Transfer function methods to measure dynamic mechanical properties of complex structures

Experimental methods to measure frequency-dependent dynamic properties of complex structures are proposed. Flexural wave propagations are analyzed using the Timoshenko beam, the classical beam, and the shear beam theories. Wave speeds, bending and shear stiffnesses of the structures are measured through the transfer function method requiring small number of vibration measurements. Sensitivity analysis to investigate the effects of experimental variables on the measured properties and to study optimal sensor locations of the vibration measurements is performed. Using the developed methods, the complex bending and shear stiffnesses of sandwich beams of different core materials and a polymer beam are measured. Continuous variations of the measured bending and shear stiffnesses and their loss factors with frequency were obtained. To further illustrate the measurements of frequency-dependent variation of dynamic properties of complex structures, the damping of structural vibration using porous and granular materials is investigated. A proper equation of motion for the structural vibration should be used to obtain reliable data. For example, the method of the Timoshenko beam is required when the bending and shear modes of vibration occur simultaneously as in the sandwich beam. With advantages from the flexibility in choosing the vibration measurement locations, the developed methods can be applied to measure dynamic properties of various complex structures and viscoelastic materials.