Topology optimization for elastic base under rectangular plate subjected to moving load
<jats:title>Abstract</jats:title> <jats:p> Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed) time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.</jats:p>
KHURSHUDYAN (2015), Generalized control with compact support of wave equation with variable coefficients International of Dynamics and, Control, doi.org/10.1007/s40435-015-0148-3 ; LENIOWSKA (2003), Active control of circular plate vibration by using piezoceramic actuators of Control, Archives Sciences, 13, 445. ; BRANSKI (2007), On the quasi optimal distribution of PZTs in active reduction of the triangular plate vibration of Control, Archives Sciences, 17, 427. ; OUZAHRA (2014), Controllability of the wave equation with bilinear controls European of, Control, 20, 57. ; RASINA (2013), Control optimization in bilinear systems and Remote, Automation Control, 74, 802. ; PRZYBYLOWICZ (2003), Active reduction of resonant vibration in rotating shafts made of piezoelectric composites of Control, Archives Sciences, 13, 327. ; KHURSHUDYAN (2014), KHURSHUDYAN and AS Optimal distribution of viscoelastic dampers under elastic finite beam under moving load of NAS of in Russian, Armenia, 67, 56. ; GOSIEWSKI (2003), Control system of beam vibration using piezo elements of Control, Archives Sciences, 13, 375. ; HASLINGER (2005), A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function Control and, Cybernetics, 34, 283. ; KHURSHUDYAN (2015), Generalized control with compact support for systems with distributed parameters of Control, Archives Sciences, 25, 5. ; STAREK (2010), Suppression of vibration with optimal actuators and sensors placement of Control, Archives Sciences, 20, 99. ; KROTOV (2011), Optimization of linear systems with controllable coefficients and Remote, Automation Control, 72, 1199. ; SARKISYAN (2015), and AS Structural optimization for infinite non homogeneous layer in periodic wave propagation problems Composite, Mechanics, 51, 277. ; JILAVYAN (2013), On adhesive binding optimization of elastic homogeneous rod to a fixed rigid base as a control problem by coefficient of Control, Archives Sciences, 23, 413. ; BEAUCHARD (2015), Bilinear control of Schrodinger PDEs In Encyclopedia of Systems and to appear in, Control, 24. ; GOSIEWSKI (2007), Optimal control of active rotor suspension system of Control, Archives Sciences, 17, 459. ; ESCHENAUER (2001), Topology optimization of continuum structures : A review ASME, Applied Mechanics Reviews, 54, 331, doi.org/10.1115/1.1388075 ; NECHES (2008), Topology optimization of elastic structures using boundary elements Engineering Analysis with Boundary, Elements, 32, 533. ; KHURSHUDYAN (2015), The Bubnov - Galerkin procedure in bilinear control problems and Remote, Automation Control, 76, 1361. ; BRADLEY (1994), Bilinear optimal control of a Kirchhoff plate Systems & Control, Letters, 22, 27.