Finding new mathematical identities via numerical computations

Based on the theory of Bernoulli-Euler beam, the differential equation of a restrained cantilever column with a tip mass subjected to a subtangential follower force is constructed, the solution of the differential equation is found, and the existence of regions of divergence instability of the system is discussed. The influence of the follower force parameter η, the tip mass parameter β and an end elastic end support on the divergence instability of the column is investigated. Several numerical computations of some cases have completed.

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Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1988.0020 ◽

1988 ◽

Vol 415 (1849) ◽

pp. 389-419 ◽

Cited By ~ 55

Keyword(s):

Anisotropic Media ◽

Wave Mode ◽

Sliding Contact ◽

Stoneley Wave ◽

Shear Stresses ◽

Wave Problem ◽

Numerical Computations ◽

Cubic Symmetry ◽

Anisotropic Elastic ◽

Wave Modes

A variant of the Stoneley-wave problem, namely slip waves between two homogeneous elastic half-spaces whose interface is incapable of supporting shear stresses, is studied. For two isotropic half-spaces there is either no or one slip-wave mode. In the case of anisotropic half-spaces, the possibility of a new slip-wave mode, called the second slip-wave mode, arises. The case of two identical anisotropic half-spaces of the same orientation is discussed in detail; criteria for the existence of a second slip-wave mode in terms of the nature of the transonic state are developed. It is concluded that for many anisotropic media a second slip-wave mode will exist within certain ranges of orientation of the slip-wave geometry. Numerical computations for iron (cubic symmetry) demonstrate that second slip-wave modes indeed exist in this material.

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Wave Propagation in a Micropolar Elastic Plate with Voids

Journal of Vibration and Control ◽

10.1177/1077546305054788 ◽

2005 ◽

Vol 11 (6) ◽

pp. 849-863 ◽

Cited By ~ 24

Author(s):

S. K. Tomar

Keyword(s):

Wave Propagation ◽

Attenuation Coefficient ◽

Elastic Material ◽

Elastic Plate ◽

Lamb Wave ◽

Specific Model ◽

Present Formulation ◽

Numerical Computations ◽

Lamb Wave Propagation ◽

Symmetric And Antisymmetric Modes

Frequency equations are obtained for Rayleigh–Lamb wave propagation in a plate of micropolar elastic material with voids. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be free from stresses. The frequency equations are obtained corresponding to symmetric and antisymmetric modes of vibrations of the plate, and some limiting cases of these equations are discussed. Numerical computations are made for a specific model to solve the frequency equations for symmetric and antisymmetric modes of propagation. It is found that both modes of vibrations are dispersive and the presence of voids has a negligible effect on these dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of voids. The results of some earlier works are also deduced from the present formulation.

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