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Joseph R Pavliga - One of the best experts on this subject based on the ideXlab platform.

  • effects of thickness and modal imperfection amplitude on Elastic collapse pressure of a cross ply imperfect ring
    Composite Structures, 2008
    Co-Authors: Joseph R Pavliga, Deokjoo Kim
    Abstract:

    Effects of thickness and modal imperfection amplitude on Mode 2 Elastic collapse pressures of thin, Moderately thick and thick cross-ply perfect and imperfect rings are investigated in detail. A recently developed nonlinear resonance (eigenvalue) based semi-analytical solution technique is employed here for computation of the Elastic Mode 2 collapse pressures of thin to thick cross-ply rings, weakened by modal or harmonic type imperfections. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the perfect/imperfect cross-ply ring. Interesting and hitherto unavailable numerical results pertaining to the effects of thickness and amplitude of modal imperfection on the hydrostatic collapse pressures of imperfect cross-ply rings and comparison with their perfect counterparts are also presented.

  • a nonlinear resonance eigenvalue approach for computing Elastic collapse pressure of a Moderately thick cross ply imperfect ring
    Composite Structures, 2008
    Co-Authors: Reaz A Chaudhuri, Deokjoo Kim, Joseph R Pavliga
    Abstract:

    A hitherto unavailable nonlinear resonance (eigenvalue) based semi-analytical solution technique for prediction of the Elastic Mode 2 collapse pressure of a Moderately thick cross-ply ring, weakened by a modal or harmonic type imperfection, is presented. A von Karman type iterative nonlinear analysis, that is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the imperfect cross-ply ring. Numerical results pertaining to the effect of modal imperfection on the hydrostatic collapse pressure of a Moderately thick cross-ply ring and comparison with its perfect counterpart are also presented. These results further demonstrate that the present iterative analysis for solving a nonlinear eigenvalue problem reduces to the linearized buckling (linear eigenvalue) analysis, associated with the conventional bifurcation theory, for a perfect Moderately thick cross-ply ring.

Deokjoo Kim - One of the best experts on this subject based on the ideXlab platform.

  • effects of thickness and modal imperfection amplitude on Elastic collapse pressure of a cross ply imperfect ring
    Composite Structures, 2008
    Co-Authors: Joseph R Pavliga, Deokjoo Kim
    Abstract:

    Effects of thickness and modal imperfection amplitude on Mode 2 Elastic collapse pressures of thin, Moderately thick and thick cross-ply perfect and imperfect rings are investigated in detail. A recently developed nonlinear resonance (eigenvalue) based semi-analytical solution technique is employed here for computation of the Elastic Mode 2 collapse pressures of thin to thick cross-ply rings, weakened by modal or harmonic type imperfections. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the perfect/imperfect cross-ply ring. Interesting and hitherto unavailable numerical results pertaining to the effects of thickness and amplitude of modal imperfection on the hydrostatic collapse pressures of imperfect cross-ply rings and comparison with their perfect counterparts are also presented.

  • a nonlinear resonance eigenvalue approach for computing Elastic collapse pressure of a Moderately thick cross ply imperfect ring
    Composite Structures, 2008
    Co-Authors: Reaz A Chaudhuri, Deokjoo Kim, Joseph R Pavliga
    Abstract:

    A hitherto unavailable nonlinear resonance (eigenvalue) based semi-analytical solution technique for prediction of the Elastic Mode 2 collapse pressure of a Moderately thick cross-ply ring, weakened by a modal or harmonic type imperfection, is presented. A von Karman type iterative nonlinear analysis, that is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the imperfect cross-ply ring. Numerical results pertaining to the effect of modal imperfection on the hydrostatic collapse pressure of a Moderately thick cross-ply ring and comparison with its perfect counterpart are also presented. These results further demonstrate that the present iterative analysis for solving a nonlinear eigenvalue problem reduces to the linearized buckling (linear eigenvalue) analysis, associated with the conventional bifurcation theory, for a perfect Moderately thick cross-ply ring.

S P Vyatchanin - One of the best experts on this subject based on the ideXlab platform.

  • parametric oscillatory instability in ligo interferometer
    Proceedings of SPIE the International Society for Optical Engineering, 2008
    Co-Authors: V B Braginsky, S. E. Strigin, S P Vyatchanin
    Abstract:

    We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with Fabry-Perot cavities in the arms. The basis for this effect is the excitation of the additional Stokes optical Mode and the mirror Elastic Mode when the optical energy stored in the main Fabry-Perot cavity Mode exceeds the certain threshold. We demonstrate that in the resonance case the parametric oscillatory instability will take place at the energy stored in the cavity of about five orders smaller than one planned for LIGO-II interferometer. The presence of anti-Stokes Modes can depress parametric oscillatory instability. However, it is very likely that the anti-Stokes Modes will not compensate the parametric oscillatory instability completely because of the existence of the Mode combinations which interact with each other quite strongly.

  • precursors of parametric oscillatory instability in ligo interferometer
    JENAM-2007 "Our Non-Stable Universe", 2007
    Co-Authors: Ilya A Polyakov, S P Vyatchanin
    Abstract:

    Abstract The basis of undesirable effect of parametric oscillatory instability in optical interferometer is provided by excitation of the additional (Stokes) optical Mode having frequency ω 1 , and the mirror Elastic Mode, having frequency ω m . It appears when optical energy stored in the main Mode, with frequency ω 0 , exceeds a certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze the time evolution of parametric instability which allows predicting the characteristics of precursors of parametric instability. Observation of such precursors may help avoid parametric instability.

  • analysis of parametric oscillatory instability in signal recycled ligo interferometer with different arms
    Physics Letters A, 2007
    Co-Authors: S. E. Strigin, S P Vyatchanin
    Abstract:

    Abstract The basis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer is the excitation of the additional (Stokes) optical Mode, with frequency ω 1 , and the mirror Elastic Mode, with frequency ω m , when optical energy stored in the main Mode, with frequency ω 0 , exceeds the certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze parametric instability in the general case when eigen frequencies of Fabry–Perot (FP) cavities in arms of interferometer are detuned from each other and show that parametric instability in this interferometer is relatively small due to small bandwidth of interferometer. We propose to “scan” the frequency range where parametric instability may take place by varying the position of signal recycling mirror.

  • analysis of parametric oscillatory instability in power recycled ligo interferometer
    Physics Letters A, 2002
    Co-Authors: V B Braginsky, S. E. Strigin, S P Vyatchanin
    Abstract:

    Abstract We present the analysis of undesirable effect of parametric oscillatory instability in signal recycled LIGO interferometer. The basis for this effect is the excitation of the additional (Stokes) optical Mode, with frequency ω 1 , and the mirror Elastic Mode, with frequency ω m , when optical energy stored in the main FP cavity Mode, with frequency ω 0 , exceeds the certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We show that possibility of parametric instability in this interferometer is relatively small due to small bandwidth of interferometer. We propose to “scan” the frequency range where parametric instability may take place varying the position of signal recycling mirror.

  • parametric oscillatory instability in fabry perot interferometer
    Physics Letters A, 2001
    Co-Authors: V B Braginsky, S. E. Strigin, S P Vyatchanin
    Abstract:

    Abstract We present an approximate analysis of a nonlinear effect of parametric oscillatory instability in Fabry–Perot (FP) interferometer. The basis for this effect is the excitation of the additional (Stokes) optical Mode with frequency ω1 and of the mirror's Elastic Mode with frequency ωm when the optical energy stored in the FP resonator main Mode with frequency ω0 exceeds the certain threshold and the frequencies are related as ω0≃ω1+ωm. This effect is undesirable in laser gravitational wave antennae because it may create a specific upper limit for the value of energy stored in FP resonator. In order to avoid it the detailed analysis of the mirror's Elastic Modes and FP resonator optical Modes structure is necessary.

Reaz A Chaudhuri - One of the best experts on this subject based on the ideXlab platform.

  • a nonlinear resonance eigenvalue approach for computation of Elastic collapse pressures of harmonically imperfect relatively thin rings
    Thin-walled Structures, 2018
    Co-Authors: Reaz A Chaudhuri
    Abstract:

    Abstract A nonlinear resonance (eigenvalue) based semi-analytical approach is employed here for computation of the Elastic Mode 2 collapse pressures of Moderately-thick to thin isotropic rings, weakened by harmonic or modal type imperfections. The Mode 2 collapse pressure is, by definition, associated with the buckled Mode shape of cos(2θ) type, and is the harmonically imperfect ring counterpart to the Euler type buckling pressure of a hydrostatically pressurized thin perfect ring. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of a harmonically imperfect ring. Interesting and hitherto unavailable numerical results pertaining to the effects of harmonic imperfections on the hydrostatic collapse pressures of imperfect metallic rings are also presented.

  • a nonlinear resonance eigenvalue approach for computing Elastic collapse pressure of a Moderately thick cross ply imperfect ring
    Composite Structures, 2008
    Co-Authors: Reaz A Chaudhuri, Deokjoo Kim, Joseph R Pavliga
    Abstract:

    A hitherto unavailable nonlinear resonance (eigenvalue) based semi-analytical solution technique for prediction of the Elastic Mode 2 collapse pressure of a Moderately thick cross-ply ring, weakened by a modal or harmonic type imperfection, is presented. A von Karman type iterative nonlinear analysis, that is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the imperfect cross-ply ring. Numerical results pertaining to the effect of modal imperfection on the hydrostatic collapse pressure of a Moderately thick cross-ply ring and comparison with its perfect counterpart are also presented. These results further demonstrate that the present iterative analysis for solving a nonlinear eigenvalue problem reduces to the linearized buckling (linear eigenvalue) analysis, associated with the conventional bifurcation theory, for a perfect Moderately thick cross-ply ring.

Mihai Anitescu - One of the best experts on this subject based on the ideXlab platform.

  • Elastic Mode algorithms for mathematical programs with equilibrium constraints global convergence and stationarity properties
    Mathematical Programming, 2007
    Co-Authors: Mihai Anitescu, Paul Tseng, Stephen J Wright
    Abstract:

    The Elastic-Mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the Elastic-Mode formulation. Here we study global convergence properties of methods based on this formulation, which involve generating an (exact or inexact) first- or second-order point of the formulation, for nondecreasing values of the penalty parameter. Under certain regularity conditions on the active constraints, we establish finite or asymptotic convergence to points having a certain stationarity property (such as strong stationarity, M-stationarity, or C-stationarity). Numerical experience with these approaches is discussed. In particular, our analysis and the numerical evidence show that exact complementarity can be achieved finitely even when the Elastic-Mode formulation is solved inexactly.

  • Global Convergence of an Elastic Mode Approach for a Class of Mathematical Programs with Complementarity Constraints
    Siam Journal on Optimization, 2005
    Co-Authors: Mihai Anitescu
    Abstract:

    We prove that any accumulation point of an Elastic Mode approach, that approximately solves the relaxed subproblems, is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satisfies the MPCC-LICQ constraint qualification, and if the solutions of the subproblem satisfy approximate second-order sufficient conditions, then the limiting point is an M-stationary point. Moreover, if the accumulation point satisfies the upper-level strict complementarity condition, the accumulation point will be a strongly stationary point. If we assume that the penalty function associated with the feasible set of the mathematical program with complementarity constraints has bounded level sets, and if the objective function is bounded below, we show that the algorithm will produce bounded iterates and will therefore have at least one accumulation point. We prove that the obstacle problem satisfies our assumptions for both a rigid and a deformable obstacle. The theoretical conclusions are validated by several numerical examples.

  • on using the Elastic Mode in nonlinear programming approaches to mathematical programs with complementarity constraints
    Siam Journal on Optimization, 2005
    Co-Authors: Mihai Anitescu
    Abstract:

    We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the Elastic Mode with a bounded penalty parameter. In this context, the Elastic Mode transforms MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by sequential quadratic programming (SQP) algorithms. One such algorithm is shown to achieve local linear convergence once the problem is relaxed. Under stronger conditions, we also prove superlinear convergence to the solution of an MPCC using an adaptive Elastic Mode approach for an SQP algorithm recently analyzed in an MPCC context in [R. Fletcher, S. Leyffer, S. Sholtes, and D. Ralph, Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints, Tech. report NA 210, University of Dundee, Dundee, UK, 2002]. Our assumptions are more general since we do not use a critical assumption from that reference. In addition, we show that the Elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen.