Knots and links have been conjectured to play a fundamental role in a wide range of scientific fields. Recently, tying isolated vortex knots in the complex optical field has been realized. However, how to construct the acoustic vortex knot is still an unknown problem. Here we propose theoretically and demonstrate experimentally the creation of acoustic vortex knots using metamaterials, with decoupled modulation of transmitted phase and amplitude. Based on the numerical simulation, we find that the knot function can be embedded into the acoustic field by designed metamaterials with only 24 × 24 pixels. Furthermore, using the optimized metamaterials, the acoustic fields with Hopf link and trefoil knot vortex lines have been observed experimentally.

Blocking broadband low-frequency airborne noises is highly desirable in lots of engineering applications, while it is extremely difficult to be realized with lightweight materials and/or structures. Recently, a new class of lightweight adaptive metamaterials with hybrid shunting circuits has been proposed, demonstrating super broadband structure-borne bandgaps. In this study, we aim at examining their potentials in broadband sound isolation by establishing an analytical model that rigorously combines the piezoelectric dynamic couplings between adaptive metamaterials and acoustics. Sound transmission loss of the adaptive metamaterial is investigated with respect to both the frequency and angular spectrum to demonstrate their sound-insulation effects. We find that efficient sound isolation can indeed be pursued in the broadband bi-spectrum for not only the case of the small resonator's periodicity where only one mode relevant to the mass-spring resonance exists, but also for the largeperiodicity scenario, so that the total weight can be even lighter, in which the multiple plate-resonator coupling modes appear. In the latter case, the negative spring stiffness provided by the piezoelectric stack has been utilized to suppress the resonance-induced high acoustic transmission. Such kinds of adaptive metamaterials could open a new approach for broadband noise isolation with extremely lightweight structures.

We propose and design a new adaptive sound absorption metamaterial targeting broadband airborne noise at extremely low frequencies. The metamaterial consists of two piezoelectric smart elements: a circular aluminum membrane with surface-bonded piezoelectric films controlled by shunting circuits enclosed with an air cavity for nearly total acoustic absorption at narrow-band frequencies; a hybrid-circuit shunted piezoelectric stack which is mechanically grounded attached to the center of the membrane for purely stiffness control to broaden this highabsorption bandwidth. A piezoelectric-structural-acoustic coupled model is firstly developed to evaluate the sound absorption of the metamaterial. We then perform analytical and numerical tests on metamaterials with and without the piezoelectric stack to design a metamaterial with broadband absorption at desired low frequencies. The underlying adaptive mechanism is to automatically regulate the effective acoustic resistance and reactance of the metamaterial to achieve impedance match conditions, according to different frequencies of inputs. Our numerical results demonstrate that the absorption coefficient of the adaptive metamaterial can be greater than 0.9 in the frequency region, 112-236 Hz with the relative bandwidth being around 0.7. The metamaterial thickness is 30 mm, which is nearly 1/65.6 wavelength of the central frequency of the absorption band. The proposed adaptive metamaterial may open a new avenue towards broadband sound absorption at extremely low frequencies.

Fragile topology is firstly demonstrated in acoustic crystals and then a realistic scheme is proposed to manipulate the transport of acoustic topological edge states (ATESs), i.e., by coupling them with side acoustic cavities. We find that single-mode cavities can completely flip the ATES pseudospin to form a perfect reflection, as long as their resonant frequencies fall into the topological band gap. The perfect reflection of the ATESs is protected by the fragile topology, which is proved by the one-dimensional topological waveguide-cavity transport theory. This fragile topologically protected perfect reflection is immune to the conventional defects (such as bending and disorder) and provides a realistic paradigm for manipulating the ATES transport. As examples, two potential applications, i.e., distance sensors and acoustic switches, are proposed based on the perfect reflection.

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