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Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

Kiełczyński P., Szalewski M., Balcerzak A., Wieja K.

Archives of Acoustics

2015

Vol. 40, No. 2

273--281

This paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2 type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

Thermodynamic Method for Measuring the B/A Nonlinear Parameter Under High Pressure

Kiełczyński P., Szalewski M., Balcerzak A., Wieja K., Rostocki A., Siegoczyński R.

Engineering Transactions

2014

Vol. 62, iss. 1

5--15

The nonlinearity parameter B/A is a measure of the nonlinearity of the equation of state for a fluid. The nonlinearity parameter B/A is a physical parameter often used in acoustics, from underwater acoustics to biology and medicine. It can provide information about structural properties of the medium, internal pressure and inter-molecular spacing. The thermodynamic method has been applied for determination of B/A parameter in diacylglycerol (DAG) oil as a function of pressure at various temperatures. Isotherms of the density and phase velocity of longitudinal ultrasonic wave as a function of pressure have been measured. Using the thermodynamic method along with measured isotherms of sound speed and density, the nonlinearity parameter B/A (for DAG oil) was evaluated as a function of pressure (up to 220 MPa) at various temperatures ranging from 20 to 50◦C.