M. Bocheński

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.

Optimization of the MFC - composite beam energy harvester

In the paper the piezoelectric Macro Fiber Composite actuator (M-8503-P1) connected to the composite cantilever beam is analyzed. The influence of different electrical conditions on the system response is observed by the beam amplitude – frequency characteristics. The main goal is the load resistance level optimization, during the system vibrates around the first or the second resonance region to maximize electrical power generated by the system. Streszczenie. Praca przedstawia wpływ elementu piezoelektrycznego (M-8503-P1) na charakterystykę kompozytowej belki wspornikowej. Obserwowano zależność pomiędzy obciążeniem elektrycznym elementu aktywnego a odpowiedzią dynamiczną układu mechanicznego śledząc zmiany na wykresach amplitudowo-częstotliwościowych. Głównym celem badań jest optymalizacja poziomu obciążenia elementu piezoelektrycznego gdy belka drga w pobliżu pierwszej bądź drugiej częstości giętnej tak, aby odzyskać od układu jak największą moc elektryczną. (Optymalizacja układu do pozyskiwania energii zbudowanej z belki kompozytowej MFC).

Analysis of the Macro Fiber Composite Characteristics for Energy Harvesting Efficiency

In recent years the energy harvesting has a wide development, especially due to increasing demand on the self-powered devices. The research of converting mechanical energy into suitable electrical is intensity develop. The efficiency of energy harvesting systems is usually as crucial purpose of many works. It depends on various input condition parameters. One of them is a load resistance of an electrical subsystem. A loaded piezoelectric by resistor has a significant influence on the dynamics of the mechanical system. It provides optimization of an output electric power, especially while mechanical system vibrating in resonance zone. In present paper the composite cantilever beam is analysed, with attached the piezoelectric Macro Fiber Composite actuator (M-8503-P1). The applied beam consists of ten prepreg M12 layers, oriented to the beam length in accordance with [+45/−45/+45/−45/0]\(_S\). The influence of different load resistances on the system response is reported by both the output beam amplitude—frequency and output power—frequency characteristics of the piezoelectric actuator. The goal of the work is maximising the root mean square of output electrical power and comparison the system behaviours at optimised load resistance levels, while vibrating at resonance zones. The results are simulated by finite element method and also validated by experimental tests.

Application of Model Reference Adaptive System in Natural Frequency Identification of an Active Beam Composite Structure

In many real-time systems we need to know the exact values of system parameters. Parameters identification for linear and stable systems can be done by taking special measurements. Problems can occur if the tested system is nonlinear and its parameters change due to certain variations or they depend on time. In such cases special procedures have to be applied. These procedures should operate quickly, and their computational time delay cannot affect on the entire control process. In this paper, determination of the frequency of cantilever beam with embedded piezoelectric actuator is studied. A short overview of Model Based Methods is described. A nonlinear equation of motion of the beam is rewritten as an equation with step wise changes of its natural frequency. Proposed mathematical identification methods use some input and output variables for identifying lack of information about certain parameters in a mathematical model. We take into account Decoupling Observers and Model Reference Adaptive System (MRAS). Due to the structure of the mathematical description, MRAS system found out to be more adequate option. Algorithms based on Model Identification Techniques (MIT), as well as an algorithm satisfying Lyapunov stability condition, were tested. The latter was robust on certain residual effects. Therefore, we chose it for the final test. Obtained results confirmed this choice. Presented figures show characteristics of natural frequency that have been identified. Therefore, the implemented adjusting algorithm satisfying Lyapunov stability found out to be suitable for an application in DSP. However, reducing the processing time is still a problem for future studies.

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.

Evaluation of Suppression Methods Used for Reduction of Vibrations of the Active Composite Beam

The paper describes methods for suppressing vibrations of a cantilever beam. A piezoelectric Macro Fiber Composite (MFC) embedded on a surface of the beam is used as an actuator. The performance of P and PD controllers, resonance filters PPF and SRF, as well as Nonlinear Saturation Controllers (NSC) were evaluated. The results demonstrated that P and NSC controllers were the most effective of these algorithms. The relevant tests were carried out using a set-up controlled by a DSP board supported by a PC system.