Active Vibration Control of Parametrically Excited Systems

Lead Research Organisation: University of Southampton
Department Name: Faculty of Engineering & the Environment


This project considers active vibration control of parametrically excited systems (PES). The problem is to develop control strategies for the suppression, or enhancement, of parametric resonances in engineering systems. Active control has the potential to control large amplitudes of vibration and modify the dynamics of the system very efficiently. It is particularly suitable for PES since the dynamics of PES are periodic-time dependent. The appearance of the periodic-time-dependent parameter in the dynamic equation results in a complex response including inherent instabilities, or combined resonances of summed or difference type. Understanding the dynamics of PES and its control is thus the main objective of this research.
The control strategy that will be used for PES is based on the receptance method developed by the applicant for linear time-invariant systems. The method has significant advantages, since there is no requirement for knowledge of system matrices, no requirement for model reduction techniques and no requirement for observers to estimate the unmeasured states. The method is entirely based on the measured vibration data; therefore the dynamics of the actuators, sensors and filters are all included in the design of the controller. Other control strategies based on the Floquet theory will also be developed. The control techniques will be implemented on a cable-supported structure, representing a cable-stayed bridge, to demonstrate the practical application of the active control on PES.
Many engineering structures are subjected to parametric excitation, which is produced by some external loads interacting with the structure. In civil engineering, Aratsu Bridge in Southern Japan is an example where parametric resonance was the origin of the cracks close to the anchorages. Parametric resonance occurs when the structural frequency coincides with a specific ratio of the parametric excitation frequency. For instance in the Skarnsundet Bridge in Norway, a vertical deck frequency was exactly twice the fundamental cable frequency. Vibration control can be achieved by moving the structural frequency away from that specific ratio using pole placement techniques.
In aerospace, parametric resonance can cause flutter of airplane wings due to the interaction of the wing with the aerodynamic loads. Recently, a fatal accident occurred involving a prototype of a business jet due to the tail-plane flutter, and the research aims to develop methods by which such instability can be controlled.
In marine engineering, parametric resonance can occur in riser systems due to the interaction of the risers with surface waves. The undesirable dynamic behaviour of these risers can be avoided using tension control. If parametric excitation is not included in the design of these risers, the wave induced vibration can result in instability and even catastrophic failure, thereby causing severe environmental and economic damage so that a more flexible method of active control would make the system safer. The research will also be beneficial in the design of the energy converters such as floaters since it can enhance the parametric resonance, which is used to extract significant amount of power from the wave energy.

Planned Impact

The potential application of the proposed project is wide since parametric excitation occurs in many engineering structures such as aeroplane wings and helicopter rotor blades in aerospace, cable-stayed bridges in civil and ships in marine industry. The applicant has made new contacts at the University of Sheffield based on this project. The applicant would like to publish her results in leading refereed journals (The list is provided in the section on Academic Beneficiaries). It is also intended to attend two UK and international conferences per year to disseminate the outcomes of the project to a wider community. The applicant is a member of MOPNET, an interdisciplinary network funded by EPSRC. The applicant will also present the work in their meeting. The dynamic behaviour of a parametrically excited system is complex and the control of an inherent unstable system is highly challenging. Success in this project opens doors for new collaboration with other academics and industrial sectors.
The project is highly beneficial to civil engineering industry for cable-supported structures. Wind induced vibration may lead to large amplitude of oscillations , which may cause structural damage such as the creation of cracks in the Aratsu Bridge in Japan or even complete destruction of the structure such as the Tacoma Bridge. The understanding of parametric excitation and its control is thus extremely beneficial to prevent the structural damage, increase the lifetime and the serviceability and reduce the maintenance costs. The applicant has established collaboration with Arup. Collaboration with Arup provides a world-wide impact of the proposed research.
In off-shore technology, risers used for oil transportation are suspended from the ocean surface to the sea floor. With the trend towards oil and gas exploration in deeper waters and harsher environments, the response of the risers under various environmental conditions and sea states becomes increasingly complex. The riser is subjected to parametric excitation due to wave forces, resulting in undesirable transverse vibration. Parametric resonance could be avoided using a systematic approach to tension control. Orcina is keen to incorporate such control strategies in their offshore dynamic modelling software.
Other interesting application is to exploit parametric oscillation. Ocean Power Technologies is interested in exploiting parametric resonance to enhance the performance of their floating buoys and to extract more energy for electrical power. This is the positive aspect of parametric oscillation. Active control of marine structures is thus an interesting area of research and the real-world examples of such dynamic problems certainly justify the time to investigate novel potential solutions. For aerospace applications, the applicant has extensive collaboration with Agusta-Westland.
The applicant will invite her industrial collaborators and will present to them the theoretical as well as the experimental results in order to maximise the impact of the project. The applicant would like to engage a wider public through media in order to promote the public awareness of the project. This will be achieved after completing the training course in public/media to acquire the required skills.
The project contributes to the training of a research assistant and a PhD student funded by the University of Southampton. She will also demonstrate the control strategy developed for the cable-supported structure to her undergraduate students as part of her teaching activities. The project provides an excellent opportunity for the applicant to establish and develop her research career at the University of Southampton. Regular meetings and a workshop will be held internally at the University and the results will be presented to other academics and researchers for evaluation and assessment. The progress reports will also be available in the Faculty's web-page for academic use.


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Dal Borgo M (2019) Identification and analysis of nonlinear dynamics of inertial actuators in Mechanical Systems and Signal Processing

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Di Monaco F (2013) Energy harvesting using semi-active control in Journal of Sound and Vibration

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Elliott SJ (2015) Nonlinear damping and quasi-linear modelling. in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

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Ghandchi Tehrani M (2016) Periodic and Chaotic Response of a Macro-Scale Tuning Fork Gyroscope in Applied Mechanics and Materials

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Ghandchi Tehrani M (2014) Extending the dynamic range of an energy harvester using nonlinear damping in Journal of Sound and Vibration

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Ghandchi Tehrani M (2015) Active control of parametrically excited systems in Journal of Intelligent Material Systems and Structures

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Ghandchi Tehrani M (2013) Receptance method for active vibration control of a nonlinear system in Journal of Sound and Vibration

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Ghandchi-Tehrani M (2014) Bifurcation control of a Duffing oscillator using pole placement in Journal of Vibration and Control

Description A novel control strategy was developed for systems when their parameters such as stiffness vary in time. An example cable stayed bridges in which the vibration of the deck can axially excite the cable. The axial excitation in the cable can change the stiffness of the cable and therefore its dynamics behaviour can change. This stiffness variation can make the system to vibrate significantly and can even cause instability and failure. Tacoma bridge was subjected to parametric excitation and failed. Therefore, in this project a control algorithm was developed to suppress the vibration due to parametric instability.
Exploitation Route Most of engineering systems can have parametric excitation due to some sort of excitation such as aerodynamic loads on aircrafts, gust loads on bridges, wave energy on ships,.... These systems have to be designed in such a way to avoid unwanted vibrations due to parametric excitation. This project is about how to design and control engineering systems taking into account parametric excitation to avoid instability, to increase safety ,serviceability and performance and to reduce maintenance costs.
Sectors Aerospace, Defence and Marine,Construction,Education,Environment

Description Industries- The outcome of the project were demonstrated to Industries including TWI, Gill, Agusta-Westland and JLR and active control was implemented to control the vibrations. Parametric instability can be observed in many engineering systems and this project demonstrated the control algorithm to control parametric instabilities. Public event- The outcome was demonstrated in open-days to students and their parents in order to demonstrate the problem of parametric instability.
First Year Of Impact 2014
Sector Education,Energy
Impact Types Societal,Economic

Description ITN training Network
Amount £900,000 (GBP)
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 06/2018 
End 06/2022
Description Marie-Curie ANTARES project
Amount £605,000 (GBP)
Funding ID ITN ANTARES(General Agreement 606817). 
Organisation European Commission 
Sector Public
Country European Union (EU)
Start 10/2014 
End 10/2018
Description Researchers Link, Newton Fund
Amount £7,000 (GBP)
Organisation British Council 
Sector Charity/Non Profit
Country United Kingdom
Start 03/2015 
End 03/2016
Description TWI
Amount £84,000 (GBP)
Organisation TWI The Welding Institue 
Sector Private
Country United Kingdom
Start 10/2014 
End 10/2017
Description Agusta-Westland 
Organisation AgustaWestland
Country United Kingdom 
Sector Private 
PI Contribution The control strategy used in this project is based on velocity feedback and pole placement. Pole placement control strategy is applicable to helicopters, since the frequency of the helicopters can be changed by implementing control forces through actuators. This ideas has been tested on W30 helicopter and the results have been published in a journal paper.
Collaborator Contribution They have provided a letter of support for my first grant. They have also allocated their facilities to test the control strategy on W30 helicopter. Peter Court gives a lecture once a year to our students about the application of the developed control strategies on helicopters.
Impact J. E. Mottershead and M. Ghandchi Tehrani, S. James and P. Court, Active Vibration Control Experiments on an Agusta-Westland W30 Helicopter Airframe, IMECHE part C, 2012, 226(6) 1504-1516, DOI: 10.1177/0954406211423609
Start Year 2010
Description University of Bergamo 
Organisation University of Bergamo
Country Italy 
Sector Academic/University 
PI Contribution I visited University of Bergamo for two weeks, one week per year during this project. I gave a presentation to the academics and colleagues in Bergamo. Dr Jonathan Salvi stayed 6 month as a visiting researcher at ISVR. We wrote a research proposal together , a newton fund fellowship.
Collaborator Contribution Professor Rizzi invited me to give a lecture about my research activities. University provided funds for my trip for two weeks. He explained the problem of parametric resonance in civil engineering structures.
Impact We submitted a research proposal together.
Start Year 2013
Description University of Exeter 
Organisation University of Exeter
Department College of Engineering, Mathematics & Physical Sciences
Country United Kingdom 
Sector Academic/University 
PI Contribution I have visited Professor Paul Reynolds at Exeter and also I have demonstrated the outcome of my research.
Collaborator Contribution Several trips have been made from Exeter to Southampton by Professor Paul Reynolds to discuss and evaluate the progress of the project. The experiments on the parametric beam and nonlinear actuators were demonstrated. He provided very instructive feedback on the choice of active control strategy.
Impact Donald Steve Nyawako, Maryam Ghandchi Tehrani and Paul Reynolds, Receptance based approach for control of floor vibrations, submitted to EACS, 2016, Sheffield.
Start Year 2012
Description University of Polytechnico di Torino 
Organisation Polytechnic University of Turin
Country Italy 
Sector Academic/University 
PI Contribution The problem of parametric excitation was introduced and presented at Turin. The results were well received and opened new collaboration to extend the work to the potential use of parametric excitation in energy harvesting. Several journal and conference papers have been published. I intend to write a book on active control with Dr Bonisoli.
Collaborator Contribution Dr Bonisoli visited Southampton 4 times during this project. His experimental experience added significant values to the project. He gave several presentations and seminars at the mini conferences and workshop organised at Southampton. He also sent several visiting researchers to work on the topics related to nonlinear dynamics , parametric excitation, active control and energy harvesting.
Impact M. Scapolan, M. Ghandchi Tehrani and E. Bonisoli, Energy harvesting using parametric resonance system due to time-varying damping, Mechanical Systems and Signal Processing, Accepted October 2015. F. Di Monaco, M. Ghandchi Tehrani, S. J. Elliott, E. Bonisoli, Energy Harvesting using semi-active control, Journal of Sound and Vibration, 332(23),2013, 6033-6043, DOI:10.1016/j.jsv.2013.06.005 M. Ghandchi Tehrani, S. J. Elliott, F. Di Monaco and E. Bonisoli, Energy harvesting using nonlinear control, Recent Advances in Structural Dynamics, RASD 2013, Pisa, July 2013. Maryam Ghandchi Tehrani, Elvio Bonisoli and Matteo Scapolan, Michal Kalkowski, Energy harvesting using Unstable Dynamics Due to Parametric Damping , ICEDYN2015. E. Bonisoli, N. Manca, M. Ghandchi Tehrani, A. Da Ronch and M. Gianfrancesco, Extended Frequency Bandwidth through MDOF Nonlinear Magneto-Mechanical Energy Harvesting, ICEDYN2015, Lagos, PT, 22 - 24 Jun 2015. 8pp. M. Ghandchi Tehrani, E. Bonisoli, M. Scapolan, Energy harvesting perspectives from parametric resonant systems, IMAC2015 XXXIII, Feb 2-5, Florida.
Start Year 2010
Description University of Sao Paolo 
Organisation University of Sao Paulo
Country Brazil 
Sector Academic/University 
PI Contribution I presented the outcome of this project at ENOC conference in Vienna. Professor Balthazar and Dr Silveira were interested about my research and they invited me to give a short course, attend a workshop and give a seminar. I implemented the outcome on a macro-scale tuning fork gyroscope, which is an example of parametrically excited system. The results from this investigation was published in ICOEV conference in 2015.
Collaborator Contribution Dr Sliveira and Prof Balthazar invited me to the University of Sao Paolo in Brazil. They provided some guidance on nonlinear dynamics and some instructive feedback on the dynamics of the beam and the interaction of the beam with the shaker.
Impact M. Ghandchi Tehrani, J. M Balthazar and M. Silveira, Parametric study of a macro-scale tuning fork Gyroscope, ICOEV2015, Ljubljana, Slovenia, 5-11 September
Start Year 2013