Experimental Methods in Wave Propagation in Solids and Dynamic Viscometry

Dual J.

The first part deals with a primarily experimental investigation of the first two axisymmetric modes of waves in filament – wound cylindrical shells. The results obtained are useful for design, the prediction of the behaviour under dynamic loading conditions, the determination of elastic material properties and for quality control of such shells. The tubes were manufactured from carbon-fibres embedded in an epoxy matrix, with 15 layers across the thickness. Their mean radius and wall thickness was 0.01475 m and 0.003 m, respectively. Five different winding angles (0°, 22.5°, 45°, 67.5° and 82.0°) were considered, such that the ratio of the modulus in the longitudinal direction to the modulus in the circumferential direction was varied from about 15 to 0.07. Dispersion curves were measured for frequencies from 1kHz to about 200 kHz. For frequencies below the cut- off frequency fc of the second mode, which is approximately equal to the plate wave speed in the circumferential direction divided by the circumference, resonance experiments were performed using standard techniques. Above fc, dispersion data was gathered using Fourier analysis of transient pulses. Either mode was selectively excited using specially designed piezoelectric transducers and measured with a heterodyne laser interferometer. An electrical signal with precisely controlled frequency content was repetitively applied to the transducers in order to allow averaging of the resulting displacements (about m) over many experiments. In order to eliminate reflections of the outgoing waves from the end opposite to the excitation elements, the tubes were partially covered with a highly viscous fluid. The strong absorption of mechanical waves by the fluid that was observed led to the development of a dynamic viscometer, which is described in the second part of the thesis.The dispersion data shows the behavior which is characteristic for tubes, however, with large variations between tubes of different winding angles. Some material properties were determined from the data based on available asymptotic theories and on a method previously described by Shul’ga. However, the material constants calculated from the long wavelength limit using classical lamination theory were not suitable to describe the behavior of the tubes for shorter wavelengths. New theories have to be developed to take into account the complex composite configuration resulting from the winding process.The dynamic viscometer, described in the second part of the thesis, consists of a torsionally vibrating rod excited to harmonic motion at a frequency of e.g. 10 kHz by piezoelectric transducers. The resulting displacement is measured piezoelectrically. Upon immersion of the sensor into the fluid, a boundary layer is produced. The fluid exerts a shear stress on the sensor. The shear stress increases the effective mass and damping of the sensor. From the additional damping, the viscosity of the fluid can be computed, if the density is known.The damping of the sensor is determined from two frequencies corresponding to two phase values of the transfer function between input and output voltage in the vicinity of a resonance frequency. A feedback loop stabilizes the phase at the proper value. Viscosity measurement is therefore reduced to the intrinsically digital measurement of two frequencies.For precise measurements of damping, the resonator must be decoupled both mechanically and electrically from the surroundings. This is achieved by using the piezoelectric elements far below their resonance frequency and by special sensor designs. For the practical applicability of such dynamic viscometers, it is crucial to develop a model that describes the interaction between fluid and sensor and allows evaluation of the viscosity from the measured damping for given density. This eliminates the formidable task to determine instrument constants, that depend on density and temperature, by calibration with known liquids.The sensor is modelled as a continuous, composite resonator. The behaviour of the fluid is determined from the linearized Navier-Stokes equations, because the maximum displacements at the surface of the sensor are extremely small ( m). Without prior calibration with known liquids, viscosity measurements were made in a range from 1 to 100 mPas with an accuracy of between 2 % and 9 % at the lower and higher end of the measurement range, respectively. The sensor can be used both under laboratory and process conditions.