Maximum amplification of a string transverse-force amplifier in fiber Bragg grating accelerometers

Fiber Bragg grating (FBG) accelerometers using transverse forces are very sensitive. When a transverse force is applied to a lightly stretched string fixed by its two ends, a much stronger axial force along the string will be induced. So, the transverse force is amplified and converted into the axial force. At a given pre-strain of the string, the maximum amplification and requirements to obtain it have not been clearly demonstrated. Here, we theoretically prove and experimentally verify that the maximum amplification occurs when the strain induced by the transverse force approximately equals the pre-strain. This revelation improves the understanding of FBG accelerometers using transverse forces.