This article traces the development of applied mechanics and its relation to science and engineering by reviewing first the history of mechanics from 1600 to 1900, the physics of the 19th century, and the engineering education in the same period. The review is followed by a discussion on modern physics and modern engineering, and the formation of applied mechanics as a discipline in science and one in engineering, which is classified into 94 subjects in 10 categories by Applied Mechanics Reviews. The article concludes with a chart to summarize the relation between science and engineering, and the interactions of applied mechanics with other disciplines. There are 15 references included in this article.

Originally published in Applied Mechanics Reviews, Vol. 51, No. 2, February 1998

The Savage-Hutter (SH) theory (1989) of dense granular avalanche flow uses an earth pressure coefficient Kx which depends on the internal angle of friction and the bed friction angle but assumes different values in diverging and converging flows. So the earth pressure coefficient is undefined when the strain rate ∂u/∂x changes sign. Steady plane flow of a finite mass of a cohesionless granular material in a permanently rotating drum admits an exact solution of the SH-equations at ∂u/∂x = 0 provided the value for Kx is prescribed. However, avalanche profiles depend on the values of Kx. Experiments on avalanche shapes in steady rotating drums offer therefore a possibility to identify the value of Kx at zero strain rate.

The method of explicit expansion in normal modes is applied to derive expressions for the Rayleigh waves generated by distributions of buried transient and harmonic forces. The derived expressions are conceptually clear, and relatively simple.

In this short note a comparison is made between the methodology of nonlinear analysis in machine systems versus structural systems. Because of strong nonlinearities in machines with parts in relative motion, chaotic-like dynamics are more likely to occur in complex multi-body machines than in structural systems. Furthermore, it is conjectured that well designed machines have evolved to where a small amount of chaos is always present and is sometimes desired.

Natural vibration frequencies and modes of repetitive structures, including symmetric, periodic, linking structures, are considered in this work. By using the repetition of the identical parts, we reduce the eigenvalue problem of the structure to a set of eigenvalue problems of lower dimensions associated with the parts. Special forms and properties of the modes of natural vibrations are observed.

The reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

This paper deals with a hybrid finite element method for wave scattering problems in infinite domains. Scattering of waves involving complex geometries, in conjunction with infinite domains is modeled by introducing a mathematical boundary within which a finite element representation is employed. On the mathematical boundary, the finite element representation is matched with a known analytical solution in the infinite domain in terms of fields and their derivatives. The derivative continuity is implemented by using a slope constraint. Drilling degrees of freedom at each node of the finite element model are introduced to make the numerical model more sensitive to the transverse component of the elastodynamic field. To verify the effects of drilling degrees freedom and slope constraints individually, reflection of normally incident P and SV waves on a traction free half space is considered. For P-wave incidence, the results indicate that the use of a slope constraint is more effective because it suppresses artificial reflection at the mathematical boundary. For the SV-wave case, the use of drilling degrees of freedom is effective in reducing numerical error at the irregular frequencies.

In this paper, a modified version of the method of steepest descent is proposed for the evaluation of Lamb's integrals which can be considered as basis functions dealing with the development of the transition matrix method which can be used to study the wave scattering in a two-dimensional elastic half-space. The formal solutions of the generalized Lamb's problem are studied and evaluated on the basis of the proposed method. After defining a phase function which presents in wavenumber integral, an exact mapping and an inverse mapping can be obtained according to the phase function. Thus, the original integration path can be deformed into an equivalent admissible path, namely, steepest descent path which passed through the saddle point, and then mapped onto a real axis of mapping plane, finally, resulted in an integral of Hermite type. This integral can be efficiently evaluated numerically in spite of either near- to far-field or low to high frequency. At the same time, the asymptotic value can easily be obtained by applying the proposed method. The numerical results for generalized Lamb's solutions are calculated and compared with analytic, asymptotic or other existing data, the excellent agreements are found. The properties of generalized Lamb's solutions are studied and discussed in details. Their possible applications for wave scattering in elastic half-space are also pointed out.

In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force poses an axisymmetric problem which is compatible with the Fourier transformation applied to the coordinates in the horizontal plane.