The team, led by Michael Roukes of Caltech studied a nanomechanical system consisting of a simple beam clamped at two ends, like a guitar string. “When a guitar string is plucked, it responds primarily with the first resonant mode, but there are other resonant modes, known as overtones, present as well,” explained team member Matt Matheny. “The pitch (or frequency) we hear is mainly due to the first resonant mode but if we were to play a harmonic, we would hear one of the other resonant modes.”

In a completely linear system, the pitch is always the same, no matter how hard the string is plucked. In a nonlinear system, on the other hand, the pitch can change if the string is plucked hard enough. Moreover, when the string is plucked hard and there is “mode-coupling”, the pitch of the overtones changes – largely thanks to the vibration of the first resonant mode. Such nonlinearities become ever more important as devices shrink down to the nanoscale, with the ultimate limit being single-layer devices made from graphene (a 1D sheet of carbon).

Highly linear pickup

Continuing with the guitar analogy, in an electric instrument, the “pickup” transduces the string’s mechanical vibrations into an electronic signal. “If this pickup changes the pitch (that is, the system becomes nonlinear), then it is difficult to determine exactly where the nonlinearly originates – in the string or the pickup itself,” said Matheny. “Much of the previous work in this field confused the string nonlinearity with the pickup nonlinearity so we decided to employ a pickup that was highly linear to avoid such complications.”

In the Caltech/Melbourne system, the pickup is in fact a metallic strain gauge and, strictly speaking, the mechanical nonlinearity of the beam lies within the linear, or dynamic, range of this electromechanical transducer.

“We succeeded in measuring the mechanical nonlinearities of our doubly clamped beam and, to boot, found excellent agreement between the Euler–Bernoulli theory (which describes such systems) and experiment,” Matheny told

According to the team, understanding such nonlinear properties will help set limits on nanomechanical devices made from graphene and graphene-like materials for use as sensors.

The work is detailed in Nano Letters.