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Papers by Mateusz Lazarek

The mitigation of vibrations is one of the crucial problems in engineering. In civil engineering ... more The mitigation of vibrations is one of the crucial problems in engineering. In civil engineering the main source of hazardous vibrations are earthquakes and strong winds. In mechanical engineering the oscillations may appear from rotations of bodies with eccentricity, dry friction or likewise in vehicles form bumpy roads. Focusing on large structures like i.e. buildings, bridges the most common solution involves tuned mass dampers (TMD). Historically, the first solution of TMD was proposed by Frahm in 1909 [1]. The device is a mass on a spring and its natural frequency is tuned to a natural frequency of a damped body. One of the main disadvantage of the TMD is narrow range of frequencies where it works efficiently. It is most effective in close neighborhood of resonance and outside this range it increases the amplitude of vibrations of main body. Den Hartog [2] added dash-pot between the TMD and damped structure which causes significant increase of TMD efficiency range. Another appr...

Keywords: tuned mass damper, inerter, control, mitigation of vibration ABSTRACT We perform the ex... more Keywords: tuned mass damper, inerter, control, mitigation of vibration ABSTRACT We perform the experimental verification of the novel tuned mass damper which enables changes of [1]. Characteristic feature of the proposed device is the presence of special type of inerter. This inerter incorporates a continuously variable transmission that enables stepless changes of inertance. Thus, it enables to adjust the parameters of the damping device to the current forcing characteristic. We present and describe the experimental rig that consists of the massive main oscillator forced kinematically and the prototype of the investigated damper. We perform a series of dedicated experiments to characterize the device and asses its damping efficiency [2]. Moreover, we perform numerical simulations using the simple mathematical model of investigated system. Comparing the numerical results and the experimental data we legitimize the model and demonstrate the capabilities of the investigated tuned mass...

Energies, 2020

In this paper, we study the dynamics of a two-degree freedom system consisting of the main body a... more In this paper, we study the dynamics of a two-degree freedom system consisting of the main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. We investigate different types of the non-linear characteristic of the dash-pot. We investigate devices in which damping coefficient change according to the relative displacement or the relative velocity between the damped mass and tuned mass damper. We also include in the investigation of different types of control functions. We show the two-parameter diagrams presenting the main body’s maximum amplitude versus the frequency of excitation of the damped body and different control parameter. We show how the application of a non-linear damper lets us control the main system’s oscillation amplitude.

MATEC Web of Conferences, 2018

In this paper we study the dynamics of two degree freedom system, which is consist of main body a... more In this paper we study the dynamics of two degree freedom system, which is consist of main body and tuned mass damper with inerter (TMDI). We add the dash-pot with variable damping coefficient to TMDI to study the overall efficiency of the device. The shape of non-linear characteristic of the dash-pot is dependent on one control parameter which governs the steepness of the function and the value of damping coefficient changes according to the relative displacement or velocity between main mass and tuned mass damper. We show the two parameters diagrams showing the maximum amplitude of the main body versus frequency of excitation of main body and controlling parameter.

The European Physical Journal Special Topics, 2020

In this paper we consider a new, highly precise model of the kinematics of the motorcycle. We pre... more In this paper we consider a new, highly precise model of the kinematics of the motorcycle. We present an iterative method which let us calculate a proper pitch angle value and position of the front wheel tyre-ground contact point. We take into account system with and without the lateral flexibility of the front forks. We reveal different behaviour during maneuver of system with finite lateral stiffness compared to rigid one. We proof the dependence between the capsize mode and the pitching behaviour. We show that presented algorithm can be applied to the electronic control units protecting from wheelie behaviour.

International Journal of Bifurcation and Chaos, 2020

In this paper, we analyze the dynamics of two externally forced Duffing oscillators interacting v... more In this paper, we analyze the dynamics of two externally forced Duffing oscillators interacting via soft impacts using the extended basin stability method. The investigated system is multistable with different types of coexisting solutions (periodic with and without impacts and chaotic). The extended basin stability method lets us estimate the occurrence probability of solution or given type of behavior for assumed parameters and initial condition ranges. We present the general study of system behavior focusing on the existence of nonimpacting periodic solutions. We show how selected controlling parameters and initial conditions affect the response of the system. The proposed method is robust and can be utilized for a variety of engineering applications where the parameters are varying.

Journal of the Franklin Institute, 2018

In this paper we investigate an inerter equipped with a prototype continuously variable transmiss... more In this paper we investigate an inerter equipped with a prototype continuously variable transmission (CVT) designed for the novel tuned mass damper. Inerter enables stepless changes of inertance via varying transmission ratio of the CVT. The main difference from classical inerter is addition of CVT, hence we present its design and properties in details. Motion of the proposed CVT is oscillatory and we test it for the actual working conditions. We derive the mathematical model of the system that include dissipation via dry friction. We analyse the actual transmission ratio, internal motion resistances and identify the inertia of CVT components using energy conservation method and validate further. Finally, we apply actual working conditions and compare the experimental and numerical exciting torques of the CVT. We obtain good agreement between them, hence the proposed model is robust and gives reliable results.

Journal of Sound and Vibration, 2017

In this paper we present the experimental verification of the novel tuned mass damper which enabl... more In this paper we present the experimental verification of the novel tuned mass damper which enables changes of inertance. Characteristic feature of the proposed device is the presence of special type of inerter. This inerter incorporates a continuously variable transmission that enables stepless changes of inertance. Thus, it enables to adjust the parameters of the damping device to the current forcing characteristic. In the paper we present and describe the experimental rig that consists of the massive main oscillator forced kinematically and the prototype of the investigated damper. We perform a series of dedicated experiments to characterize the device and asses its damping efficiency. Moreover, we perform numerical simulations using the simple mathematical model of investigated system. Comparing the numerical results and the experimental data we legitimize the model and demonstrate the capabilities of the investigated tuned mass damper. Presented results prove that the concept of the novel type of tuned mass damper can be realized and enable to confirm its main advantages. Investigated prototype device offers excellent damping efficiency in a wide range of forcing frequencies.

Meccanica, 2016

In this paper we propose a new method to detect and classify coexisting solutions in nonlinear sy... more In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that in the given range of parameters and initial conditions the expected solution is the only possible or at least has dominant basin of attraction. We propose an algorithm to estimate the probability of reaching the solution in given (accessible) ranges of initial conditions and parameters. We use a modified method of basin stability (Menck et al. in Nat Phys 9(2):89-92, 2013). In our investigation we examine three different systems: a Duffing oscillator with a tuned mass absorber, a bilinear impacting oscillator and a beam with attached rotating pendula. We present the results that prove the usefulness of the proposed algorithm and highlight its strengths in comparison with classical analysis of nonlinear systems (analytical solutions, path-following, basin of attraction ect.). We show that with relatively small computational effort (comparing to classical analysis) we can predict the behaviour of the system and select the ranges in parameter's space where the system behaves in a presumed way. The method can be used in all types of nonlinear complex systems.

Journal of Computational and Nonlinear Dynamics, 2013

We study the synchronization of two rotating pendula mounted on a horizontal beam, which can roll... more We study the synchronization of two rotating pendula mounted on a horizontal beam, which can roll on the parallel surface. The pendula are forced to rotate by different driving torques. It has been shown that after a transient two different types of synchronization between the pendula can be observed. The approximate analytical methods allow us to derive the synchronization conditions and explain the observed types of synchronous configurations. The energy balance in the system allows us to show how the energy is transferred between the pendula via the oscillating beam.

Mechanism and Machine Theory, 2018

In this paper we show the design of a novel tuned mass damper with inerter that enables changes o... more In this paper we show the design of a novel tuned mass damper with inerter that enables changes of inertance. We present the details of the experimental rig that is used to test the prototype device and provide technical documentation of its crucial elements. The mathematical model of the system is derived based on the Lagrange equations of the second type. We identify the parameters of the system: masses, stinesses of springs and damping coecients. We pay special attention to identication of energy dissipation model composed of viscous damping and Coulomb damping. We use two step procedure to nd the proper values of damping coecients with high precision. To validate the model we compare the numerical and experimental time traces. Good matching of the results prove well-posedness of the model and conrm the obtained parameter values.