On adhesive binding optimization of elastic homogeneous rod to a fixed rigid base as a control problem by coefficient

December 2013
Problems of Improving the Efficiency of Infrastructure;2013, Vol. 23 Issue 4, p413
Academic Journal
The problem of finite, partially glued to a fixed rigid base rod longitudinal vibrations damping by optimizing adhesive structural topology is investigated. Vibrations of the rod are caused by external load, concentrated on free end of the rod, the other end of which is elastically clamped. The problem is mathematically formulated as a boundary-value problem for one-dimensional wave equation with attenuation and variable controlled coefficient. The intensity of adhesion distribution function is taken as optimality criterion to be minimized. Structure of adhesion layer, optimal in that sense, is obtained as a piecewise-constant function. Using Fourier real generalized integral transform, the problem of unknown function determination is reduced to determination of certain switching points from a system of nonlinear, in general, complex equations. Some particular cases are considered.


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