Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (theta(z)) and torsion rotation (theta(s)). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of `flexureless torsion' and `torsionless flexure' and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. (C) 2015 Elsevier B.V. All rights reserved.

Benchmark analytical solutions from beams with shared eigenpair

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.

Nonrotating Beams Isospectral to Tapered Rotating Beams

In this paper, we seek to find nonrotating beams that are isospectral to a given tapered rotating beam. Isospectral structures have identical natural frequencies. We assume the mass and stiffness distributions of the tapered rotating beam to be polynomial functions of span. Such polynomial variations of mass and stiffness are typical of helicopter and wind turbine blades. We use the Barcilon-Gottlieb transformation to convert the fourth-order governing equations of the rotating and the nonrotating beams, from the (x, Y) frame of reference to a hypothetical (z, U) frame of reference. If the coefficients of both the equations in the (z, U) frame match with each other, then the nonrotating beam is isospectral to the given rotating beam. The conditions on matching the coefficients lead to a pair of coupled differential equations. Wesolve these coupled differential equations numerically using the fourth-order Runge-Kutta scheme. We also verify that the frequencies (given in the literature) of standard tapered rotating beams are the frequencies (obtained using the finite-element analysis) of the isospectral nonrotating beams. Finally, we present an example of beams having a rectangular cross-section to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these isospectral nonrotating beams to calculate the frequencies of the rotating beam.

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.

Polarization Self-Modulation Phenomenon in a Free Oscillated Nd: YAG Laser

Polarization self-modulation effect in a free oscillated Nd:YAG laser is investigated after a quarter wave plate is introduced independently in the two positions of the cavity. As described in the previous experiments, the intensity components in the orthogonal directions are modulated with a period of the round-trip time or twice. Different pulse shapes reveal that the seed field from the spontaneous emission is not uniform and seems to be stochastic for each pulse.

Surface amorphous and crystalline microstructure by alloying zirconium using Nd : YAG pulsed laser

A novel composite coating was synthesized by laser alloying of zirconium nanoparticles on an austenite stainless steel surface using a pulsed Nd:YAG laser. The coating contained duplex microstructures comprising an amorphous phase and an austenitic matrix. A discontinuous zirconium-containing region formed at a depth of 16 mum below the surface. The amorphous phase was present in the zirconium-rich region, with the composition of zirconium ranging from 7.8 to 14.5 at. pet. The formation of the amorphous phase was attributed to the zirconium addition. The hardness, corrosion, and wear-corrosion resistance of the irradiated coating were evidently enhanced compared to those of the stainless steel.

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is presented.

Microstructure and wear resistance of in situ TiCp composite coating by laser cladding

A new in situ method was realized by one step laser cladding to produce Ni-base alloy composite coating reinforced by in situ reacted and gradiently distributed TiCp particles. The submicron TiCp particles were formed and uniformly distributed because of the in situ reaction and trapping effect under the rapid solidification condition. And, TiCp particles were of gradient distribution on a macro scale and their volume fraction increased from 1.86% at the layer/substrate interface to a maximum 38.4% at the surface of the layer. Furthermore, the in situ generated TiCp/gamma-Ni interfaces were free from deleterious surface reactions. Additionally, the clad coating also revealed a high microhardness of gradient variation with the layer depth and the superior abrasive wear resistance.

Intensity Distribution Design for Laser-Induced Thermal Loading Based on Numerical Simulation

To accomplish laser-induced thermal loading simulation tests for pistons,the Gaussian beam was modulated into multi-circular beam with specific intensity distribution.A reverse method was proposed to design the intensity distribution for the laser-induced thermal loading based on finite element(FE) analysis.Firstly,the FE model is improved by alternating parameters of boundary conditions and thermal-physical properties of piston material in a reasonable range,therefore it can simulate the experimental resul...

Effects of La2O3 on Microstructure and Wear Properties of Laser Clad gamma/Cr7C3/TiC Composite Coatings on TiAl Intermatallic Alloy

The effects of La2O3 addition on the microstructure and wear properties of laser clad gamma/C(r)7C(3)/TiC composite coatings on gamma-TiAl intermetallic alloy substrates with NiCr-Cr3C2 precursor mixed powders have been investigated by optical microscopy (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD) and energy-dispersive spectrometer (EDS) and block-on-ring wear tests. The responding wear mechanisms are discussed in detail. The results are compared with that for composite coating without La2O3. The comparison indicates that no evident new crystallographic phases are formed except a rapidly solidified microstructure consisting of the primary hard Cr7C3 and TiC carbides and the gamma/Cr7C3 eutectics distributed in the tough gamma nickel solid solution matrix. Good finishing coatings can be achieved under a proper amount of La2O3-addition and a suitable laser processing parameters. The additions of rare-earth oxide La,03 can refine and purify the microstructure of coatings, relatively decrease the volume fraction of primary blocky Cr7C3 to Cr7C3/gamma eutectics, reduce the dilution of clad material from base alloy and increase the microhardness of the coatings. When the addition of La2O3 is approximately 4 wt.%, the laser clad composite coating possesses the highest hardness and toughness. The composite coating with 4 wt.%La2O3 addition can result the best enhancement of wear resistance of about 30%. However, too less or excessive addition amount of La2O3 have no better influence on wear resistance of the composite coating.

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness. (C) 2000 Optical Society of America.

Microstructure of Zr-alloyed coating using pulsed laser

Coatings were synthesized by laser alloying of zirconium (Zr) particles using a pulsed Nd:YAG laser on an austenite stainless steel. The distribution of Zr is uneven, in a depth of 18 mum just below the surface of the pool. The coating consisted of duplex microstructures, i.e. metallic glass (MG) and austenite. The MG formed in Zr-contained regions, with the Zr composition ranging from 7.6 to 16.8 at.%. The formation of the MG was attributed to an increase in glass-forming ability by Zr addition.

Application of the Conjugate Gradient Optimization Algorithm of Neural Network on Laser Machining

在应用激光技术加工复杂曲面时,通常以采样点集为插值点来建立曲面函数,然后实现曲面上任意坐标点的精确定位。人工神经网络的BP算法能实现函数插值,但计算精度偏低,往往达不到插值精确要求,造成较大的加工误差。提出人工神经网络的共轭梯度最优化插值新算法,并通过实例仿真,证明了这种曲面精确定位方法的可行性,从而为激光加工的三维精确定位提供了一种良好解决方案。这种方法已经应用在实际中。