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Approximation of the Statistical Characteristics of Piecewise Linear Systems with Asymmetric Damping and Stiffness under Stationary Random Excitation

Author

Listed:
  • Tudor Sireteanu

    (Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141 Bucharest, Romania)

  • Ana-Maria Mitu

    (Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141 Bucharest, Romania)

  • Ovidiu Solomon

    (Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141 Bucharest, Romania
    Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Romana Square, RO-010374 Bucharest, Romania)

  • Marius Giuclea

    (Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141 Bucharest, Romania
    Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Romana Square, RO-010374 Bucharest, Romania)

Abstract

In this paper, the dynamic response of piecewise linear systems with asymmetric damping and stiffness for random excitation is studied. In order to approximate the statistical characteristics for each significant output of piecewise linear system, a method based on transmissibility factors is applied. A stochastic linear system with the same transmissibility factor is attached, and the statistical parameters of the studied output corresponding to random excitation having rational spectral densities are determined by solving the associated Lyapunov equation. Using the attached linear systems for root mean square and for standard deviation of displacement, the shift of the sprung mass average position in a dynamic regime, due to damping or stiffness asymmetry, can be predicted with a good accuracy for stationary random input. The obtained results are compared with those determined by the Gaussian equivalent linearization method and by the numerical integration of asymmetric piecewise linear system equations. It is shown that the piecewise linear systems with asymmetrical damping and stiffness characteristics can provide a better vibration isolation (lower force transmissibility) than the linear system.

Suggested Citation

  • Tudor Sireteanu & Ana-Maria Mitu & Ovidiu Solomon & Marius Giuclea, 2022. "Approximation of the Statistical Characteristics of Piecewise Linear Systems with Asymmetric Damping and Stiffness under Stationary Random Excitation," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4275-:d:973709
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    References listed on IDEAS

    as
    1. Andrey Borisov & Alexey Bosov & Gregory Miller, 2022. "Optimal Stabilization of Linear Stochastic System with Statistically Uncertain Piecewise Constant Drift," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
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