Andrzej Mitura

Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with non- linear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controllers parameters for effective vibrations suppression are presented.

Dynamics of a Self-Balancing Double-Pendulum System

Modeling and analysis of a system of two self-balancing pendulums is presented in this paper. Such systems are commonly used as elements of automotive door latch mechanisms that can be subjected to oscillatory excitation or vibratory inertia forces occurring during crash events. In order to avoid an unwanted behavior such as opening of the door, the considered mechanism should be properly designed and its dynamical response well understood and predictable. One pendulum of the double-pendulum system, playing the role of a counterweight (CW), is used to reduce the second (or main) pendulum motion under inertia loading. The interaction force between the pendulums is defined as the reaction of a holonomic constraint linking the rotations of both pendulums. Another reaction force acts between one of the pendulums and the support, reinforced by the action of a preloaded spring. An important aspect of the model is its discontinuous nature due to the presence of a gap in the interface area. This may result in impacts between both pendulums and between one of the pendulums and the support. High-frequency/high-acceleration amplitude vibratory motion of the base part provides inertia input to the system. Classical multibody dynamics approach is adopted first to solve the equations of motion. It is shown that the considered system under certain conditions responds with a high-amplitude irregular motion. A special methodology is used in order to study the regions of chaotic motion, with the goal to gain more understanding of the considered system dynamics. Bifurcation diagrams are presented together with quantitative and qualitative analysis of the motion. The sensitivity of solutions to variation of system parameters and input characteristics is also analyzed in the paper.

Effect of sub-loops in SMA ear system

The main aim of this paper is modelling the hysteresis effect in shape memory alloys. The stress versus strain relation is approximated by idealized curves. The adopted characteristics is modelled using the piecewise linear model. Transmission between individual line segments is dependent on the proposed conditions if(…). Performed numerical research allows to evaluate the possibilities of hysteresis sub-loops modelling. Finally, this model is used in a specific system – the biomechanical model of the middle ear to find the reconstructed ear response.

Influence of the piezoelectric parameters on the dynamics of an active rotor

The main aim of this paper is an experimental and numerical analysis of the dynamic behavior of an active rotor with three composite blades. The study focuses on developing an effective FE modeling technique of a macro fiber composite element (denoted as MFC or active element) for the dynamic tests of active structures. The active rotor under consideration consists of a hub with a drive shaft, three grips and three glass-epoxy laminate blades with embedded active elements. A simplified FE model of the macro fiber composite element exhibiting the d33 piezoelectric effect is developed using the Abaqus software package. The discussed transducer is modeled as quasi-homogeneous piezoelectric material, and voltage is applied to the opposite faces of the element. In this case, the effective (equivalent) piezoelectric constant d33* is specified. Both static and dynamic tests are performed to verify the proposed model. First, static deflections of the active blade caused by the voltage signal are determined by num...

Foldover effect and energy output from a nonlinear pseudo-maglev harvester

Dynamics analysis and energy harvesting of a nonlinear magnetic pseudo-levitation (pseudo-maglev) harvester under harmonic excitation is presented in this paper. The system, for selected parameters, has two stable possible solutions with different corresponding energy outputs. The main goal is to analyse the influence of resistance load on the multi-stability zones and energy recovery which can help to tune the system to improve the energy harvesting efficiency.

Nonlinear Dynamics of a Vibration Harvest-Absorber System. Experimental Study

This paper presents experimental analysis prospect of using a vibration absorber for possible energy harvesting results. To achieve this goal, a classical pendulum-oscillator system (dedicated to vibration suppression) is modified by adding an electromagnetic harvester device. The electromagnetic energy harvester consists of a two fixed and one levitating magnets. The induced energy results from relative movement between magnet and coil, which produces a voltage in the coil by electromagnetic induction phenomenon. When an external excitation is applied to the harvest-absorber system, the levitating magnet will start to oscillate due to the magnetic repulsion of the two fixed magnets. The main goal of this work is to show induced energy of a pendulum-oscillator system with added harvester device, near the main resonance region. The influence of frequency of excitation and resistance load is shown. Additionally, a mathematical model of magnetic levitating force is proposed.

Nonlinear phenomena in mechanical system dynamics

The goal of the paper is to present selected, untypical, and intuitively unexpected phenomena from nonlinear mechanics. Particular attention is paid to the dynamics of self-, parametric and external excited systems. Interactions between these various vibration types lead mainly to quasi-periodic responses. However, in the selected domains of system parameters, the effect of frequency locking is observed. Furthermore, external harmonic force imposed on such a system produces a specific internal loop inside a resonance zone. As an example of nonlinear autoparametric systems, a structure (oscillator) with an attached pendulum is presented. The nonlinear terms introduced by pendulum motion cause instabilities in the resonance region. This instability transits the pendulum to rotation or chaotic motion. An application of nonlinear couplings for the reduction of unwanted vibrations is also studied. In order to reduce vibrations, the main structure is coupled to an electrical oscillator by a quadratic term. It has been shown that such a coupling leads to the amplitude saturation phenomenon which can then be used to design a nonlinear control strategy.

Optimal control methods for vertical and horizontal beam dynamics

An application of the Macro Fiber Composite (MFC) actuators for damping of a composite beam is presented in this paper. The effectiveness of vibration reduction by a selected control method is tested for vertical and horizontal position of the beam. The original model has been studied numerically by using Galerkins discretisation method. The numerical results for the vertical and horizontal beams are compared.