Stanislaw Pietrzko

Feedback control of sound transmission through a double glazed window

Abstract One way to tackle the control of stochastic noise in three dimensions is to reduce the sound transmission to the zone of interest. In buildings, windows are often the weak link in protecting the interior from outside noise. In particular, double glazed windows have a poor sound insulation at low frequency around the mass–air–mass resonance (double wall resonance). Since passive means for windows are exhausted, an active controller that increases the transmission loss in the low-frequency range is an attractive approach to reduce the noise level in buildings. Previously suggested feedforward controllers need reference microphones to measure the disturbance outside and error microphones for the adaptation somewhere in the room. For a real window this is unpractical or even unfeasible. These limitations can be overcome with the feedback controller presented here, which only uses sensors and actuators in the cavity of the double glazed window. Four different controllers—two feedforward and two feedback strategies—are designed, implemented and compared. With feedback the noise transmission around the mass–air–mass resonance can be reduced by 13 dB , compared to 18 dB with a feedforward controller.

Free vibration analysis of stepped beams by using Adomian decomposition method

Abstract The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of a stepped Euler–Bernoulli beam consisting of two uniform sections. Each section is considered a substructure which can be modeled using ADM. By using boundary condition and continuity condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions, step ratios and step locations are presented. Comparing the results using ADM to those given in the literature, excellent agreement is achieved.

Structural Vibration Control via R-L Shunted Active Fiber Composites

This article presents a successful extension of passive R-L shunt damping to piezoelectric ceramic elements working in direct 3-3 mode and a performance comparison to elements working in indirect 3-1 mode. A new circuit topology is implemented to synthesize the very large inductances required by the low inherent piezoelectric device capacitance at relatively low frequencies. This allows for efficient tuning of the R-L circuit to the structure resonance frequency to be damped. The vibration suppression performance of monolithic piezoelectric ceramic actuators and active fiber composites is compared in this study. For this purpose, different actuators are bonded on aluminum cantilever plates. An integrated FE model is implemented for the prediction of structure resonance frequencies, optimum values for electric components, and the resulting vibration suppression performance. The passive structure, bonded active patch, and shunted electrical network are analyzed within the same FE model. Active fiber composite patches working in the direct 3-3 mode show equivalent specific damping performance compared to conventional monolithic 3-1 actuated patches. Issues related to the sensitivity of R-L shunts to variations in environmental and operational conditions are discussed in this study. In short, monolithic actuators operating on the 3-1 piezoelectric effect seem to be the best for use in R-L shunting.

The influence of temperature and bonding thickness on the actuation of a cantilever beam by PZT patches

The goal of this work is to investigate the sensitivity of transfer of piezoelectric actuation efficiency to a cantilever beam due to variations in the environmental temperature and possible variations in the thickness of the adhesive layers bonding actuators to a beam. Investigations are first done analytically on the basis of a static linear longitudinal strain distribution along the whole beam/bonding/actuators section, as well as the shear lag model. In addition to the known conditions for transfer of actuation efficiency such as impedance matching, one obtains further requirements for a transfer of this actuation efficiency, of which the most important is a small thickness of the adhesive layer. However, the influences of temperature and of bonding thickness are smaller than expected; that is, variations induced by practical mounting and by use outside the laboratory have no pronounced effect on the transfer of the actuation efficiency. Using then the finite element program ANSYS, the complete system was modelled, including the adhesive layers. For the FEM calculations, the temperature dependences of all material properties were linearized. Results show that the eigenfrequencies of the beam vibration decrease only slightly at higher temperature and for thicker adhesive layers, without any reduction in the resonance amplitude. The findings are partly validated by experimental measurements.

Active Vibration Isolation Using an Electrical Damper or an Electrical Dynamic Absorber

This paper describes a theoretical and experimental study to show how an electrical damper or an electrical dynamic absorber, implemented using an electromagnetic actuator and an accelerometer, can control vibration transmission through a vibration isolator. The electrical damper is realized by feeding back the equipment velocity to the actuator with constant gain. The electrical dynamic absorber is realized by feeding back the equipment acceleration through a second-order low-pass filter. Because it is found that the plant on a flexible base is asymptotically similar to that on a rigid base, the optimal parameters of the control filter are determined analytically, independent of the base dynamics. Experimental results show that the electrical dynamic absorber has a similar performance to the electrical damper. The maximum reduction in transmitted vibration achieved was about 38 dB for both methods. It is also shown that the electrical dynamic absorber is more robust to undesirable dynamics outside the control bandwidth. Another advantage of the electrical dynamic absorber is that it does not require an integrator to transform acceleration into velocity.

Adaptive resonant shunted piezoelectric devices for vibration suppression

This paper presents a new adaptation technique for R-L shunted piezoelectric patches (PZT) bonded on mechanical structures for single mode vibration suppression. For the implementation of the adaptive R-L shunt circuit, a new variable inductor circuit controlled by transistors is developed. Additionally, a new modeling method for shunted PZTs based on equivalent transformer and gyrator circuits is presented. This leads to a comprehensive model that simplifies the search for optimal shunt circuits. Furthermore, it allows simulating the system consisting of the structure, the PZT patch and a complex transistor or other non-linear shunts on standard electronic simulators like PSpice or Saber. Damping performance of R-L shunted piezoelectric devices is very sensitive to environmental factors changing the circuit’s resonance frequency corresponding to the damped vibration mode. This requires fast adaptive tuning of the R-L shunted circuit, which is implemented using a new adaptation technique. The tuning direction of this adaptation law is obtained by detecting the phase shift between the velocity of the mechanical structure and the current in the shunt circuit. As the exact value of the phase for this technique is not required, one can reduce the adaptation problem to multiplication and integration of current and velocity. The performance of the presented new adaptive R-L shunt is compared with the common adaptation law based on minimizing the RMS value of the strain and then experimentally verified. The adaptive R-L shunt, which minimizes the phase-shift, can tune to the optimal parameters within seconds, but it needs an additional velocity sensor. In contrast, the R-L shunt minimizing the RMS value works without extra sensors, but needs some minutes to tune optimally. The new adaptive R-L shunt circuit can be implemented in small analog electronic chips that allows integrating it in smart materials.

Prediction of A-weighted aircraft noise based on measured directivity patterns

Abstract A technique of predicting the A-weighted time history of flyover noise making use of directivity patterns is presented. These directivity patterns of aircraft noise radiation are based upon simultaneous recording of the acoustical and geometrical data. The acoustical measurements are performed at various ground positions and synchronized with tracking radar information. In the data processing, the effects of spherical spreading, atmospheric absorption and the delay time between source and receiver are taken into account. The result is a simple analytical description of the directivity pattern of aircraft in flight, in the form of a group of coefficients assigned to each aircraft type. The coefficients are obtained by curve fitting, based on the acoustical and geometrical data. They are applied in a set of polynomials, yielding valid results over a wide range of distances and emission angles. The A-weighted sound level for subsonic aircraft in flight can thus be predicted accurately. Furthermore, the time history of the flyover noise can be simulated for any observer point relative to the flight path.

Free vibration analysis of a type of tapered beams by using Adomian decomposition method

Abstract The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of tapered Euler–Bernoulli beams with a continuously exponential variation of width and a constant thickness along the length under various boundary conditions. Based on ADM the governing differential equation for the tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions and non-uniformity ratios are presented. The accuracy is assured from the convergence and comparison published results.

A new control approach for switching shunt damping

This paper presents a new control approach for piezoelectric switching shunt damping. Recently, semi-active controllers have been used to switch piezoelectric materials in order to damp vibration. These switching shunt circuits allow a small implementation and require only little power supply. However, the control laws to switch these shunts are derived heuristically and therefore it remains unclear, if a better control law for a given shunt topology exists. We present a new control approach based on the Hybrid System Framework. This allows the modelling of the switched composite system as a hybrid system. Once the hybrid system description is obtained, a receding horizon optimal control problem can be solved in order to get the optimal switching sequence. As the computation time to solve this optimisation problem is too long for real-time applications, we will show that the problem can be solved off-line and the solution stored in a look-up table. This allows a real-time implementation of the switch controller. Moreover, control rules can be derived from this look-up table, and we will demonstrate that in some situations the controllers proposed in previous papers generate near optimal switching. In this paper, we will investigate several shunt topologies with switches and compare the performance between the heuristically derived control laws and the optimal new control laws. Simulations and experiments show the improvement with the new controllers. This is very promising, since this new control approach can be applied for more complex shunt circuits with many switches, where the derivation of a switching law would be very difficult.

Design of Shaped Piezoelectric Modal Sensor for a Type of Non-Uniform Beams Using Adomian-Modified Decomposition Method

In this article, a solution to the problem of finding the shape of piezoelectric modal sensors for a non-uniform beam with continuously exponential varying width under general boundary conditions is proposed using the Adomian modified decomposition method (AMDM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function and the beam width function. Based on the AMDM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then, the shapes of the designed modal sensors are obtained. Finally, several numerical examples are given to demonstrate the feasibility of the proposed modal sensors with various boundary conditions.