Numerical study of resonant frequencies in multi-material microstructures excited by ultrasonic vibrations

Surface structuring has become an important tool to adjust for instance optical, tribological or adhesive properties of surfaces. It is well known that materials, especially thermosets and elastomers, can change their mechanical properties compared to the bulk behaviour at certain length scales. Several concepts of microstructures exist, differing in shape, size, combination of materials and manufacturing approach for example. Taking into account the potential fields of application, it is of importance to develop nondestructive testing (NDT) and quality control concepts for e.g. reliability and safety considerations. However, conventional characterization techniques, such as nanoindentation are limited in their ability to evaluate superimposed properties resulting from a complex physical and mechanical assembly. Ultrasound is a well-known method to measure elastic constants. Furthermore the resonance frequencies induced by ultrasonic excitation and the velocity and attenuation of ultrasonic waves depend on the combination of geometrical dimensions as well as material properties. This allows correlating mechanical properties of microstructures with characteristics of ultrasonic waves. In this work, we focus on multi-material structures with a cylindrical shape known to modulate surface interaction. To define the ultrasonic requirements of an adequate NDT-system to assess the elastic properties of structures in the micrometer range, we theoretically studied the dependency of the material properties and different geometry concepts on the resonant frequencies. A systematic study of parameters including different wave types and frequencies based on numerical simulations will enable the effective design of experiments to validate the theoretical approach and open up a field of possible applications for ultrasonic characterisation of microstructures.