A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method

Zhou, LePing; Tang, Dawei

doi:10.1016/j.optlastec.2006.06.003

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…Typically, the FGM microbeam is formed using bimaterials, such as graded ceramic diffused in metal. The ceramic constituent of the material provides the high temperature resistance owing to its low thermal conductivity, while the ductile metal constituent accommodates the high thermal stresses resulting from the high thermal transients [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

Meguid

et al. 2014

Proc. R. Soc. A.

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In this paper, we provide a unified and selfconsistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The nonuniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam.

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Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

Meguid

et al. 2014

Proc. R. Soc. A.

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“…Based on these assumptions, finite element method (FEM) is widely used to solve the thermoelastic equation for analyzing the thermal deformation of mirror surface. In these studies, the influence of channel dimension [14, 15], shape and configuration of the flow channels [16, 17], properties of materials, and the intensity of the laser radiation [18, 19] were investigated. However, the assumption may lead to great discrepancy between the predictions and the facts, since the heat transfer performance shows different properties along the flow directions, especially when the flow passage and the hydraulic diameter are short [20, 21].…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer and Thermal Deformation Characteristics of Liquid-Cooled Laser Mirror

Zhu

et al. 2014

Advances in Mechanical Engineering

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A coupled finite volume-element method is developed to simulate the transient thermal deformation of water-cooled mirror by considering fluid flow and convective heat transfer. The simulation process consists of two steps: the 3D finite volume models of fluid flow and heat transfer equation are solved to obtain the time-dependent temperature field by using CFD; then, the obtained temperature field used as final temperature field is unidirectionally coupled to the finite element model for solving the thermoplastic equation. It is concluded that fluid flow not only affects the magnitude of temperature rise and thermal deformation, but also affects the distribution of temperature and thermal deformation. The temperature gradient in the thickness direction (z direction) is found to be much larger than that in transverse direction. It is found that the temperature and the consequent deformation of water-cooled mirror increase significantly in the first seconds and gradually become steady state in the subsequent time. Experiments are conducted to estimate the precision of numerical models, and the experimental results agree well with the simulated results.

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“…A glass laser system uses several thousand large optics, which are usually mounted on a support frame, to produce high energy. Surface shape errors of these large optics, which are mainly affected by gravity, fixture supports, and temperature gradients, will create perturbations in laser beam transmission and cause aberrations and even failure of laser systems [1,2]. In general, the surface shape errors include: (a) thermal deformation of the optical material under laser heating or temperature gradient distribution, and (b) mechanical deformation introduced by the clamping forces of the support frame.…”

Section: Introductionmentioning

confidence: 99%

“…In the optical community, much effort has been devoted to reducing the deformation of the optics with the selection and cooling of optical materials or by optimal design of the support frame [1][2][3][4]. However, our paper does not discuss the choice of optical material, which is purely an optical material application problem, but focuses on the support frame design to eliminate or reduce surface shape errors of the large glass laser optics caused by clamping forces or the thermal residual stress of the support frame.…”

Section: Introductionmentioning

confidence: 99%

Optimization of fixture layouts of glass laser optics using multiple kernel regression

Cao

Qiao

2014

Appl. Opt.

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We aim to build an integrated fixturing model to describe the structural properties and thermal properties of the support frame of glass laser optics. Therefore, (a) a near global optimal set of clamps can be computed to minimize the surface shape error of the glass laser optic based on the proposed model, and (b) a desired surface shape error can be obtained by adjusting the clamping forces under various environmental temperatures based on the model. To construct the model, we develop a new multiple kernel learning method and call it multiple kernel support vector functional regression. The proposed method uses two layer regressions to group and order the data sources by the weights of the kernels and the factors of the layers. Because of that, the influences of the clamps and the temperature can be evaluated by grouping them into different layers.

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A functionally graded structural design of mirrors for reducing their thermal deformations in high-power laser systems by finite element method

Cited by 10 publications

References 13 publications

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam

Heat Transfer and Thermal Deformation Characteristics of Liquid-Cooled Laser Mirror

Optimization of fixture layouts of glass laser optics using multiple kernel regression

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