The dynamic bulk modulus of elasticity has been measured for 14 different rubbery elastomers: three natural rubbers, five neoprenes, three polyurethanes, and one each of butyl, nitrile, and butadiene types. The measurements ranged in temperature from −10 to +40°C, at frequencies from 5 to 3000 Hz, but mostly in the range 100–1000 Hz, at 2.5 MPa pressure. Values of the real (storage) part of the modulus fell within 35% of the mean value of 2.9 GPa for all elastomers, whereas loss moduli were a few percent of the storage moduli. Master curves were obtained for two neoprenes, a polyurethane, and a butyl rubber. These were fitted by hyperbolic functions with four adjustable parameters. Effects of room‐temperature aging in artificial sea water were also studied. Aging versus time profiles fell into two distinct forms. Natural rubbers were least stable, neoprenes were intermediate, and urethanes proved most stable in bulk modulus.
AGENCY USE ONLY (Leave blank) 12 REPORT DATE REPORT TYPE AND DATES COVERED TITLE AND SUBTITLE FUNDING NUMBERS ABSTRACT (Maximum 200 words) iThe longitudinal (d 3 3 ) and transverse (d 3 1 ) piezoelectric coefficients of a piezoelectric composite material (NTK PR-306) are determined as functions of frequency and temperature by using laser Doppler vibrometry to measure the strain induced in the sample by an electric field. Measurements are performed over the temperature range from -50 0 C to 50 0 C and over a frequency range from 0.1-10 kHz. Some measurements were made at frequnecies up to 100 kHz in order to demonstrate the ability of the technique at frequencies in the vicinity of an electromechanical resonance. The results show that the viscoelastic relaxation affects the piezoelectric response of the composite material primarily through the dielectric stiffness rather than the elastic stiffness. The d 3 3 coefficient is observed to relax in a normal fashion near the glass transition of the polymer phase wheras the relaxation in the d 3 1 coefficien varies over the entire measured range of temperature. SUBJECT TERMS 15. NUMBER OF PAGES GENERAL INSTRUCTIONS FOR COMPLETING SF 298The Report Documentation Page (RDP) is used in announcing and cataloging reports. It is important that tis information be consistent with the rest of the report, particularly the cover and title page. The longitudinal (d 3 ,) and transverse (d 31 ) piezoelectric coefficients of a piezoelectric composite material (NTK PR-306) are determined as functions of frequency and temperature by using laser Doppler vibrometry to measure the strain induced in the sample by an electric field. Measurements are performed over the temperature range from -50 C to 50 C and over a frequency range from 0. 1-10 kHz. Some measurements were made at frequencies up to 100 kHz in order to demonstrate the ability of thetechnique at frequencies in the vicinity of an electromechanical resonance. The results show that the viscoelastic relaxation affects the piezoelectric response of the composite material primarily through the dielectric stiffness rather than the elastic stiffness. The d 33 coefficient is observed to relax in a normal fashion near the glass transition of the polymer phase whereas the relaxation in the d 31 coefficient varies over the entire measured range of temperature.
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An analytical expression is presented for the correction factor that relates the effective shear modulus in Timoshenko–Mindlin plate theory to the actual shear modulus, for an unloaded plate. This expression is obtained by comparison of the approximate theory with exact elasticity theory. A thick-plate theory is developed for extensional waves, which also introduces an effective shear modulus, with a corresponding correction factor. It is shown analytically that both correction factors produce the proper high-frequency value for the phase speed, namely, the Rayleigh wave speed. Reflection of sound by a plate is described when both flexural and extensional waves are excited. Both types of waves are described by the expressions derived in thick-plate theory. A structural response function of the plate for reflection is given for each of the two wave types separately. The structural response function pertaining to the case where both wave types occur simultaneously is expressed in terms of the two individual response functions in the same way that the total impedance of a pair of impedances in parallel is expressed in terms of the values of the individual impedances. The distribution of kinetic energy over the two types of waves as a function of the angle of incidence is shown.
Materials are under development that match density (ρ) and dilatational sound speed (c) to the values of seawater as closely as possible while maintaining sufficient rigidity to serve for structural purposes. Another paper in this meeting by C. M. Thompson and J. R. Griffith (preceding abstract) describes the composition of the material and some of its properties. Matching of density and speed results in transparency for fluids only; the shear modulus in a solid admits the presence of a shear wave which causes deviation from ideal ρ-c behavior. In this paper, the effect of a finite shear modulus on the reflection of plane waves by an infinite plane is analyzed. The shear modulus of the material was measured following a method developed by R. L. Adkins in 1966. Examples are given of the reflection coefficient as a function of incidence angle for values of ρ and c close to those of the medium, and various ratios of plate thickness to dilatational wavelength. The effect of a finite loss tangent in the shear modulus is shown. [Work supported by the Office of Naval Research.]
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