly small nonclassical damping, can evade detection by the modal phase collinearity metric, and are relevant to system identification of mechanical systems in which nonclassical damping is present.
Abstract Mode veering, a phenomenon where the frequencies of dispersion bands converge and then diverge while exchanging band characteristics, is critical for designing dynamic systems and predicting structural behavior. Although extensively observed in chiral metamaterial systems, the underlying mechanism governing this phenomenon remains inadequately understood, hindering the development of effective active control strategies. This study presents an actively tunable metamaterial chain consisting of compression–torsion coupling oscillators with dual independent control mechanisms: dynamically adjustable interoscillator coupling stiffness and modifiable rotational inertia. Through precise parameter modulation, continuous and reversible regulation of energy redistribution and polarization switching between the torsional flat band and the longitudinal dispersion band is achieved, enabling on-demand induction of mode veering. Further investigation of this process reveals that this phenomenon originates from an inherent conflict between band reversal and oscillatory incompatibility—a paradox resolved through shifts in the torsional natural frequency of the oscillator. Crucially, the interplay between this frequency shift and band trajectories is identified as the fundamental mechanism governing mode veering. Moreover, this study found that the nonlinear compression–torsion coupling effects can suppress the energy localization induced by the torsional flat band. These works establish a new paradigm for active elastic wave manipulation with promising applications in adaptive vibration isolation and programable metamaterial design.
Abstract Dynamic excitation enables rapid state switching of bistable beams under small forcing amplitudes, yet a controllable switching strategy relies on accurate prediction of beam dynamics. The Galerkin method offers a reliable and efficient approach, but the choice of trial functions varies across studies, leaving the optimal selection for both efficiency and accuracy unresolved. This article investigates the three most commonly used modal sets for a bistable curved beam: straight-beam buckling modes, straight-beam vibration modes, and curved-beam vibration modes. Substituting these trial functions into the governing equation with increasing truncation orders, we numerically compute and compare the dynamic response patterns. One-mode and two-mode truncations yield similar patterns across the three sets but fail to fully capture the primary resonance and main harmonic regions. The three-mode truncation, however, reveals significant discrepancies in the subharmonic interwell region between the buckling modes and the two vibration modes. These discrepancies arise from the axial force effects included in the buckling problem but neglected in the vibration problems, a mechanism substantiated by an axial-to-bending energy ratio analysis. This indicates faster convergence of the buckling modes, which is confirmed by the five-mode results, where all predictions converge and agree qualitatively with the three-mode buckling predictions. Finite element simulations and a parametric study further validate these findings. The study demonstrates that the buckling modes exhibit superior convergence and that a five-mode truncation is generally required to capture the full dynamics, providing a clear and reasoned basis for selecting trial functions and truncation order for bistable curved beams.
