Suggestion of a new dimensionless number for dynamic plastic response of beams and plates

A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is defined as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are reflected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical influence of the structure on the dynamic response. For an impulsively loaded beam or plate, the final dimensionless deflection is solely dependent upon the response number. When the secondary effects of finite deflections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape.

Measurement of the diffraction-limit wavefront with double-shearing interferometers

In order to measure the diffraction-limit wavefront, we present three types of common-path double-shearing interferometers based on the theory of double shearing. Two pairs of half-aperture or whole-aperture wedge plates are used to introduce opposite tilt to realize the double-shearing function. By comparing the fringe widths in two fields, the marginal wavefront aberration can be obtained. In the paper, we give three different configurations: half-aperture configuration, whole-field configuration and double-interferometer configuration. The half-aperture configuration has the features of high sensitivity, stabilization and easy alignment. For the whole-field configuration, the interference fringes are displayed in two whole fields. Consequently, the divergent or convergent characteristic and aberration types of a wavefront can be identified visually. The whole-field configuration can be changed to the double-interferometer configuration for continuous test. Both small and large wavefront aberrations can be measured by the double-interferometer configuration. The minimum detectable wavefront aberration (W-0)(min) comes to 0.03 lambda. Lastly, we present the experimental results for the three types of double-shearing interferometers.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.

Modeling Study on the Characteristics of Laminar and Turbulent Argon Plasma Jets Impinging Normally upon a Flat Plate in Ambient Air

Modeling study is performed to compare the flow and heat transfer characteristics of laminar and turbulent argon thermal-plasma jets impinging normally upon a flat plate in ambient air. The combined-diffusion-coefficient method and the turbulence-enhanced combined-diffusion-coefficient method are employed to treat the diffusion of argon in the argon-air mixture for the laminar and the turbulent cases, respectively. Modeling results presented include the flow, temperature and argon concentration fields, the air mass flow-rates entrained into the impinging plasma jets, and the distributions of the heat flux density on the plate surface. It is found that the formation of a radial wall jet on the plate surface appreciably enhances the mass flow rate of the ambient air entrained into the laminar or turbulent plasma impinging-jet. When the plate standoff distance is comparatively small, there exists a significant difference between the laminar and turbulent plasma impinging-jets in their flow fields due to the occurrence of a large closed recirculation vortex in the turbulent plasma impinging-jet, and no appreciable difference is found between the two types of jets in their maximum values and distributions of the heat flux density at the plate surface. At larger plate standoff distances, the effect of the plate on the jet flow fields only appears in the region near the plate, and the axial decaying-rates of the plasma temperature, axial velocity and argon mass fraction along the axis of the laminar plasma impinging-jet become appreciably less than their turbulent counterparts.

Elastic Waves in a Hybrid Multilayered Piezoelectric Plate

An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a hybrid multilayered piezoelectric plate. In this method, the multilayered piezoelectric plate is divided into a number of layered elements with three-nodal-lines in the wall thickness, the coupling between the elastic field and the electric field is considered in each element. The associated frequency dispersion equation is developed and the phase velocity and slowness, as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. Examples provide a full understanding for the complex phenomena of elastic waves in hybrid multilayered piezoelectric media.

Coherent Structures in Transition of a Flat-Plate Boundary Layer at Ma=0.7

Direct numerical simulation (DNS) of a spatially evolving flat-plate boundary layer transition process at free stream Mach number 0.7 is performed. Tollmien-Schlichting (T-S) waves are added on the inlet boundary as the disturbances before transition. Typical coherent structures in the transition process are investigated based on the second invariant of velocity gradient tensor. The instantaneous shear stress and the mean velocity profile in the transition region are studied. In our view, the fact that the peak value of shear stress in the stress concentration area increases and exceeds a threshold value during the later stage of the transition process plays an important role in the laminar breakdown process.

The relationship of SIF between plate and plane fracture problems and the effect of the plate thickness on SIF

In the present paper, it is shown that the zero series eigenfunctions of Reissner plate cracks/notches fracture problems are analogous to the eigenfunctions of anti-plane and in-plane. The singularity in the double series expression of plate problems only arises in zero series parts. In view of the relationship with eigen-values of anti-plane and in-plane problem, the solution of eigen-values for Reissner plates consists of two parts: anti-plane problem and in-plane problem. As a result the corresponding eigen-values or the corresponding eigen-value solving programs with respect to the anti-plane and in-plane problems can be employed and many aggressive SIF computed methods of plane problems can be employed in the plate. Based on those, the approximate relationship of SIFs between the plate and the plane fracture problems is figured out, and the effect relationship of the plate thickness on SIF is given.

A New Designed Two-Dimensional Bifurcation Parallel-Plate Flow Chamber

解决平行平板流槽每次实验只能观测壁面培养细胞受一种剪应力作用的问题。作者在平行平板流槽的基础上,首次提出了一种改进后的流槽--二维平板分叉流槽。通过数值模拟,给出了流体作定常流动时,流速和壁面剪应力的分布。结果发现,利用这种二维平板分叉流槽可以研究壁面培养的细胞在不同大小剪应力作用下的力学行为。该研究结果为流槽的合理设计和使用,并分析剪应力空间分布对内皮细胞的影响有重要实际意义。

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

Surface Stability of Epitaxial Elastic Films by Casimir Force

We investigate the morphological stability of epitaxial thin elastic films on a substrate by the Casimir force between the film surface and a flat plate. Critical undulation wavelengths are derived for two different limit conditions. Consideration of the Casimir force in both limit cases decreases the critical wavelength of the surface perturbation.

A contact crack problem in an infinite plate

The problem of an infinite plate with crack of length 2a loaded by the remote tensile stress P and a pair of concentrated forces Q is discussed. The value of the force Q for the initial contact of crack face is investigated and the contact length elevated, while the Q force increases. The problem is solved assuming that the stress intensity factor vanishes at the end point of the contact portion. By the Fredholm integral equation for the multiple cracks, the reduction of stress intensity factor due to Q is found. (C) 1999 Elsevier Science Ltd. All rights reserved.

Internal resonance of an L-shaped beam with a limit stop .1. Free vibration

Real-life structures often possess piecewise stiffness because of clearances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex mode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple internal resonances, which involve interactions among the first five modes and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the natural frequency of a higher mode. The conditions for the existence of internal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbone curves. A method to compute such intersections by using only one harmonic in the free vibration solution is proposed. (C) 1996 Academic Press Limited

Internal resonance of an L-shaped beam with a limit stop .2. Forced vibration

A limit stop is placed at the elbow of an L-shaped beam whose linear natural frequencies are nearly commensurable. As a result of this hardening device the non-linear system exhibits multiple internal resonances, which involve various degree of coupling between the first five modes of the beam in free vibration. A point load is so placed as to excite several modes and the resulting forced vibration is examined. In the undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with multiple branches and interactions between the first four modes. The amplitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Consequently parts of the resonance curve may be eliminated, with the resulting response comprising different distinctive branches. (C) 1996 Academic Press Limited