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This paper aims to develop a size-dependent large deformable model to study the flexural–flexural quasi-static motion of cantilever-based micro-gyroscopes based on the modified couple stress theory. The micro-cantilever is assumed to undergo non-planar bending–bending–twisting motion. Based on this assumption, the displacement field associated with a point placed on the cross-section of the micro-beam is introduced. Employing the introduced displacement field, the components of the Green–Lagrange strain and curvature tensors are obtained. Neglecting the terms with the time derivatives, the nonlinear, coupled and higher-order equations governing on three-dimensional quasi-static motion of in-extensional cantilever-based micro-gyroscopes and their corresponding boundary conditions are then obtained. Normalizing the strain and kinetic energies as well as the works done by the external forces, the reduced equations governing the quasi-static motion of micro-gyroscopes are obtained through employing the Ritz method with linear mode-shapes of clamped-free beams as the approximating functions. Vanishing the Jacobian of the reduced equations, the governing stability equations of the system are then obtained. Afterward, employing the achieved reduced equations, both the stable and unstable branches of the micro-gyroscope equilibrium paths are extracted. To validate the accuracy of the present model, several verifications have been conducted. The performed verifications demonstrate that the current model can be considered as a promising tool in capturing the influence of small scales on micro-gyroscopes undergoing extremely large deformations. • A modified couple stress large deformable beam-based micro-gyroscope model is developed. • Normalized reduced equations governing the quasi-static motion of the system are obtained. • Both the stable and unstable equilibrium paths of the system are provided. • Influences of small scales, large deformations and lateral excitation are studied in detail. [ABSTRACT FROM AUTHOR]

Abstract: The complexity of the human gait manifests itself by lots of parameters that can evoke different changes in the walking manner. They can be divided into two groups: inherent, like anthropometric features or peculiar psychomotor type, and those related to the external conditions. The aim of the paper is to analyze the influence of three parameters, i.e. external load, ground slope and gait velocity, on the locomotion characteristics and the gait stability. Within the framework of investigations for different values of the mentioned parameters a film registration of the trajectories of selected kinematic nodes during some gait cycles has been carried out. The obtained data was a subject of numerical calculation aimed at extracting the essential properties of the principal gait characteristics. [ABSTRACT FROM AUTHOR]

Abstract: This paper uncovers some interesting extension of an optimal discrete control methodology partially included in Proceedings and presented at the international conference on “Dynamical Systems Theory and Applications”. There has been applied a scheme for realisation of active control strategy with numerically estimated linear optimal quadratic index of performance in reduction of impact-induced deformation of human chest loaded by a point mass at the central point of upper-torso body. We focused on application of one active element attached between torso’s upper back (looking from posterior direction) and a fixed support. As the practical result we provide values of quality and reaction matrices, some useful deformation and energy dissipation time-characteristics and the resulting shape of control force time-characteristics that would be the demanding one for a hypothetical real implementation. [ABSTRACT FROM AUTHOR]

Abstract: In the present work hysteresis is simulated by means of internal variables. It was shown that Masing’s imitating mechanism of the energy dissipation presented in the differential equations of Bouc-Wen’s structure allows to simulate hysteresis from very different fields. The constructed analytical models of different types of hysteresis loops are simple, enable major and minor loops reproducing and provide a high degree of correspondence with experimental data. The models of such structure are convenient for the further investigation. Hysteretic systems under harmonic excitation described by models of such structure may reveal chaotic behaviour. Using an effective algorithm based on analysis of the wandering trajectories , an evolution of chaotic behaviour regions of oscillators with hysteresis is presented in various parametric planes. Substantial influence of a hysteretic dissipation value on the form and location of these regions, and also restraining and generating effects of the hysteretic dissipation on a chaos occurrence are ascertained. Conditions for pinched hysteresis are defined. [Copyright &y& Elsevier]

Abstract: A novel thermomechanical model of frictional self-excited stick-slip vibrations is proposed. A mechanical system consisting of two masses which are coupled by an elastic spring and moving vertically between two walls is considered. It is assumed that between masses and walls a Coulomb friction occurs, and stick-slip motion of the system is studied. The applied friction force depends on a relative velocity of the sliding bodies. Stability of stationary solutions is considered. A computation of contact parameters during heating of the bodies is performed. The possibility of existence of frictional auto-vibrations is illustrated and discussed. [Copyright &y& Elsevier]

A new one-dimensional thermoelastic frictional pair contact model of a shaft–bush system is proposed. The assumed model includes a study of vibration processes and contact characteristics exhibited by a relative velocity between the two mentioned bodies, contact temperature, pressure and wear. Some important conclusions are formulated. [Copyright &y& Elsevier]