Point mass identification in rectangular plates from minimal natural frequency data

• We present a method for identifying a small point mass in a plate by resonant data.
• The method is based on an explicit expression of the eigenfrequency sensitivity.
• The inverse problem is formulated in terms of minimal eigenfrequency data.
• Closed form expressions for the mass size and position are provided.
• The sensitivity of the method is fully documented and discussed.

The inverse problem of determining the location and size of a point mass attached on a simply supported, isotropic and homogeneous rectangular plate from minimal natural frequency data is considered in this paper. Under the assumption that the size of the mass is small compared to the total mass of the plate, we show that the problem can be formulated and solved in closed form in terms of point mass-induced changes on the first three natural frequencies. Numerical simulations indicate that the method allows for accurate identification, provided that measurement/modelling errors are smaller than eigenfrequency changes.