A membrane actuator includes a magnetically actuatable membrane and a magnetic trigger. The membrane includes a shape memory alloy (SMA), and the magnetic trigger is configured to induce a martensitic transformation in the SMA, to produce a larger force than would be achievable with non-SMA-based materials. Such a membrane actuator can be beneficially incorporated into a wide variety of devices, including fluid pumps, shock absorbing systems, and synthetic jet producing devices for use in an aircraft. The membrane/diaphragm can be formed from a ferromagnetic SMA, or a ferromagnetic material can be coupled with an SMA such that the SMA and the ferromagnetic material move together. A hybrid magnetic trigger, including a permanent magnet and an electromagnet, is preferably used for the magnetic trigger, as hybrid magnetic triggers are easy to control, and produce larger magnetic gradients than permanent magnets or electromagnets alone.