Structural dynamics branch research and accomplishments to FY 1992

This publication contains a collection of fiscal year 1992 research highlights from the Structural Dynamics Branch at NASA LeRC. Highlights from the branch's major work areas--Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are included in the report as well as a listing of the fiscal year 1992 branch publications

Eigenvalue and eigenmode synthesis in elastically coupled subsystems

A method to synthesize the modal characteristics of a system from the modal characteristics of its subsystems is proposed. The interest is focused on those systems with elastic links between the parts which is the main feature of the proposed method. An algebraic proof is provided for the case of arbitrary number of connections. The solution is a system of equations with a reduced number of degrees of freedom that correspond to the number of elastic links between the subsystems. In addition the method is also interpreted from a physical point of view (equilibrium of the interaction forces). An application to plates linked by means of springs shows how the global eigenfrequencies and eigenmodes are properly computed by means of the subsystems eigenfrequencies and eigenmodes.Peer ReviewedPostprint (author's final draft

Transient response of a vibration isolation system

A practical procedure for investigating the performance of a vibration isolation system under transient conditions is presented. For this investigation, an induction motor with an unbalanced rotor is studied during the period when it accelerates to its operating speed from rest. Using Newton\u27s second law of motion, equations of motion are derived, first neglecting and then considering the effect of inertia torque . This torque is produced by the inertia force resulting from vertical acceleration of the unbalanced mass. The equations are solved on a digital computer using the Runge-Kutta method of order 4. The results obtained are compared with those obtained using Simpson\u27s and Runge-Kutta methods of order 4 of the Continuous System Modeling Program. For the case when there is no external load, an attempt was made to obtain the responses of the system by the Convolution Integral Solution of the K. A. Foss method. A study of steady state and transient analyses for inertia and no inertia cases is carried out. From the results obtained, graphs are plotted and guidelines useful for design of vibration isolators are given --Abstract, page ii

Active Vibration Cancellation of a Free-Piston Linear Generator Engine

A free-piston linear generator engine (LG) is a device that couples a free-piston combustion engine with a linear electric generator. The engine is consisted with a part called piston-rod assembly (PRA), where two pistons are connected by a rod attached with permanent magnet. During the operation of LG, PRA will linearly reciprocate between two internal combustion chambers on the opposite sides. However, when the PRA is on one side of the engine, an unbalanced impact force is created. The unbalanced forces provide an undesirable impact force acting on the engine block, causing the engine to vibrate. The control of vibration for the LG becomes crucial, because proper vibration controls maintain a consistent electricity output and maximize the efficiency of the engine. Current work proposed using a linear motor (LM) to create an anti-phase momentum into the system to counter the impact forces created by PRA. The works are based on analytical modeling with MATLAB used for simulation. Simulation shows the system instability characteristics, the time and frequency responses for LG. The results showed the existence of a real pole at the right hand side of complex plane which contribute to the system instability. The non-proportional damped time response obtained using state-space approach shows the overall interaction between mass forcer and PRA decreased with respect to time. The frequency responses showed that with the application of active vibration cancellation, the resonance can be delayed and the magnitude of the resonance can be reduced. A lumped-mass quarter car suspension model is used for validation. Case study is carried out to decide the best available driven forces that drive the LG. The conclusion of current study showed that with proper vibration control for the LG, the vibration level of LG can be reduced to a desirable level while maintaining the optimum operating conditions

Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $p=2$ spherical disordered kind. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable system. We take initial conditions in thermal equilibrium and we subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian. We identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We obtain the {\it global} dynamical observables with numerical and analytic methods and we show that, in most cases, they are out of thermal equilibrium. We note, however, that for shallow quenches from the condensed phase the dynamics are close to (though not at) thermal equilibrium. Surprisingly enough, for a particular relation between parameters the global observables comply Gibbs-Boltzmann equilibrium. We next set the analysis of the system with finite number of degrees of freedom in terms of $N$ non-linearly coupled modes. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the $N-1$ integrals of motion and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of global observables. We elaborate on the role played by these constants of motion in the post-quench dynamics and we briefly discuss the possible description of the asymptotic dynamics in terms of a Generalised Gibbs Ensemble

Closed form solutions to the optimality equation of minimal norm actuation

This research focused on the problem of minimal norm actuation in the context of partial natural frequency or pole assignment applied to undamped vibrating systems by state feedback control. The result of the research was the closed form solutions for the minimal norm control input and gain vectors. These closed form solutions should took open loop eigenpairs and the desired frequencies of the controlled system and outputted the optimal controller parameters. This optimization technique ensures that the system’s dynamics will be effectively controlled while keeping the controller effort minimal. The controller must then be able to shift only the desired the system poles anywhere in the complex s-plane in order to give the system certain desired characteristics with no spillover. The open loop system dynamics were found by applying a discrete model of the studied vibrating system and then finding the eigenvalue problem associated with the second-order open loop system equations. A first order realization was then performed on the system in order to know its response to certain initial conditions. The system’s dynamics where to be modified via closed loop control. Partial natural frequency assignment was chosen as the control technique so that certain system frequencies could be left untouched to ensure that the system will not respond in an unexpected manner. The control was to be optimized by minimizing the norm of the control input and gain vectors. A closed form solution for these vectors was found in so that these vectors could be simply calculated using an algorithm that takes the open loop eigenpairs and the desired eigenvalues of the system and outputs the two vectors. This closed form solution was successful implemented and the controller parameters found were applied to a vibrational system. A simulation for the un-optimized and optimized cases was performed applying both controllers to the same system. The response and controller forces for both cases were plotted in MATLAB and compared. Both systems showed the desired system response meaning that they both had the same effect on the system. Inspecting both controller efforts showed that the optimal control case simulation showed less controller effort than the arbitrary case thus showing successful implementation of minimal norm actuation

Quenched dynamics of classical isolated systems: The spherical spin model with two-body random interactions or the Neumann integrable model

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body random interactions. In the statistical physics framework, the potential energy is of the so-called p = 2 kind, closely linked to the scalar field theory. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable model. We take initial conditions from the Boltzmann equilibrium measure at a temperature that can be above or below the static phase transition, typical of a disordered (paramagnetic) or of an ordered (disguised ferromagnetic) equilibrium phase. We subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian, obtained from an instantaneous global rescaling of the elements in the interaction random matrix. In the limit of infinitely many degrees of freedom, , we identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We next set the analysis of the system with finite number of degrees of freedom in terms of N non-linearly coupled modes. We argue that in the limit the modes decouple at long times. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the N - 1 integrals of motion, notably, their scaling with N, and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of the global observables. We elaborate on the role played by these constants of motion after the quench and we briefly discuss the possible description of the asymptotic dynamics in terms of a generalised Gibbs ensemble.Fil: Cugliandolo, Leticia Fernanda. Université Pierre et Marie Curie; Francia. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; FranciaFil: Lozano, Gustavo Sergio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Nessi, Emilio Nicolás. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Picco, Marcos Fernando. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; FranciaFil: Tartaglia, Alessandro. Université Pierre et Marie Curie. Laboratoire de Physique Théorique et Hautes Energies; Franci

Localized vibrations of disordered multi-span beams - Theory and experiment

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76120/1/AIAA-1986-934-814.pd