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, the dynamic behavior of a hip level joint device of an active exoskeleton used in the medical field is analyzed. The finite element method is used in order to determine the first frequencies and the eigenmodes, necessary for the fatigue testing in the resonance regime.

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.

This article presents a non-destructive method, based on the response to free vibrations, which can be used with efficiency and reliability to determine the Young’s modulus of polymer composite materials reinforced with natural or synthetic fibers. The non-destructive tests are carried out by measuring the frequencies of bending free vibrations of cantilever beams with additional masses. By using inverse methods, the experimental values of elasticity modulus E are assessed and validated by numerical simulation, using the finite element method (FEM). For FEM modeling, the materials are considered linear, homogeneous, isotropic, and viscoelastic.

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.

This paper analyzed the behavior of polymer composite materials reinforced with randomly oriented short natural fibers (hemp, flax, etc.) subjected to external stresses under quasistatic contact conditions with dry Coulomb friction. We presumed the composite body, a 2D flat rectangular plate, being in frictional contact with a rigid foundation for the quasistatic case. The manuscript proposes the finite element method approximation in space and the finite difference approximation in time. The problem of quasistatic frictional contact is described with a special finite element, which can analyze the state of the nodes in the contact area, and their modification, between open, sliding, and fixed contact states, in the analyzed time interval. This finite element also models the Coulomb friction law and controls the penetrability according to a power law. Moreover, the quasi-static case analyzed allows for the description of the load history using an incremental and iterative algorithm. The discrete problem will be a static and nonlinear one for each time increment, and in the case of sliding contact, the stiffness matrix becomes non-symmetric. The regularization of the non-differentiable term comes from the modulus of the normal contact stress, with a convex function and with the gradient in the sub-unit modulus. The non-penetration condition was achieved with the penalty method, and the linearization was conducted with the Newton–Raphson method.