Magnetic-controlled programmable soft lattice phononic crystals with sinusoidally-shaped-like ligaments for band gap control

•A new magnetically programmable soft lattice FE model was developed.•The soft lattice PnC with programmable magnetic anisotropy encoding modes can exhibit great band gap tunability.•Increasing the number of wave peaks determined by the encoding mode has significant advantages in inducing high-frequency broadband and multiband.•Mechanical compression broadens the tunability and a large strain enables great tunability in broadband and multiband. Realizing the active adjustment of the elastic wave band gap has attracted extensive attentions and become one of the most important issues for phononic crystals (PnCs). In this paper, we present a new magnetically programmable soft lattice PnC that can allow the straight ligaments to be deformed into the sinusoidal ligaments with different numbers of wave peaks through programmable magnetic anisotropy encoding modes and thus exhibits a great band gap tunability. The proposed soft lattice PnC uses hard-magnetic soft materials (HmSMs), whose band gap width can be effectively tuned via applying a magnetic field to induce the band gap. It has been demonstrated that the number of wave peaks, determined by the encoding mode, has more significant advantages in inducing high-frequency broadband and multiband. The subsequent application of mechanical compression significantly broadens the tunability and a large strain enables a great tunability in broadband and multiband.