Broadband passive nonlinear acoustic diode

In dynamical and acoustical systems, breaking reciprocity is achievable by employing external biases, spatial temporal variations of material properties, or nonlinearities. In this present work, we propose, theoretically analyze, and experimentally demonstrate the first passive broad-band mechanical diode, by adding an asymmetric local nonlinear interface to an otherwise linear waveguide. It is shown that for a broad range of input energies and frequencies, three different types of nonreciprocal behavior are obtained, (i) different transmitted energies depending on the direction of wave propagation, (ii) transmission of acoustic waves allowed in one direction but not in the reverse direction, and (iii) arrest of propagating waves at the nonlinear interface only in one (preferred) direction. A unique feature of the proposed acoustic device compared with previous designs is its capability to achieve passive nonreciprocity without altering or distorting the frequency content of the sending signal. The proposed system can pave the way for designing passive acoustic or thermal diodes, and adaptable nonreciprocal wave transmission devices of enhanced robustness that are tunable with, and passively adaptive to energy.

Figure 1

System model. Schematic of a one-dimensional chain composed of two identical linear waveguides and a connecting nonlinear interface (blue masses marked with orange dashed lines). Each linear domain (i.e., waveguide) contains $N$ grounded masses (green connections) connected through linear springs (blue connections). For the nonlinear domain, three different masses are connected through nonlinear springs (red connections with black arrows). A harmonic force $F_0$ at each end provides equal and opposite forces to initiate waves into the system. Note that none of the masses at the nonlinear interface are grounded.

Figure 2

The normalized transmitted energy by sweeping input amplitude and frequency. (a) Purely linear system when initial wave travels from left to right (LR). (b) Purely linear system when initial waves travel from right to left (RL). (c) Proposed system incorporating a nonlinear interface, when initial waves travel from left to right (LR). (d) Proposed system incorporating a nonlinear interface, when initial waves travel from right to left (RL). For the system with a nonlinear coupling, black dashed lines separate different nonreciprocity zones on the frequency-amplitude graphs. Note that, each of the stars in panels (c) and (d) represents a case with a different type of nonreciprocity.

Figure 3

$A\text{−}A$ energy transmission. (a) Normalized transmitted energy for $F_0=2$ and $\omega =2\pi f=1.9$, when the initial wave propagates from left to right, (b) Normalized transferred energy for $F_0=2$ and $\omega =2\pi f=1.9$, when the initial wave propagates from right to left. For both graphs, blue represents the normalized energy of the left domain, red is for the right domain, green is for the nonlinear interface, and purple is for the total energy. Note that this case is marked by black stars in Figs. 2 and 2.

Figure 4

$B\text{−}A$ spatiotemporal energy graphs. (a) Energy distribution of each unit cell as a function of time and location, and (b) normalized transferred energy for $F_0=1.6$ and $\omega =2\pi f=2.05$, when the initial wave propagates from left to right. (c) Energy distribution of each unit cell as a function of time and location, and (d) normalized transferred energy for $F_0=1.6$ and $\omega =2\pi f=2.05$, when the initial wave propagates from right to left. For panels (b)–(d), green represents the normalized energy of the left domain, and red is the normalized energy of the right domain. Note that the red vertical lines in panels (a) and (b) indicate the boundaries of the nonlinear interface.

Figure 5

$B\text{−}C$ energy localization. (a), (b) Spatiotemporal energy distribution of each unit cell. (c), (d) Normalized energy of each domain as a function of time. (e), (f) Wavelet response of the input force entering the nonlinear gate. (g), (h) Wavelet response of the output force leaving the nonlinear domain, at $F_0=6$, and $\omega =2\pi f=2.1$. Note that the graphs on the left (right) side represent the condition in which the initial waves propagate from left (right) to right (left). In addition, in panels (c) and (d), blue represents the normalized energy of the left domain, red is the normalized energy of the right domain, and purple is the normalized energy of the nonlinear domain. Also, the red horizontal dashed lines in panels (e) and (h) indicate the passband boundaries of the linear waveguides, and yellow arrows indicate the created mode outside of the passband.

Figure 6

Experimental setup. Schematic of the experimental setup.

Figure 7

Experimental results. (a) Experimentally measured wave response of the signals at input and output when the source is on the left end. (b) Experimentally measured wave response of the input and output when the source is on the right end. (c) Frequency response of the outputs for both propagation directions when $V_0=2sin(30\times 2\pi t)\text{mm/s}$. (d) Experimentally measured wave response of the input and output when the source is on the left end. (e) Experimentally measured wave response of the signals at the input and output when the source is on the right end. (f) Frequency response of the outputs for both propagation directions when $V_0=2sin(30\times 2\pi t)\text{mm/s}$. For all of these plots, blue lines represent the response of the first mass on the left side ($X_1$), and red lines represent the response of the first mass on the right side ($Y_1$). Note that, for the frequency graphs, the amplitude of the signal is normalized with respect to the higher peak.