Sound field shaping in thermoacoustic cells via a synergistic hybrid tuning framework: Symmetry breaking, active excitation and impedance tuning

Sound field shaping, particularly in the contexts of acoustic focusing and cloaking, remains one of the most challenging tasks in modern wave manipulation, necessitating precise control over energy distribution and propagation paths. However, conventional passive methods frequently have fundamental limitations in tunability and dynamic response, resulting in inefficient manipulation under complex boundary conditions. To address these issues, this paper proposes a synergistic hybrid tuning framework for thermoacoustic cells that achieves a sound-pressure-level control range of Δ L p = 189 dB by jointly combining temperature-gradient-driven symmetry breaking, active acoustic excitation, and general impedance boundary tuning. Each mechanism, applied in isolation, is inherently bounded: symmetry breaking cannot inject energy, active excitation cannot reconfigure the modal landscape, and impedance tuning operates within a passive design space. Their coordinated integration, however, yields a control authority that far exceeds the sum of their individual contributions. To realize this framework computationally, a spectral improved-Fourier-Galerkin method is developed for solving the linear thermoacoustic governing equations under full thermo-viscous coupling, enabling efficient free-modal and forced-response analyses with general impedance boundary conditions. A preliminary experimental validation, carried out on a thermoacoustic cell with one rigid and one open termination, confirms the predicted onset frequencies to within 1.6 %. Free-modal analysis reveals that the temperature gradient shifts the first eigenfrequency upward by 18.8 % and induces topological twists in eigenvector trajectories, thereby breaking the spatiotemporal separability of the sound field. In forced response, the boundary auxiliary function autonomously adapts its spectral weights to boundary impedance variations, confirming its capacity for dynamic boundary reconfiguration without reformulating basis functions. A parametric study across the three control degrees of freedom quantitatively demonstrates that only their synergistic coordination reaches the full 189 dB control range; any subset of mechanisms yields substantially narrower dynamic ranges. This control range is a theoretical upper bound obtained under linear conditions. The framework provides a theoretical foundation for high-authority sound field control in thermoacoustic systems, with direct implications for the design of adaptive thermoacoustic actuators and controllable acoustic waveguides.