Modeling and semigroup formulation of charge or current-controlled active constrained layer (ACL) beams; electrostatic, quasi-static, and fully-dynamic assumptions

A three-layer active constrained layer (ACL) beam model, consisting of a piezoelectric elastic layer, a stiff layer, and a constrained viscoelastic layer, is obtained for cantilevered boundary conditions by using the reduced Rao-Nakra sandwich beam assumptions through a consistent variational approach. The Rao-Nakra sandwich beam assumptions keeps the longitudinal and rotational inertia terms. We consider electrostatic, quasi-static and fully dynamic assumptions due to Maxwell's equations. For that reason, we first include all magnetic effects for the piezoelectric layer. Two PDE models are obtained; one for the charge-controlled case and one for the current-controlled case. These two cases are considered separately since the underlying control operators are very different in nature. For both cases, the semigroup formulations are presented, and the corresponding Cauchy problems are shown to be well- posed in the natural energy space.Comment: 2 figure

Well-posedness and stabilization of a type three layer beam system with Gurtin-Pipkin's thermal law

The goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a triple beam system commonly known as the Rao-Nakra beam model. We consider the effect of Gurtin-Pipkin's thermal law on the outer layers of the beam system. Using standard semi-group theory for linear operators and the multiplier method, we establish the existence and uniqueness of weak global solution, as well as a stability result

Vibro-acoustical analysis and design of a multiple-layer constrained viscoelastic damping structure

The goal of this research is to provide a framework for vibro-acoustical analysis and design of a multiple-layer constrained damping structure. The existing research on damping and viscoelastic damping mechanism is limited to the following four mainstream approaches: modeling techniques of damping treatments/materials; control through the electrical-mechanical effect using the piezoelectric layer; optimization by adjusting the parameters of the structure to meet the design requirements; and identification of the damping material’s properties through the response of the structure. This research proposes a systematic design methodology for the multiple-layer constrained damping beam giving consideration to vibro-acoustics. A modeling technique to study the vibro-acoustics of multiple-layered viscoelastic laminated beams using the Biot damping model is presented using a hybrid numerical model. The boundary element method (BEM) is used to model the acoustical cavity whereas the Finite Element Method (FEM) is the basis for vibration analysis of the multiple-layered beam structure. Through the proposed procedure, the analysis can easily be extended to other complex geometry with arbitrary boundary conditions. The nonlinear behavior of viscoelastic damping materials is represented by the Biot damping model taking into account the effects of frequency, temperature and different damping materials for individual layers. A curve-fitting procedure used to obtain the Biot constants for different damping materials for each temperature is explained. The results from structural vibration analysis for selected beams agree with published closed-form results and results for the radiated noise for a sample beam structure obtained using a commercial BEM software is compared with the acoustical results of the same beam with using the Biot damping model. The extension of the Biot damping model is demonstrated to study MDOF (Multiple Degrees of Freedom) dynamics equations of a discrete system in order to introduce different types of viscoelastic damping materials. The mechanical properties of viscoelastic damping materials such as shear modulus and loss factor change with respect to different ambient temperatures and frequencies. The application of multiple-layer treatment increases the damping characteristic of the structure significantly and thus helps to attenuate the vibration and noise for a broad range of frequency and temperature. The main contributions of this dissertation include the following three major tasks: 1) Study of the viscoelastic damping mechanism and the dynamics equation of a multilayer damped system incorporating the Biot damping model. 2) Building the Finite Element Method (FEM) model of the multiple-layer constrained viscoelastic damping beam and conducting the vibration analysis. 3) Extending the vibration problem to the Boundary Element Method (BEM) based acoustical problem and comparing the results with commercial simulation software

Exact boundary controllability and feedback stabilization for a multi-layer Rao-Nakra beam

We prove exact boundary controllability for the Rayleigh beam equation with a single boundary control active at one end of the beam. This result is used to prove exact boundary controllability of the multilayer Rao-Nakra beam, which contains the Rayleigh beam as one of its component equations. We consider all combinations of clamped and hinged boundary conditions. In each case, exact controllability is obtained on the space of optimal regularity. We also obtain corresponding uniqueness and exact observability results for the dual observed system. Then we are able to obtain exponential stability of the multilayer Rao-Nakra beam system using an appropriate boundary feedback. We also formulate an abstract version of the closely related Mead-Marcus sandwich beam model and prove its boundary controllability using the multipliers technique.</p

Technology for large space systems: A bibliography with indexes (supplement 07)

This bibliography lists 366 reports, articles and other documents introduced into the NASA scientific and technical information system between January 1, 1982 and June 30, 1982. Subject matter is grouped according to systems, interactive analysis and design, structural concepts, control systems, electronics, advanced materials, assembly concepts, propulsion, solar power satellite systems, and flight experiments