Experimental study of flame driving function in an acoustically excited duct with anchored flames

This research experimentally investigates the flame driving function in an acoustically excited vertical duct with a laminar, premixed flame anchored on a grid. The flame driving function is determined from the measured acoustic intensity upstream and downstream of the flame zone, which relates both the acoustic velocities and pressures on either side of the flame zone. Results of this research reveal that the location of the flame zone on the acoustic field plays the main role in determining the sign and magnitude of the flame driving function. The flame equivalence ratio plays a role only in the magnitude of the flame driving function. This study also shows that the characteristics of the flame driving function can be qualitatively predicted by knowing the imaginary part of nonreactive acoustic admittance at the flame location. Received: 20 September 2000/Accepted: 15 May 2001     

Multi-modal approach for large natural flexural vibrations of thermally stressed plates

By means of Berger's approximation, suitable for plates with immovable edges, the geometrically nonlinear problem is considerably simplified. Thermally loaded plates with polygonal planform under hard-hinged support conditions are considered, taking into account the effect of shear in transverse isotropy. The class of symmetric vibrations about the flat plate position is represented by a homogeneous and coupled set of Duffing-oscillators as a result of a multi-mode expansion. A unifying non-dimensional closed-form solution for the corresponding nonlinear natural vibration periods is given, which is independent of the special planform. The individual shape of the plate enters the transformation into real time through the linear natural frequencies, or, equivalently, through the linear eigen-values of an effectively prestressed membrane of the same planform.     

Experimental critical loads for perforated square plates

Experimentally determined critical loads are presented for simply supported square plates with a circular central hole under the action of uniform edge displacements for hole diameters varying up to seventenths the dimension of the plate. The critical load is defined as the inflection point on the load-deflection curve as measured by a set of dial gages at the edge of the hole. Least-squares-curve fitting techniques are used for reducing all experimental data and the entire set of computations is carried out on the electronic digital computer. Finally, it is shown that the experimental results agree well with the theoretical critical loads as determined by the Ritz energy method.     

Experimental eigenvalues and mode shapes for flat clamped plates

Experimental eigenvalues of both square and rectangular clamped flat plates were measured using digital spectrum analysis. Individual mode shapes were recorded experimentally using holographic interferometry. Plate spectra showing the first 35 modes of vibration for each of the square and rectangular piates were recorded, allowing the experimentally determined eigenvalues to be compared with published theoretical predictions. Over 25 modes for a square plate and 16 modes for a rectangular plate with aspect ratio of 2/3 were recorded holographically. Selected recorded mode shapes are compared with beam mode shapes as well as with modified Bolotin mode shapes, both of which are popular assumed mode shapes in current numerical techniques. It was found that both of these assumed mode shapes agree favorably with the experimental results. The beam mode shapes agree better in some modes; the modified Bolotin mode shapes agree more favorably in others.     

Experimental eigenvalues and mode shapes for flat clamped plates

Experimental eigenvalues of both square and rectangular clamped flat plates were measured using digital spectrum analysis. Individual mode shapes were recorded experimentally using holographic interferometry. Plate spectra showing the first 35 modes of vibration for each of the square and rectangular plates were recorded, allowing the experimentally determined eigenvalues to be compared with published theoretical predictions. Over 25 modes for a square plate and 16 modes for a rectangular plate with aspect ratio of 2/3 were recorded holographically. Selected recorded mode shapes are compared with beam mode shapes as well as with modified Bolotin mode shapes, both of which are popular assumed mode shapes in current numerical techniques. It was found that both of these assumed mode shapes agree favorably with the experimental results. The beam mode shapes agree better in some modes; the modified Bolotin mode shapes agree more favorably in others.     

Experimental techniques for testing unstiffened plates in compression and bending

We present details of a dual-actuator rig developed for testing rectangular plates supported on three sides, with the remaining (longitudinal) edge free, under combined uniaxial compression and in-plane bending. Particular attention is given to ensuring a constant strain gradient at the loaded ends, as opposed to a constant load eccentricity, in order to determine the post-buckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated. Attention is also given to ensuring simply supported boundary conditions, and the methods used for anchoring the tensile stresses that develop at the loaded edges as a result of large plate deflections. Details of the methods for controlling the applied displacements are given, for which a system of four laser displacement devices was employed in order to achieve the required strain gradient. The operation of the rig is verified against established theoretical solutions.     

Fokker-Planck operator for free-molecular,nonspherical, thermally nonequilibrium Brownian particles

The Fokker-Planck collision operator entering into the kinetic equation for the velocity distribution function of convex nonspherical rigid homogeneous Brownian particles in a traveling inhomogeneous monatomic gas is derived. The regime of flow past the particles is free-molecular, i.e., the characteristic particle dimensions are much smaller than the average free path of the gas molecules, the interaction between the particles and their effect on the gas phase can be neglected, and a specular-diffuse law of interaction between the molecules and the particle surface holds. The particle temperatures T _p are the same and differ from the local gas temperature T. Thermal nonequilibrium (T _p ≠ T) leads to violation of the well-known relations between the diffusion coefficients in the spaces of the translational and angular velocities and the coefficients of forces and moments exerted on a particle. The coefficients in the unknown operator are calculated for the particles in the form of bodies of revolution with longitudinal symmetry. Data characterizing the effect of the nonsphericity of the particles, i.e., spheroids and sphere-cylinders, on the degree of violation are given.     

Experimental study on heat transfer of thermally developing and developed, turbulent, horizontal pipe flow of dilute air-solids suspensions

Heat transfer characteristics of a turbulent, dilute air-solids suspension flow in thermally developing/developed regions were experimentally studied, using a uniformly heated, horizontal 54.5 mm-ID pipe and 43-μm-diameter glass beads. The local heat transfer was measured at 27 locations from the inlet to 120-dia downstream of the heated section over a range of Reynolds numbers 3×10⁴−1.2×10⁵ and solids loading ratio 0–3, and the fully developed profiles of air velocity/temperature and particle mass flux were measured at a location 140-dia downstream of the heated section using specially designed probes, inserted into the suspension flow. The effects of the Reynolds number, solids loading ratio, and azimuthal/longitudinal locations on the heat transfer characteristics and their interactions are discussed through comparison of the present results with the data obtained by other investigators. Received on 14 October 1996     

Experimental full field investigations of resonant vibrations for piezoceramic plates by an optical interferometry method

The experimental measurement of resonant frequencies for piezoelectric material is generally performed by impedance analysis. In this paper we employ an optical interferometry method, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), to investigate the vibration characteristics of piezoceramic plates. This method demonstrates its advantages of combining noise reduction, like the subtraction method, and high fringe sensitivity, like the time-averaged method. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Based on the fact that clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding mode shapes are obtained experimentally at the same time. Excellent quality for the interferometric fringe patterns of the mode shapes is demonstrated. We find from experimental results that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extension) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, numberical finite element calculations are also performed, and the results are compared with the experimental measurements. Excellent agreement for the resonant frequencies and mode shapes are obtained from both results.     

Experimental wall correction factors of single solid spheres in triangular and square cylinders,and parallel plates

To examine wall effects, the steady state settling velocities of single solid spheres of various diameters were measured in triangular and square cylinders, and between parallel plates, which were filled up with highly viscous aqueous milet jelley solutions. The wall effect for the steady state motion of single spheres in a narrow space has to date been correlated by the wall correction factor. The wall correction factors of single solid spheres were correlated in such apparatus in the creeping flow region.     

Geometrically-exact,intrinsic theory for dynamics of moving composite plates

A geometrically-exact and fully intrinsic theory is presented for dynamics of composite plates undergoing large deformation. To say that the formulation is intrinsic means that it is without displacement and rotation variables. Although the equations are geometrically-exact, the highest degree nonlinearities are quadratic; there are no singularities associated with finite rotation. Methods for posing problems in this framework along with advantages of the formulation are discussed.     

A comprehensive analytical solution for free vibration of rectangular plates with classical edge coditions: Experimental verification

The problem of obtaining free vibration frequencies and mode shapes of rectangular plates resting on combinations of classical (i.e., clamped, simply supported, or free) edge supports is one that has been investigated for more than one hundred years. More recently, the superposition method has been developed for obtaining accurate analytical-type solutions for this family of problems. The object of this paper is to report on the results of numerous experimental tests carefully performed in order to verify the superposition method and associated computer software. Experimental and computed results are compared for a wide range of plate configurations. Very good agreement between theory and experiment has been obtained with regard to both plate natural frequencies and mode shapes. It is concluded that this computational procedure constitutes a powerful new tool for analysis of rectangular plate vibration problems.     

Kinetic Fokker-Planck equation for free-molecular,thermally nonequilibrium Brownian particles in an inhomogeneous gas

A kinetic equation for the translational and angular velocity distribution function of spherical rigid Brownian particles in an inhomogeneous monatomic gas is derived. The particle diameters are much smaller than the average free path of the gas molecules and the interaction between the particles and their effect on the carrier (gas) phase are neglected. The particle temperatures T _p are the same and differ from the local gas temperature T. The molecular velocity distribution function is specified by the first approximation of the Chapman-Enskog method. The difference between the characteristic phase velocities is small as compared with the mean thermal molecular velocity. The dependences of the diffusion coefficients in velocity space on the ratio T _p/T, which characterize the effect of thermal nonequilibrium, i.e., violation of the thermodynamic equilibrium between the phases of the disperse system, are found using a specular-diffuse law of reflection of the molecules from the particle surface.     

A dynamic model for a disc excited by vertically misaligned,rotating, frictional sliders

This paper presents a dynamic model for a disc subjected to two sliders rotating in the circumferential direction over the top and bottom surfaces of the disc. The two sliders are vertically misaligned and each is a mass-spring-damper system with friction between the slider and the disc. The moving loads produced by misaligned sliders can destabilise the whole system. Stability analysis is carried out in a simulated example. This model is meant to explain the friction mechanism for generating unstable vibration in many applications involving rotating discs.     

Stress-strain state for bending of rectangular,transversally isotropic plates of variables thickness

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Pikladnaya Mekhanika, Vol. 28, No. 6, pp. 14–22, June, 1992.     

An exact solution for transversely isotropic,simply supported and layered rectangular plates

Levinson's solution for the problem of a simply supported rectangular plate of arbitrary thickness by normal surface loads is extended to the transversely isotropic and layered case. The exact closed form solution is obtained by using the propagator matrix method in a system of vector functions. As a special case of the layered medium, the normal displacement or deflection of a homogeneous plate of arbitrary thickness by normal surface loads is also given. It is shown that it approaches the classical solution for the transversely isotropic thin plate as the thickness approaches zero on the one hand, and on the other hand reduces to the thick plate expression as given by Levinson when the medium is isotropic.     

A new trigonometric shear deformation theory for isotropic,laminated composite and sandwich plates

A new trigonometric shear deformation theory for isotropic and composite laminated and sandwich plates, is developed. The new displacement field depends on a parameter “m”, whose value is determined so as to give results closest to the 3D elasticity bending solutions. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. Plate governing equations and boundary conditions are derived by employing the principle of virtual work. The Navier-type exact solutions for static bending analysis are presented for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature. The results show that the present model performs as good as the Reddy’s and Touratier’s shear deformation theories for analyzing the static behavior of isotropic and composite laminated and sandwich plates.     

A Bending-Gradient model for thick plates,Part II: Closed-form solutions for cylindrical bending of laminates

In the first part (Lebée and Sab, 2010a) of this two-part paper we have presented a new plate theory for out-of-plane loaded thick plates where the static unknowns are those of the Kirchhoff–Love theory (3 in-plane stresses and 3 bending moments), to which six components are added representing the gradient of the bending moment. The new theory, called Bending-Gradient plate theory is an extension to arbitrarily layered plates of the Reissner–Mindlin plate theory which appears as a special case when the plate is homogeneous. Moreover, we demonstrated that, in the general case, the Bending-Gradient model cannot be reduced to a Reissner–Mindlin model. In this paper, the Bending-Gradient theory is applied to laminated plates and its predictions are compared to those of Reissner–Mindlin theory and to full 3D (Pagano, 1969) exact solutions. The main conclusion is that the Bending-Gradient gives good predictions of deflection, shear stress distributions and in-plane displacement distributions in any material configuration. Moreover, under some symmetry conditions, the Bending-Gradient model coincides with the second-order approximation of the exact solution as the slenderness ratio L/h goes to infinity.     

Failure criterion for reinforced concrete beams and plates subjected to membrane force,bending and shear

In this paper, a failure criterion for reinforced concrete plates is derived through the kinematic method in the framework of the limit analysis theory. This criterion is expressed in terms of the stress resultant variables: membrane force, shear force and bending moment at once. The aim of the authors is to be able to predict the failure of reinforced concrete plate structures in statics or in slow dynamics using directly the internal forces (membrane and shear forces and moment) resulting from a finite-element computation.In a first step, a beam criterion is derived. The closed form expression of the criterion shows that it is made up of two parts, one independent of the moment (i.e. depending only on the normal force and the shear force) and one depending on the normal force, the shear force and the bending moment. This structure of the criterion allows to determine two failure modes: shear failure and bending failure.Then in a second step, the beam criterion is extended to the case of reinforced concrete plates. The obtained criterion is partly numerical and partly a close form expression. It gives an upper bound of the load, and when this limit load is reached, the criterion is able to supply, on one hand, the failure mode (as seen in the beam case) and, on the other hand, the angles of the failure plane in the reinforced concrete plate section.Thirdly, the criterion is implemented in the finite element software Europlexus and validated with respect to punching experimental tests. We show that the criterion must be used with an effectiveness factor applied on the concrete compressive strength.