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

For a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. Besides, although the stability for many problems of dynamical systems may not be mathematical asymptotical stability, it is actual asymptotical stability — namely “pragmatical asymptotical stability” which can be introduced by the concept of probability. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, one pragmatical asymptotical stability theorem on partial region and one pragmatical asymptotical stability theorem on partial region for partial variables are given and applications for gyroscope systems are presented.

An alternative technique for the determination of ultimate moment capacities of round prestressed concrete poles is presented in this paper. The traditional concrete compression area of poles is determined using the conventional iterative design process, the compatibility and equilibrium approach. Moreover, the area of annulus defined by the neutral axis is multiplied by an area reduction factor. It is possible to use numerical methods to calculate the centroid of the reduced annulus. However, the concrete compression zone and strain variation in the longitudinal reinforcement makes the calculation awkward. This paper addresses the problem from a different perspective. No reference to area reduction factor is required in the course of locating the neutral axis. The results are compared in a very satisfactory manner with that obtained using PCI approach. The purpose is to provide formulations that can be easily computerized and implemented on relevant software for the design of round prestressed concrete poles.

The paper, summarizing studies presented in seven journal papers using the method of continuous analysis, is written to honor Professor Y.H. Pao of the Institute of Applied Mechanics at the National Taiwan University on his seventieth birthday for his many significant contributions and leadership in the field of mechanics. These seven papers contain investigations concerning stress, buckling, and vibration analyses of beams and plates having disbonds. The authors feel privileged to have this opportunity to join with Professor Pao's many friends, colleagues and students to participate in this joyous occasion. Being able to appear in this prestigious special issue of the Chinese Journal of Mechanics, the authors believe that the spread of each of the seven papers in the structural mechanics community must at least be increased by ten fold. Hence, the numbering of the reference papers is amplified by a factor of ten which amounts to a total number of seventy as being used in the listing of papers under References. We use this number of seventy to wish Professor Y.H. Pao to have many happy returns on his seventieth birthday.

In this paper we introduce a fundamentally new concept in the field of wave-propagation in periodic structures. We show that a phenomenal amount of simplification can be achieved by using symmetry arguments. Problems which ordinarily lead to (2n × 2n) determinantal eigenvalue equations, can effectively be reduced to two (n × n) determinantal equations. We state the final result in the form of a factorization theorem and then with the help of a simple problem, we show the superiority of this new result over the traditional methods of solution.

In this paper the modified differential quadrature method (MDQM) is proposed for static and vibration analyses of beams. Modified weighting matrices are developed and a new formulation process is presented for incorporating boundary conditions such that the numerical error induced by using the δ-method in the original DQM is reduced. The present method is applied to various beam problems, such as static deflections of Euler beams, buckling loads of columns, and free vibrations of Timoshenko beams. Numerical results of the present method are shown to have excellent accuracy when compared to exact values and are more accurate than those obtained by the original DQM. The accuracy and efficiency of the present method have been demonstrated.

This research applied the method of direct acoustic admittance measurement to investigate effects of the flame character and the burner acoustic admittance on the flame-driving behavior. The acoustic admittance data were obtained by directly measuring the amplitudes of pressure and velocity oscillations, and the phase relations between the pressure and velocity oscillations. Results of this research reveal that the flame-driving characteristic is mainly dominated by the nonreactive burner admittance not the flame. Whether the flame is to drive or damp the acoustic field is detcrmined by the acoustic admittance of the burner system. The flame equivalence ratio plays a role mainly in determining the magnitude of the flame driving/damping.

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.

In this study, the problem of creeping flow relative to an isolated porous spherical shell has been examined. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region (shell region) and free fluid region (inside the core and outside the shell), respectively. The stress jump boundary conditions at the porous media/free fluid interfaces are included and the exact solution has been found. The drag experienced by the porous shell has been discussed for various jump parameters and shell thickness.

The importance of nonreactive acoustic admittance at a burner exit plane on the flame-driving characteristic was discussed using the measured phase difference between the velocity and pressure oscillations, and the acoustic wave structure inside the duct. Also, the flame-driving characteristics were investigated by flame radiation measurements, and results were compared with those obtained previously from admittance studies. Results show that the comparisons are in good agreement. Also, the flame-driving characteristics are closed related to the acoustic wave structure at the burner exit plane, and could be qualitatively predicted by knowing the imaginary part of nonreactive burner acoustic admittance.

Band-limited acoustic sources of small spatial extent produce radiation patterns well approximated by those of multi-poles. Assumed limits on dimensionless size Ka and source efficiency lead to explicit rules for the necessary length of the multi-pole series.

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.

This paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise),and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.

The endochronic cyclic plasticity with finite element analysis (EndoFEM) is employed to simulate plasticity-induced crack closure phenomenon of Al 2024-T3 CCT specimens under maximum cyclic stress of 80MPa and 0.1 stress ratio (R). Various fatigue crack lengths are generated by a rc dominated-node-released strategy. The suitability of element-mesh planning around crack tip is supported by the real simulations in the decreasing tendencies of crack opening load (Pop) with increased distance behind the crack tip, and the enough elements to reflect the reversed plastic responses at minimum load.

EndoFEM results of vertical stress ahead of the crack tip show a typical distribution of small scale yield (SSY) in the realm of fracture mechanics; and Pop/Pmax ratio determined at 1mm behind crack tip is kept constant i.e. Kmax-independent. In these cases, fatigue parameters based on either the far field loading parameter ΔK, the effective ΔK (ΔKeff) with crack closure effect, or the mechanical responses ahead of crack tip (e.g. stress parameter, reversed (plastic) strain at 1mm) are all equivalent and are linearly correlated with the stage II fatigue crack growth (FCP) rate. However, for longer crack length with the ligament bending effect or shorter crack length with the starter notch effect, the Pop/Pmax ratio decreases and changes the SSY stress distribution. This result reduces the usefulness of the above fatigue parameters. As a consequence, a nonlinear correlation of FCP rates with ΔK or ΔKeff are purely empirical. The Kmax-dependent ΔKeff must be considered in the correlation as suggested by the present study of EndoFEM.

The stress distribution in a shrink fit with solid inclusion subject to homogeneous heating and subsequent cooling is investigated. It is presumed that both components are in a state of plane stress and exhibit the same elastic-plastic material behavior. Based on Tresca's yield condition and the associated flow rule, the modification of the stress distribution is studied analytically. In particular, the reduction of the interface pressure — and therefore of the transferable moment — caused by the occurrence of plastic deformation is discussed, and the criteria for the avoidance of yielding of the inclusion or full plasticization of the hub are given.

This paper applies the method of self-similar potentials to analyze the dynamic behaviors of the problems of mode-I, mode-II, and mode-III cracks propagating along the x-axis with constant speed, while the constant speeds of both crack tips are not the same, called nonsymmetric crack expansion. It is assumed that an unbound homogeneous isotropic elastic material is at rest for time t < 0. However, for time t ≥ 0, a central crack starts to extend from zero length along the x-axis. On the crack surfaces of x ≥ 0, there exists uniform distributed load such that the rightmost crack tip propagates with speed ms, while the leftmost crack tip with speed s, where m > 1 and is constant. First, the complete solutions of the mode-I, mode-II, and mode-III problems are obtained. After the complete solutions are found, attention is focused on the crack surface displacements and dynamic stress intensity factors. The results of this study show that the DSIF is equal to the static SIF when the crack-tip speed is zero, and DSIF is zero as the crack-tip speed approaches the Rayleigh-wave speed. Moreover, for the special case m = 1 which indicates that the velocities of both crack tips are the same, the DSIFs of this three modes in this study is the same as those of Ref. [15].

An inverse method for identifying the element rigidities of frame structures is developed in this paper. The primary input of this method is the longitudinal strains of the frame elements measured in transient tests. The spectral element method is employed to formulate the equilibrium equation of the frame in the frequency domain. The equilibrium equation is rewritten in terms of the strains of the frame elements. The identification problem is then formulated as an optimization program in which the error norm of the equilibrium equation is minimized. The proposed method is applicable to total structure identification as well as substructure identification. The issue of identifiability is addressed in this study. A numerical example is presented to illustrate the proposed method. The influence of noise is investigated through the example.

It is shown that when the thermodynamic fluxes are included as independent thermodynamic state variables of the generalized entropy density, the constitutive equations for the conserved state variables and the evolution equations for the nonconserved state variables of elastic type-II superconductors can be derived systematically. In particular, the transport equations generalizing the Fourier law for heat transport and the time-dependent Ginzburg-Landau equation for the relaxation of superelectron are proposed in this paper.

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.