Non-linear piezoelectric resonance analysis using burst mode: a rigorous solution

The burst mode experiment is commonly used to measure non-linear piezoelectric material properties. However, the theory that is often employed is highly simplified, making use of linear results. Here we represent a more rigorous theory based closely on the underlying non-linear partial differential equations. Since time domain solutions are not available analytically, the approach is in two parts: the PDE is solved in the frequency domain, then an auxilliary non-linear ordinary differential equation is solved in the time domain. Comparison of the two yields the material parameters. Also, we suggest the excitation portion of the I(t) curve be studied rather than the decay part normally used since the former contains more features, has a well-defined initial condition (current and charge both zero) and is less susceptible to experimental artefacts.