Discussion on “Rectangular Plates with Free Edges on Elastic Foundations”

This paper points out the former work does not fulfill the boundary conditions that the concentrated force at the four corner points should not exist. Therefore, Ritz method adopted by the author concerned in the illustrative example will not be convergent in the best way. Moreover, Garlerkin method which is illustrated in this paper may carry out incorrect results if we apply its formulae. We have proved that the boundary conditions which govern the concentrated force equal to zero at the four corner points are indispensable if the problem is properly set.     

Analysis of Stability on Elastic Plates with Initial Imperfections

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Elastic Critical Buckling of Welded Thin Steel Rectangular Plates∗

A theoretical approach for the study of the effect of residual stresses due to welding on the elastic critical buckling behavior of thin steel rectangular plates is described. A finite difference technique is utilized for the determination of in-plane residual stresses due to a weld, and the Rayleight-Ritz method is used for the critical buckling problem, with stresses due to external loads being superimposed on the residual stresses. A number of illustrative examples are included, showing the possible detrimental effect of residual stresses due to welding. An approximately linear relationship is shown to exist between the square of the natural frequency of lateral vibration and the drop in buckling strength, for certain loading conditions     

Vibration of Shallow Shells with Two Adjacent Edges Clamped and the Others Free∗

ABSTRACT

Considerable information is available in the published literature on the free vibration frequencies and mode shapes of rectangular flat plates having two adjacent edges clamped and the other two free. However, no results appear to have been published previously for shallow shells having such edge conditions. The present work uses the Ritz method with displacement components in the form of algebraic polynomials to obtain accurate frequencies. Frequencies are determined for the first eight modes of shallow shells having spherical, cylindrical, and hyperbolic paraboloi-dal curvatures and square planforms. Beginning with the plate, the curvatures are incrementally increased in each case to the limits of shallow     

Longitudinal Free Vibration of Inhomogeneous Elastic Straight Strut with a Variable Cross Section

The scope of the present article,motivated by the case of the composite wooden propeller of anairplane,is to deal tentatively with the longitudinal free vibrationproblem of an elastic straight bar witha more general mathematical treatment.In this analysis,we have assigned to the modulus of elasticity,the bar cross section as well as themass per unit length of the bar an exponential function variation,and then found a general solution,wherein three parameters were considered as the main factors to affect the longitudinal free vibrationof the inhomogeneous elastic straight bar with a variable cross section.     

Discussion on“General Solutions of Axial Symmetrical Ring Shells”

There is one point to be mentioned about the decay constant of homogeneoussolution in the paper“General Solutions of Axial Symmetrical Ring Shells”(No.3.1980 of this Journal).There is an infinite number of rootsλ.The general form ofthese roots is     

Comments on “Particle swarm optimization with fractional-order velocity”

In this paper, some comments on the paper Solteiro Pires et al. (Nonlinear Dyn. 67:893–901, 2010) are presented. We demonstrate that the authors of the above paper have deduced the incorrect formula about the velocity updating strategy of the fractional-order particle swarm optimization algorithm. This paper deduces the modified updating formula, and verified experiments are also conducted.     

Comment on “Particle swarm optimization with fractional-order velocity”

This comment points out to a mistake in the main equation of Solteiro Pires et al. (Nonlinear Dyn. 61:295–301, 2010) concerning the fractional velocity in particle swarm optimization. The correct fractional velocity equation is provided and simulation experiments are redone in the comment.     

Paradox of “Self-Outflow” of a Free Liquid Jet

The effect of accumulation of reversible strains on the pressure head is analyzed theoretically for elastic and viscoelastic liquid flow from convergent channels. It is shown that, depending on the rheological features of the liquids, the pressure head can both increase and decrease as compared with the pressure determined by the Bernoulli formula. In particular, a situation in which a liquid flows out without any pressure head applied (paradox of self-outflow) is possible within the framework of the model. Transition to different viscoelastic liquid flow regimes as a function of the constitutive parameters is considered with reference to a channel with a sharp bottleneck (abrupt decrease in the cross-section).     

Comment on “Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers”

It is noted that the evaluation of the mean free path of ions by Park et al. [HEDP 8 (2012), 38–45] is incomplete without taking into account ion–electron collisions for colliding streams of high-speed laser-produced plasmas. As a result, the calculated scale of their interaction, ～few mm, can be explained by Coulomb collisions rather than as claimed in the paper, by the formation of a laboratory collisionless shock that simulates astrophysical shocks mediated by a Weibel-like instability. Advantages of CO₂-laser's irradiation and plane targets for such kind of experiments are discussed.     

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.     

Comments on “Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays”

In this note some points for paper [Huabin Chen, Chuanxi Zhu, Peng Hu, Yong Zhang, Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays, Nonlinear Dyn. (2012), doi:10.1007/s11071-012-0324-3] are presented.     

Further Comments on “Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work”

This note is concerned with the assertion of Barletta and Nield (2009a) that “a fluid with a thermal expansion coefficient greater than that of a perfect gas (β > β _perfect gas) is of marginal or no interest in the framework of convection in porous media”, and that for a remark of Magyari (Transp. Porous Media, 2009) about the forced convection eigenflow solutions, the circumstance β > β _perfect gas does not represent “a sound physical basis”. Here, it is shown, however, that these assertions are in contradiction with the experimentally measured values of β for important technical fluids as e.g., air, nitrogen, carbon dioxide, and ammonia where, in the temperature range between −20 and +100°C, just the inequality β > β _perfect gas holds.     

Remarks on the notion of “pressure”

In addition to understanding the various meanings attached to the word “pressure” one also has to comprehend the meanings of the phrases in which the term “pressure” appears. For instance one comes across the following combinations: “static-fluid pressure”, “thermodynamic pressure”, “mechanical pressure”, “contact pressure”, “stagnation pressure”, “vapor pressure”, “electro-osmotic pressure”, etc., One also often comes across the comment that “pressure is the Lagrange multiplier that enforces the constraint of incompressibility” and that “pressure is the mean normal stress”. In general the word “pressure” with different significations, is used with gay abandon without paying proper attention to its usage¹. The distinction in the meanings of the above terms assumes paramount significance when discussing properties of materials, which could possibly depend on “pressure”. In this short note we discuss the distinction between various significations of the word “pressure”, and their implications with regard to response relations for bodies.