42 research outputs found
Controlling nonlinear resonances in thin-walled structures: modeling, simulations, and experiments
A plate with a saw-cut : simulated experimental modal analysis and model updating
Goal
The course Numerical and Experimental Analysis of Linear Dynamical Systems at Eindhoven
University of Technology discusses the topic indicated by its name. However, despite that
there is quite an emphasis on the experimental analysis, the course is finished by doing only
numerical assignments. It would be nice if students also could practice with the experimental
part of the course. Therefore some kind of experimental setup, consisting of a relatively
simple structure, is needed. In this work, a proposal for such an experiment is made. All the
necessary steps for the proposed experiment for model updating are investigated theoretically
to verify the feasibility of the proposed experiment.
The proposed experiment
The proposed experimental setup consists of two clamped-free-free-free (CFFF) plates: one
with a saw-cut, one without. First, students will make a finite element model of the CFFF
plate and verify its correctness by comparing its natural frequencies with the analytic solution
and measurements on the CFFF plate. Second, students will do measurements on the CFFF
plate with saw-cut to find its natural frequencies. Finally, students will update the CFFF plate
model using the natural frequencies of the CFFF plate with saw-cut by updating the
thicknesses of the elements in the saw-cut. Since the plate thickness in the saw-cut is zero, the
thickness of the saw-cut elements should converge to this value during the model update. This
means that students can easily verify the results of the model update, which is a nice feature
of the proposed experiment.
Results
First, finite element models have been made for both plates. The models have been verified by
comparing their natural frequencies and mode shapes with the analytic solution (when
available) and Marc Mentat. Second, optimal sensor location to simulate FRF measurements
have been determined. Third, simulated FRF measurements have been done. The results have
been verified by comparing them with the analytic FRFs of modal superposition. Fourth, a
modal parameter fit procedure in the frequency domain has been used to extract the modal
parameters from the simulated FRF measurements. Fifth, the extracted natural frequencies of
the CFFF plate with saw-cut are used by a model update algorithm that updates the CFFF
plate model by updating the saw-cut thicknesses. During the model update, the saw-cut
thicknesses go to zero, which means that the CFFF plate model is successfully updated to a
CFFF plate with saw-cut model. Finally, the influence of noise, which will always be present
in a real world experiment, is investigated. Noise causes the simulated FRF measurements to
become less accurate, which results in less accurate natural frequencies found by the model
parameter fit procedure. Despite this, the model update will still converge to a thickness of
zero for the saw-cut elements, although more iterations are necessary.
Conclusions
The results in this work have shown that all the necessary steps for the proposed experiment
for model updating can be taken successfully in theory. Therefore, it is recommended to
fabricate the proposed experimental setup, make it ready for FRF measurements and perform
the proposed experiment. This be a good topic for a work of a next student. If that would not
reveal any problems, the experiment for model updating would be ready to be done by
students of the NEALDS course
Theoretical and experimental nonlinear dynamics of a clamped-clamped beam MEMS resonator
Microelectromechanical resonators feature nonlineardynamic responses. A first-principles based modeling approach is proposed for a clamped-clamped beam resonator. Starting from the partial differential equation for the beam including geometric and electrostatic nonlinear effects, a reduced-order model is derived. The model captures the experimentally observed nonlinear dynamic behaviour of the resonator and allows for fast simulation and prediction of its response
Reduction of steady-state vibrations in a piecewise linear beam system using proportional and derivative control
Control based on Proportional and/or Derivative feedback (PD control) is successfully applied to a piecewise linear beam system in order to reduce steady-state vibration amplitudes. Two control objectives are formulated: 1) to minimize the transversal vibration amplitude of the midpoint of the beam at the frequency where the first harmonic resonance occurs, and 2) to achieve this in a larger excitation frequency range. The vibration reduction that is achieved in simulations and validated by experiments is very significant for both objectives. Current results obtained with active PD control are compared with earlier results obtained using a passive linear Dynamic Vibration Absorber
A combined semi-analytical and experimental approach for multiphysical nonlinear MEMS resonators
A combined semi-analytical and experimental approach is proposed for predictive modelling of the nonlinear dynamic behaviour of microelectromechanical resonators. The approach is demonstrated for a clamped-clamped beam resonator, for which the mechanical, electrical, and thermal domains are relevant. Multiphysics modelling is applied, based on first principles, to derive a reduced-order model of the resonator. A qualitative correspondence between numerical and experimental steady-state responses has been obtained. Depending on the excitation values, both simulations and experiments show hardening and softening nonlinear dynamic behaviour. Since the model captures the observed experimental behaviour, it can be used to optimize the resonator behaviour with respect to nonlinear dynamic effects
Switching between coexisting stable periodic solutions by impulsive forces with an application to a vibrating plate
Single-degree-of-freedom nonlinear mechanical systems under periodic excitation may possess coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. We propose two algorithms to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution. Both algorithms have a variant that requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity
Design and numerical analysis of an electrostatic energy harvester with impact for frequency up-conversion
Integration of vibration energy harvesters (VEHs) with small-scale electronic devices may form an attractive alternative for relatively large batteries and can, potentially, increase their lifespan. However, the inherent mismatch between a harvester’s high-frequency resonance, typically in the range 100 - 1000 Hz, relative to the available low-frequency ambient vibrations, typically in the range 10–100 Hz, means that low-frequency power generation in microscale VEHs remains a persistent challenge. In this work, we model a novel electret-based, electrostatic energy harvester (EEH) design. In this design, we combine an out-of-plane gap-closing comb (OPGC) configuration for the low-frequency oscillator with an in-plane overlap comb configuration for the high-frequency oscillator and employ impact for frequency up-conversion. An important design feature is the tunability of the resonance frequency through the electrostatic nonlinearity of the low-frequency oscillator. Impulsive normal forces due to impact are included in numerical simulation of the EEH through Moreau’s time-stepping scheme which has, to the best of our knowledge, not been used before in VEH design and analysis. The original scheme is extended with time-step adjustments around impact events to reduce computational time. Using frequency sweeps, we numerically investigate power generation under harmonic, ambient vibrations. Results show improved low-frequency power generation in this EEH compared to a reference EEH. The EEH design shows peak power generation improvement of up to a relative factor 3.2 at low frequencies due to the occurrence of superharmonic resonances
Nonlinear rotordynamic-thermal analysis of micro gas turbines
A compliant tilting pad air bearing concept has been proposed as a solution for low power micro gas turbines. In this paper, the nonlinear dynamic models for this bearing concept are extended with a thermal model. With simulations and experiments it is demonstrated that the thermal expansion of the bearing journals may negatively affect the power loss, and the nonlinear rotordynamic response of the rotor and these bearings. Therefore, designing these bearings for a micro gas turbine requires both a nonlinear rotordynamic model and a thermal model of the micro turbine