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.

In this paper, an effective approach to the simulation of wide-sense stationary random time-series, defined by its power spectral density (PSD) is presented. This approach is based on approximating the sample paths of target random process by finite series of sample functions of random processes, obtained as the outputs of suitably chosen set of second-order linear filters to independent limited band Gaussian white noise inputs. Thus, the Gaussian distribution of simulated time-series is obtained without applying the central limit theorem. Also, the Fourier spectra of the simulated sample paths are not discrete functions, as in the case of the multisine random time-series representation used by most classical simulation methods. The method can be applied to any analytical or nonparametric representation of the specified PSD. The proposed approach is applied to simulation of road input sample paths, compatible with PSDs described by analytical forms that can or cannot be derived by linear shape filters. The method is validated by comparison of spectral response of a half-car model to the input induced by a measured road profile with that obtained for the simulated road input. This input is derived from the nonparametric PSD, determined by third-octave filtering of the measured profile. The advantages of the proposed approach are highlighted by its comparison with a conventional method, based on the representation of simulated road input by a sum of harmonics with random phases.

The theory of evolutionary algorithms on continuous space gravitates around the evolution strategy with one individual, adaptive mutation and elitist selection, optimizing the symmetric, quadratic SPHERE function. The classic, normal mutation theory consists of three main building-blocks: i) a two-term formula for the local (constant mutation) expected progress; ii) an exponential formula for the global behavior of the (adaptive mutation) algorithm; iii) linear convergence time with respect to both space dimension n and (logarithm of) initial distance to optimum. We show that the three main results still hold if we replace the normal mutation with uniform inside the sphere and also with the sum of two uniforms. That makes the case for an important conclusion: the linear convergence time of the algorithm is not a consequence of the normal mutation, but of the elitist selection and 1/5 success rule. A simplified version of the 1/5-rule allows also for an intuitive representation of the algorithm, as a sequence of constant-mutation, independent and identical (expected) length cycles.

The output of a single-degree-of-freedom (SDOF) piecewise linear system with asymmetric damping and linear stiffness excited by Dirac impulse excitation is studied. Analytical solutions of the response for piecewise linear systems are obtained by replacing the equation of motion with Dirac excitation by a homogeneous differential system with zero initial displacement and a given initial velocity. A significant improvement of the response consisting in a substantial reduction in the after-shock vibrations was obtained. The obtained results are applied to the damping optimization of a shock isolation system for forging hammers.

In this study, a novel approach for linearization of piecewise linear systems is applied to approximate the root mean square output of a quarter car model with semiactive control. The on–off control strategies, balance logic, skyhook, groundhook, and hybrid are modeled by piecewise linear systems with variable friction. By the proposed method, one can attach, for each output of practical interest, a linear system with the same transmissibility factor. The obtained transmissibility factors are used to approximate the root mean square output of considered semiactive systems using the power spectral density input–output relationships for constant parameter linear systems with stationary random inputs. The method is applied for optimization of hybrid control strategy with respect to a performance index defined in terms of sprung mass acceleration, suspension travel, and dynamic contact force.

In this paper, a statistical linearization method based on Rayleigh distribution is proposed for hysteretic systems described by the Ramberg-Osgood model. The method is based on the assumption that a set of hysteresis loops can be determined either from an analytical model or by laboratory experiments for imposed harmonic motion with different amplitudes, viewed as deviates from a Rayleigh distribution. A set of equivalent linear stiffness and damping coefficients, dependent on the distribution parameter, are assessed as functions of imposed motion amplitudes. Both the dissipated energy and stored elastic energy per cycle are determined using an accurate and simple analytical approximation of secant modulus, developed in the paper. The proposed method is applied for statistical linearization of a single-degree-of-freedom system equipped by hysteretic bracing devices with restrained buckling. The method is validated through numerical simulation of the output of the hysteretic and equivalent linear ...