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Showing 1 to 20 of 23 for “"Characteristic equation"”.
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Stability theory of differential equations
… the stability of a set of linear differential equations has been of interest to mathematicians and engineers for a considerable length of time. The problem is attacked by obtaining the characteristic equation of the original set of equations and determining the stability of this equation. The …
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Nonlinear dynamics of blood flow in simple microvascular networks
… into state dependent time delay differential equations, DDE's. The DDE's are then linearized about a steady state and normalized.</p><p>The characteristic equation for the network is found by assuming the linearized DDE's have a nontrivial exponential solution. The solutions of the …
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Estudo teórico da estabilidade lateral de hastes submetidas a uma protensão externa
… on stability by means of the parameters of the characteristic equation obtained from the eigenvalue problem.
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New Results on Time-Delay Systems Towards Model-Based Design
… methods are developed based on the corresponding characteristic equation following a frequency sweeping test and constant matrix tests. Rewriting the quasi-polynomial equation, the coefficients can be found and then the roots of the characteristic equation can be plotted in a complex plane. If the …
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Modeling the coupled rotor/fuselage response of the H-3 Sea King utilizing the NPS full nonlinear response
… rotorcraft. The parameters of the 11-3 from the characteristic equation of a modeled mass-spring- damper system are inputted into a five-bladed model initially utilizing MAPLE to process LaGrange's equation defining the helicopter's full set of nonlinear equations of motion. Results are converted …
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Method for theoretically determining the locus and location of the transmission zeros in microwave filter networks
… closed-forms of expressions called the TZ characteristic equation (TZCE) are obtained in terms of element values of the filter network. The locations and loci of TZ's are obtained by solving the relevant equations. These TZCE's are derived by taking advantage of the bridged-T structure for …
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Buckling of cantilever thin plate with free end subjected to uniform shear
… a system of n linear homogeneous algebraic equations ot n parameters which are introduced in the assumed displacement. For a non-trivial solution, the determinant of the coefficients must vanish. This gives a characteristic equation from which the buckling load is determined. The author has …
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Supersonic flutter of sandwich panels: effects of face sheet bending stiffness, rotary inertia, and orthotropic core shear stiffnesses
… The linear system of partial differential equations governing the lateral deflection and the two transverse shear angles is eighth order and has constant coefficients. For simply supported edges parallel to the flow these equations have a separable solution. The characteristic equation …
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Asymptotic analysis of vibrations of thin cylindrical shells
… of asymptotic integration of the vibration equations of thin shells, developed by Goldenveizer, Lidsky and Tovstik. A linear shell theory of the Kirchhoff-Love type is employed. The equations describing the vibrations of thin shells contain several parameters, the main of which is the small …
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Random perturbations of delay differential equations at the verge of instability and periodically driven nonlinear oscillators
… small noise perturbations on delay differential equations (DDE) whose fixed point is on the verge of instability. With appropriate scaling of coordinates, the dynamics close to the fixed point can be cast in the form of a linear DDE perturbed by small noise and small nonlinearities. The …
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Thermal-fluid modeling of the Missouri S&T reactor
… and velocity as a function of core power. A characteristic equation for the parallel-plate model was obtained based on Forchheimer's flow equation. The inertial resistance tensor and viscous resistance tensor were found to be 281005 kg/m^4 and 7121.6 kg/m^3 respectively. The MSTR core was …
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Dynamic stability of shear deformable viscoelastic composite plates
… edge loads. In deriving the associated governing equations, a hereditary constitutive law is assumed. In addition, having in view that composite-type structures exhibit weak rigidity in transverse shear, the associated governing equations account for the transverse shear deformations, as well as …
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The internal performance of iterative feedback tuning
… one degree of freedom control structure all the characteristic equations of the loop transfer functions will be the same. Four methods are proposed for avoiding pole-zero cancellation by concentrating on the input disturbance. These methods are using: a model for input disturbance rejection, …
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Investigations into solar powered diffusion-absorption cooling machines
… Cycle has been modelled using the constant characteristic equation of sorption chillers. An expanded, steady-state model which includes additional specific components of the DACM was developed based on the exact solution of the internal mass and energy balances of each component as well as …
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Effects of fractional time derivatives in predator-prey models
… find an approximate analytical solution for the characteristic equation of the incommensurate system when the two fractional orders α and β are similar and both close to the critical value of the fractional order of the commensurate system.;In this case, we are able to map out the stable and …
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Precise energy decay rates for some viscoelastic and thermo-viscoelastic rods
… In the first part, a linear viscoelastic wave equation with infinite memory is examined. It is shown that under appropriate conditions on the kernel and initial history, the total energy is integrable against a particular weight if the kinetic energy component of the total energy is integrable …
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Integration of glass microspheres and planar waveguides for microsphere lasers
… This high Q value represents many promising characteristics such as low cavity loss, long cavity life time, and narrow band width. With their remarkable characteristics, microsphere resonators can be used in various applications such as the narrow band filter, add-drop multiplexer, …
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Stability Analysis of Three-Phase AC Power Systems Based on Measured D-Q Frame Impedances
… grid condition are reported and analyzed using characteristic equation of the system. This research proposes a more design oriented analysis approach based on the negative incremental resistance concept of grid-tied inverters. Grid synchronization stability issues are well explained under the …
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Use of Admittance-Wall Models in Analysis of Radiating Line Antennas
… of computation. It was shown that the general characteristics of the radiation patterns of ANSERLIN elements can be obtained using only a small number of circularly polarized spherical modes in the field expansion. A first-order model is obtained by solving for the fields of a closed waveguide …
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