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  • 1
    Electronic Resource
    Electronic Resource
    Approximation by interpolation of certain real compact analytic surfaces (1967)
    Springer
    Mathematische Zeitschrift 100 (1967), S. 272-281 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01109736
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal control of a Timoshenko beam by distributed forces (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 451-461 
    Details
    ISSN: 1573-2878
    Keywords: Distributed control problems ; Timoshenko beams ; maximum principle ; initial boundary-value problems ; partial differential equations ; elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present paper considers the problem of optimally controlling the deflections and/or velocities of a damped Timoshenko beam subject to various types of boundary conditions by means of a distributed applied force and moment. An analytic solution is obtained by employing a maximum principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938631
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  • 3
    Electronic Resource
    Electronic Resource
    Passive optimal control of an antisymmetric angle-ply laminate (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 227-242 
    Details
    ISSN: 1573-2878
    Keywords: Passive optimal control ; maximum principle ; antisymmetric angle-ply laminate ; singular mass matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using the maximum principle of Ref. 1, a procedure to find numerical solutions of certain optimal control problems is given. As an application of this procedure, the optimal control of an antisymmetric angle-ply laminate is worked out in detail. Numerical solutions are given in the form of graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939536
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  • 4
    Electronic Resource
    Electronic Resource
    Maximum principle for optimal control of distributed-parameter systems with singular mass matrix (1990)
    Springer
    Journal of optimization theory and applications 66 (1990), S. 211-226 
    Details
    ISSN: 1573-2878
    Keywords: Distributed-parameter systems ; optimal control ; maximum principle ; singular mass matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939535
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  • 5
    Electronic Resource
    Electronic Resource
    Maximum principle for the optimal control of a hyperbolic equation in one space dimension, part 1: Theory (1995)
    Springer
    Journal of optimization theory and applications 87 (1995), S. 33-45 
    Details
    ISSN: 1573-2878
    Keywords: Maximum principle ; distributed-parameter systems ; optimal control ; structural control ; hyperbolic partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A maximum principle is developed for a class of problems involving the optimal control of a damped-parameter system governed by a linear hyperbolic equation in one space dimension that is not necessarily separable. A convex index of performance is formulated, which consists of functionals of the state variable, its first- and second-order space derivatives, its first-order time derivative, and a penalty functional involving the open-loop control force. The solution of the optimal control problem is shown to be unique. The adjoint operator is determined, and a maximum principle relating the control function to the adjoint variable is stated. The proof of the maximum principle is given with the help of convexity arguments. The maximum principle can be used to compute the optimal control function and is particularly suitable for problems involving the active control of structural elements for vibration suppression.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192040
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  • 6
    Electronic Resource
    Electronic Resource
    Maximum principle for the optimal control of a hyperbolic equation in one space dimension, part 2: Application (1995)
    Springer
    Journal of optimization theory and applications 87 (1995), S. 287-300 
    Details
    ISSN: 1573-2878
    Keywords: Maximum principle ; optimal control ; vibrating beams ; structural control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal open-loop control of a beam subject to initial disturbances is studied by means of a maximum principle developed for hyperbolic partial differential equations in one space dimension. The cost functional representing the dynamic response of the beam is taken as quadratic in the displacement and its space and time derivatives. The objective of the control is to minimize a performance index consisting of the cost functional and a penalty term involving the control function. Application of the maximum principle leads to boundary-value problems for hyperbolic partial differential equations subject to initial and terminal conditions. The explicit solution of this system is obtained yielding the expressions for the state and optimal control functions. The behavior of the controlled and uncontrolled beam is studied numerically, and the effectiveness of the proposed control is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192565
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  • 7
    Electronic Resource
    Electronic Resource
    Maximum Principle for Optimal Boundary Control of Vibrating Structures with Applications to Beams (1998)
    Springer
    Dynamics and control 8 (1998), S. 355-375 
    Details
    ISSN: 1573-8450
    Keywords: Maximum principle ; boundary control ; structural control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A maximum principle is derived for open-loop boundary control of one dimensional structures undergoing transverse vibrations. The optimal control law is obtained using a maximum principle and the applicability of the results to the boundary control of vibrating beams is demonstrated. The method of solution involves the transformation of the original problem into one with homogeneous boundary conditions for a general set of boundary forces and torques. An adjoint variable is introduced and used in the formulation of a Hamiltonian function which in turn leads to the derivation of the maximum principle. The effectiveness of the proposed control mechanism is illustrated numerically and it is shown that the implementation of the optimal boundary control using one force actuator can lead to substantial decrease in the dynamic response of a vibrating beam.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008208727964
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  • 8
    Electronic Resource
    Electronic Resource
    Flow past symmetric convex profiles with open wakes (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 1301-1314 
    Details
    ISSN: 0271-2091
    Keywords: Cavities ; Fixed Domain Method ; Free Streamlines ; Schwarz Alternating Iteration ; Wakes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A fixed domain approach and a Baiocchi type transformation in conjunction with a modified Schwarz alternating iteration scheme are used to solve problems of flow past truncated convex shaped profiles between walls in a logarithmic hodograph plane. The flows are such that an open wake or cavity is formed behind the profile. The basic numerical scheme consists of the successive over-relaxation finite difference approach over the whole domain of the problem with the use of a projection operation over only part of the domain. The numerical results that are obtained using this approach for the cases of a truncated circular arc profile and a wedge profile are compared with published results and are found to be in good agreement.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650071202
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  • 9
    Electronic Resource
    Electronic Resource
    Free surface seepage from nonsymmetric channels (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1547-1563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of steady, two-dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions - one for the flowrate and one for the value of the new dependent variable at the left-hand side free surface-channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the literature.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181009
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  • 10
    Electronic Resource
    Electronic Resource
    Numerical solutions to some free surface flows through nonhomogeneous media (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 143-167 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Steady-state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over-relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200111
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