Jan Awrejcewicz

LARGE AMPLITUDE FREE VIBRATION OF ORTHOTROPIC SHALLOW SHELLS OF COMPLEX SHAPES WITH VARIABLE THICKNESS

The present formulation of the analysed problem is based on Donell’s nonlinear shallow shell theory, which adopts Kirchhoff’s hypothesis. Transverse shear deformations and rotary inertia of a shell are neglected. According to this theory, the non-linear strain-displacement relations at the shell midsurface has been proposed. The validity and reliability of the proposed approach has been illustrated and discussed, and then a few examples of either linear or non-linear dynamics of shells with variable thickness and complex shapes have been presented and

MODELING AND ANALYSIS OF THERMAL PROCESSES IN MECHANICAL FRICTION CLUTCH — NUMERICAL AND EXPERIMENTAL INVESTIGATIONS

Thermal processes occurring in the mechanical clutch or brake systems have a great influence on the strength of elements of these systems as well as on their dynamics. The contact problems exhibited by such systems include heat generated by dry friction contact surfaces. The contact dynamics in general depends on many system parameters, and it attracted attention of many researches focused on analysis of the mentioned phenomena in different kinds of mechanical systems like clutches, brakes, and others. In this work a mathematical model describing the processes of heat generation and its propagation in the mechanical friction clutch is presented. The presented model takes into account the unequal distribution of flux density of produced heat in the clutch, the thermal conductivity of materials of friction linings, and the heat transfer between the friction linings of clutch and its environments. The analyzed object is described by a set of algebraic linear homo- and heterogeneous equations, and it is derived using a computer numerical method. Many interesting numerical and experimental results are obtained, illustrated and discussed. Presented numerical results coincide with experimental data.

On the Hexapod Leg Control with Nonlinear Stick-Slip Vibrations

In the paper the control problem of the six-legged walking robot is studied. In order to find the relationship between commonly used by insects gaits (trajectory of the foot point) and stable trajectory of mechanical systems, at first we analyse various previous papers and the gaits of the real insects. For control the motion of the tip of the robot leg a nonlinear mechanical oscillator describing stick-slip induced vibrations further referred as central pattern generator (CPG) has been proposed. The advantages of the proposed model has been presented and compared with other previous applied mechanical oscillators. The possibility of control of the tip of the robot leg via changing parameters characterized oscillator working as a CPG has been discussed. Time series of the joints and configurations of the robot leg during walking are presented. The obtained numerical solutions indicate some analogies between the characteristics of the simulated walking robot and animals found in nature. Moreover, some aspects of an energy efficiency analysis (in order to reduce the energy costs) are discussed for the analysed system and the whole hexapod robot. In particular, we discuss the interplay of the proposed gait patterns and the system energy cost.

Mathematical model, computer aided design and programming of a multifunctional flying object

The quadrocopter, an unmanned aerial vehicle (UAV), is a type of aerodynamic object using thrust generated by the propellers revolving around the rotor mast. The main areas of focus for complete design and engineering research should be on its stabilization and realization of tasks to be performed during flight. To accomplish these tasks, it is necessary to consider the following stages: modeling of motion dynamics, computer-aided design, programming of the control unit, precise implementation, carefully selected motors and sensors, i.e. a gyroscope, accelerometer, camera, communication module, GPS module, and others. The presented results of research and experiments carried out at Lodz University of Technology in the Department of Automation and Biomechanics take into consideration most of these issues.

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony’s decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov’s exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific ”fingerprint” characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems.

Nonlinear Elastic Problems

We begin with a multi-layer composite material, composed of interacting components ({{varOmega }^{(1)}}) and ({{varOmega }^{(2)}}) (Fig. 8.1).

Effects of severe hallux valgus on metatarsal stress and the metatarsophalangeal loading during balanced standing: A finite element analysis

The internal stress of the human foot enables efficient parametric evaluation of structural and functional impairments associated with foot deformities, such as hallux valgus (HV). However, the status of the internal stress of such a deformed foot remains insufficiently addressed due to the difficulties and limitations of experimental approaches. This study, using finite element (FE) methodology, investigated the influence of severe HV deformity on the metatarsal stress and the metatarsophalangeal (MTP) joint loading during balanced standing. FE models of a normal foot and a severe HV were constructed and validated. Each FE model involves 28 bones and various cartilaginous structures, ligaments, and plantar fascia, as well as encapsulated soft tissue. All the materials except for the encapsulated soft tissue were considered isotropic and linearly elastic, while the encapsulated soft tissue was set as nonlinear hyperelastic. Hexahedral elements were assigned to the solid parts of bones, cartilage, and the encapsulated soft tissue. Link elements were assigned to ligaments and plantar fascia. A plate was created for simulating ground support. A vertical force of a half-body weight was applied on the bottom of the plate for simulating balanced standing loading. The superior surfaces of the encapsulated soft tissue, distal tibia, and distal fibula were fixed. Stress distribution in the metatarsals, contact pressure, and force at the MTP joints were comparatively analysed. Compared to the normal foot, the HV foot showed higher stress concentration in the metatarsals but lower magnitude of MTP joint loading. In addition, the region with high contact pressure at the first MTP joint shifted medially in the HV foot. Knowledge of this study indicates that patients with severe HV deformity are at higher risk of metatarsal injuries and functional impairment of the MTP joints while weight bearing.

An Overview of ATmega AVR Microcontrollers Used in Scientific Research and Industrial Applications

Nowadays, microcontrollers are commonly used in many fields of industrial applications previously dominated by other devices. Their strengths such as: processing power, low cost, and small sizes enable them to become substitutes for industrial PLC controllers, analog electronic circuits, and many more. In first part of this article an overview of the Atmel AVR microprocessor family can be found, alongside with many scientific and industrial applications. Second part of this article contains a detailed description of two implementations of ATmega644PA microprocessor. First one is a controller with PID regulation that supports a DC motor driver. Second one is a differential equation solver with 4-th order Runge-Kutta method implemented. It is used for solving a torsion pendulum dynamics. Finally, some general conclusions regarding the two presented implementations are made.

Modeling And Parameter Identification Of Vibrations Of A Double Torsion Pendulum With Friction

Abstract The purpose of this paper is to investigate a double torsion pendulum with planar frictional contact. The single torsion pendulum with one-degree-of-freedom is an angular equivalent of the linear harmonic oscillator. The second degree of freedom has been obtained by adding a free body to the inverted single torsion pendulum. The free body’s angular displacement is caused by frictional forces appearing in the interface (contact zone) between the free body and the pendulum column’s head kinematically excited at its base by a mechanism with torsion spiral spring. An experimental station has been set up and run to find most unknown parameters of the pendulum from the time series of state variables taken as inputs to the Nelder-Mead method of identification. The obtained results proved significant usability of the identification method in the case of numerical simulation of the pendulum’s dynamical model. It has not been satisfactorily proved in the case of time characteristics coming from a real system that exhibits also some unrecognized physical effects.

Kinematic and dynamic simulation of an octopod robot controlled by different central pattern generators

The goal of the study was to perform both kinematic and dynamic simulation of an octopod robot walking on a flat and hard surface. To drive robot legs, different non-linear mechanical oscillators were employed as central pattern generators. Aside from using some well-known oscillators, a new model was proposed. Time series of robot’s kinematic and dynamic locomotion parameters were computed and discussed. Displacement and velocity of the centre of gravity of the robot, ground reaction forces acting on the robot legs, as well as some aspects of energy consumption of a walking robot were analysed to assess the central pattern generators. The obtained kinematic and dynamic parameters showed some advantages of the applied generator. In particular, the gait of the robot was most stable when the robot was driven by the proposed central pattern generator model.