Engineering topics
Publications and source records attributed to Zak, M. A..
Theoretical developments enable suppression of chaotic structual motions. Theory enables prediction, avoidance, and suppression of chaotic vibrations in structures, especially using dynamic feedback stabilization. In new formulation, motion both repeatable and predictable.
Developments reported in modeling of fluid turbulence as superposition of number of interpenetrating velocity fields. Multivalued-velocity model has practical implications in design of aircraft, turbines, nozzles, pumps, and other systems that involve turbulent flow. In both viscous and inviscid cases, equations made to predict stable regine of oscillations, both finite and independent of initial conditions as in case of real turbulence.
Report presents multi-valued-velocity model used in calculations of turbulence formation. Developed as part of continuing study of turbulent fluid motion, model expected to evolve into comprehensive mathematical tool to explain origin and effects of turbulence. Model has great theoretical and practical value in such fields as aerodynamics, meteorology, and combustion.
Recent report presents derivation of equations of motion for wrinkles forming in planar films under compressive in-plane stress. Study was prompted by wrinkling of thin film solar-cell arrays with consequent reduction in collection efficiency. Lack of adequate theoretical understanding made it difficult to design large film structures and specify oscillation tests for large solar array systems.
Report presents theoretical investigation on nonlinear shearing characteristics of wrinkling films under applied shear stress. Report helps explain force/deflection characteristic of in-planeboom and solar-array blanket structural combinations.
Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.
Certain cases of turbulence as a postinstability state of a fluid in motion modeled by the introduction of multivalued velocity fields are examined. The turbulence is regarded as occurring in the form of random pulsations which grow until the external energy input in the average flow is balanced by the dissipated energy of pulsations by means of turbulent friction. Closed form analytic solutions are shown to be possible when the considered velocity fields, the pulsation velocity and the fluid velocity, are decoupled.
This paper presents the results of analytical investigations of nonlinear effects in in-plane and out-of-plane vibrations of solar arrays caused by surface wrinkling of solar array blankets. It is shown that nonlinearities generated by wrinkles are important even for small deformations. Approximate analytical solutions describing the frequency and damping dependencies of the amplitudes of in-plane vibrations are derived. A new phenomenon - a parametrical resonance of out-of-plane vibrations induced by in-plane vibrations - is described.