Multi-material topology optimization of viscoelastically damped structures using a parametric level set method

The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.

[1]  Conor D. Johnson,et al.  Finite Element Prediction of Damping in Structures with Constrained Viscoelastic Layers , 1981 .

[2]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[3]  P. Mourey,et al.  Passive Damping Devices For Aerospace Structures , 2002 .

[4]  M. Erdmann,et al.  Gaia basic angle monitoring system , 2012, Other Conferences.

[5]  Y. Xie,et al.  Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials , 2009 .

[6]  Bing Qin Wang,et al.  Topology Optimization for Constrained Layer Damping Plates Using Evolutionary Structural Optimization Method , 2014 .

[7]  G. Allaire,et al.  MULTI-PHASE STRUCTURAL OPTIMIZATION VIA A LEVEL SET METHOD ∗, ∗∗ , 2014 .

[8]  G. Cheng,et al.  On topology optimization of damping layer in shell structures under harmonic excitations , 2012 .

[9]  Bijan Samali,et al.  Use of viscoelastic dampers in reducing wind- and earthquake-induced motion of building structures , 1995 .

[10]  N. Tschoegl.  The Phenomenological Theory of Linear Viscoelastic Behavior , 1989 .

[11]  H. Guan,et al.  Topology Optimization of Viscoelastic Materials Distribution of Damped Sandwich Plate Composite , 2013 .

[12]  Charles W. Bert,et al.  Material damping: An introductory review of mathematic measures and experimental technique , 1973 .

[13]  M. Wang,et al.  Radial basis functions and level set method for structural topology optimization , 2006 .

[14]  Ying-Jie Wang,et al.  VIBRATION SUPPRESSION OF TRAIN-INDUCED MULTIPLE RESONANT RESPONSES OF TWO-SPAN CONTINUOUS BRIDGES USING VE DAMPERS , 2013 .

[15]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[17]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[18]  Liping Chen,et al.  A semi-implicit level set method for structural shape and topology optimization , 2008, J. Comput. Phys..

[19]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[20]  Mohan D. Rao,et al.  Recent applications of viscoelastic damping for noise control in automobiles and commercial airplanes , 2003 .

[21]  Z. Kang,et al.  A multi-material level set-based topology and shape optimization method , 2015 .

[22]  C. W. Bert,et al.  Material damping - An introductory review of mathematical models, measures and experimental techniques. , 1973 .

[23]  E. Kerwin.  Damping of Flexural Waves by a Constrained Viscoelastic Layer , 1959 .

[24]  Hui Zheng,et al.  Optimization of partial constrained layer damping treatment for vibrational energy minimization of vibrating beams , 2004 .

[25]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[26]  P. Grootenhuis.  The control of vibrations with viscoelastic materials , 1970 .

[27]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[28]  Ole Sigmund,et al.  Design of multiphysics actuators using topology optimization - Part I: One-material structures , 2001 .

[29]  G. K. Ananthasuresh,et al.  Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme , 2001 .

[30]  Xiaoming Wang,et al.  Color level sets: a multi-phase method for structural topology optimization with multiple materials , 2004 .

[31]  Fred van Keulen,et al.  Integrated topology and controller optimization of motion systems in the frequency domain , 2015 .

[32]  R. Plunkett,et al.  Length Optimization for Constrained Viscoelastic Layer Damping , 1970 .

[33]  Adel Elsabbagh,et al.  Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach , 2011 .

[34]  A. Baz,et al.  Topology optimization of unconstrained damping treatments for plates , 2014 .

[35]  R. Haftka,et al.  A discourse on sensitivity analysis for discretely-modeled structures , 1991 .

[36]  Kurt Maute,et al.  Level-set methods for structural topology optimization: a review , 2013 .

[37]  Yanchu Xu,et al.  Revised modal strain energy method for finite element analysis of viscoelastic damping treated structures , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[38]  Craig Underwood,et al.  Energy Dissipation in Spacecraft Structures Incorporating Bolted Joints Operating in Macroslip , 2008 .

[39]  Michael Yu Wang,et al.  Shape and topology optimization of compliant mechanisms using a parameterization level set method , 2007, J. Comput. Phys..

[40]  C. D. Johnson,et al.  Design of Passive Damping Systems , 1995 .

[41]  Roger Lundén,et al.  Optimum distribution of additive damping for vibrating beams , 1979 .

[42]  Qibai Huang,et al.  Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate , 2013 .

[43]  A. Lumsdaine,et al.  SHAPE OPTIMIZATION OF UNCONSTRAINED VISCOELASTIC LAYERS USING CONTINUUM FINITE ELEMENTS , 1998 .