Optimization of an acoustic rectifier for uni-directional wave propagation in periodic mass–spring lattices

We perform optimization studies on the construction of acoustic rectifiers, which allow uni-directional propagation of acoustic waves, from a periodic array of masses and springs arranged in one- and two- dimensions. An acoustic rectifier is achieved by pairing a nonlinear material, which can up-convert an input excitation frequency to a higher harmonic, with a bandgap material whose dispersion relation has a bandgap region for the input frequency range but a bandpass region at the higher harmonic. First, we analyze the mass and stiffness parameters that lead to acoustic rectification in infinite mass–spring arrays with the largest possible range of working frequencies. A combination of analytical techniques, numerical simulations, and particle swarm optimization is used to identify the optimal acoustic rectifier. Next, we study the practical working range of acoustic rectifiers of finite size and examine how the rectification properties change as a function of the lattice size and damping. Finally, we perform numerical simulations of an acoustic rectification device in which a Duffing oscillator is attached to the end of a tri-atomic mass–spring chain.