Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates

A large and growing number of original papers on both the experimental and the theoretical aspects of stress wave propagation is appearing in the scientific literature, and two international conferences solely concerned with the subject have been held during the last five years. The purpose of this paper is to review recent experimental and theoretical advances in the propagation of deformation waves of arbitrary shape through elastic and anelastic solids, and also to attempt to outline the problems on which present efforts are being directed and to predict probable lines of future development.

Stress Waves in Solids

Dynamics of transversely vibrating beams using four engineering theories

The elastic constants of pyrolytic graphite which has been highly ordered by annealing under compressive stress have been determined by ultrasonic, sonic resonance, and static test methods. Ultrasonic tests yielded the elastic constants c11, c12, c33, c44 = 1/s44, and the stress derivative of c33. The moduli 1/s11 and c44 were determined from the free flexural resonant vibrations of bars, and the shear modulus c44 also was determined from the fundamental torsional resonance of the bars and from the resonance of compound torsion oscillators composed of thin graphite disks with steel end pieces. Static tension, compression, and torsion tests on the pyrolytic graphite yielded a complete set of compliances (s11, s12, s13, s33, and s44). The following self‐consistent set of elastic constants (cij in units of 1011 dyn/cm2; sij in 10−11 cm2/dyn) has been deduced from the results: c11 = 106±2, c12 = 18±2, c33 = 3.65±0.10, c13 = 1.5±0.5, c44 = 0.018 to 0.035, 1/s11 = 102±3, 1/s33 = 3.65±0.10, s12 = −0.0016±0.0006,...

Elastic Constants of Compression-Annealed Pyrolytic Graphite

Wave propagation in carbon nanotubes (CNTs) is studied with two nonlocal continuum mechanics models: elastic Euler-Bernoulli and Timoshenko beam models [Philos. Mag. 41, 744 (1921)]. The small-scale effect on CNTs wave propagation dispersion relation is explicitly revealed for different CNTs wave numbers and diameters by theoretical analyses and numerical simulations. The asymptotic phase velocities and frequency are also derived from nonlocal continuum mechanics. The scale coefficient in nonlocal continuum mechanics is roughly estimated for CNTs from the obtained asymptotic frequency. In addition, the applicability and comparison of the two nonlocal elastic beam models to CNTs wave propagation are explored through numerical simulations. The research findings are proved effective in predicting small-scale effect on CNTs wave propagation with a qualitative validation study based on the published experimental reports in this field.

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Wave propagation in carbon nanotubes via nonlocal continuum mechanics

(1921). LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 41, No. 245, pp. 744-746.

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Stephen P. Timoshenko

Papers

LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars