Analytical Ultrasonics in Materials Research and Testing

adhesive alloys aluminum amplitude Analytical Ultrasonics anisotropic anisotropic materials applied attenuation coefficient attenuation measurements beam ceramics characterization circular convolution components composite materials continuous-time signal convolution crack crystal curves density detection determined diffraction direction displacement domain effects elastic wave energy equation experimental factor feature vector flaw Fourier transform frequency dependence grain size inhomogeneous input interface wave isotropic laser layer linear longitudinal waves mean grain mechanical properties Metals method microstructure mode modulus Nondestructive Evaluation obtained optical output Papadakis parameters particle displacement phase piezoelectric plate polycrystalline pore porosity predicted pulse quantitative Rayleigh wave reflection coefficient region sample scattering Schematic shear modulus shear waves shown in figure Snell's law specimen steel stress wave structure surface techniques temperature tensile tion transducer ultrasonic attenuation ultrasonic velocity ultrasonic waves ultrasound unit-sample response variations velocity measurements wave propagation wave velocity wavelength X-ray Xa(j