A thermoacoustic driver incorporates a linear electrodynamic motor having electrical terminals and a moving part, a driver suspension housing, a piston, and a stiffness-enhancing device for raising the mechanical resonance frequency of the electrodynamic motor without reducing the piston stroke. The stiffness enhancement is accomplished by the use of specially optimized suspension spring structures and/or by attaching one or more electrical inductors to the electrical terminals of the driver. The stiffness enhancement using mechanical springs incorporates one or more starfish structures extending between the driver suspension housing and the piston and rigidly clamped to both. The starfish structures comprise radially extending legs, which are leaf springs or beams of varying width. The shape of the beams and the shape of the overall spring structure are optimized to enhance flexural or torsional stiffness and relieve arc tension within the constraints of cost-effectiveness. In one version, two modified triangular (trapezoidal) cantilever beams are connected through a straight middle section and form a bow-tie shaped beam.