Bending Wave Propagation in Rods and Plates

Abstract

Rods exhibit some very complex vibrational characteristics. The ends behave like cavity resonators in a narrow frequency band and vibrate with amplitudes as much as 80 times the amplitude of the incident wave. At low frequencies, bending vibrations of rods are described by the complex Young's modulus, and the Bernoulli theory of bending leads to the same result as the exact theory. At high frequencies, bending vibrations are described by the shear modulus, and the loss factor approaches or becomes equal to that of shear waves. Plates exhibit a behavior similar to bending vibrations in rods. At low frequencies, Young's modulus and its loss factor describe the vibrational behavior of a thin plate. As the frequency increases, the modulus approaches the shear modulus, and the loss factor approaches the loss factor for shear waves after fluctuating in a periodic manner between the loss associated with Young's modulus and that of the shear modulus. The measurement, of the loss factor by bandwidth and decay methods agree, provided a narrow bandpass filter is used so that the low-frequency modes, which are always excited by a point force, are suppressed.