NDLI: On the failure of the ‘Similar Piezoelectric Control’ in preventing loss of stability by nonconservative positional forces

Content Provider	Springer Nature Link
Author	Luongo, Angelo Rosi, Giuseppe D’Annibale, Francesco
Copyright Year	2014
Abstract	A control strategy for continuous, autonomous, linear mechanical systems, controlled via piezoelectric devices, and suffering Hopf bifurcations, triggered by positional nonconservative forces, is discussed. The strategy is based on the ‘principle of similarity’, proved in the literature to be successful in controlling externally excited systems. A continuous metamodel of Piezo-Electro-Mechanical system, loaded by position-dependent forces, is derived via the Extended Hamilton Principle. The similarity principle is introduced in the model, demanding for certain relations among mechanical and piezoelectric properties to be satisfied. A stability analysis is carried out via perturbation methods, also accounting for small deviations from similarity. It is shown that the similar control has always a detrimental effect in preventing the loss of stability of the mechanical systems and that this effect is robust under slight imperfections. As an example, a Generalized Beck beam is studied, internally and externally damped, under the simultaneous action of a follower and a dead load, for which the previous asymptotic results are corroborated by an exact analysis.
Ending Page	1968
Page Count	20
Starting Page	1949
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	4
Volume Number	66
Language	English
Publisher	Springer Basel
Publisher Date	2014-11-09
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stability Hamilton's principle Linear vibration theory Theoretical and Applied Mechanics Hamiltonian and Lagrangian mechanics Generalized Beck beam Control Mathematical Methods in Physics Perturbation methods Piezo-Electro-Mechanical systems Control of mechanical systems Circulatory systems Hopf bifurcation Stability problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Linear stability of piezoelectric-controlled discrete mechanical systems under nonconservative positional forces

Improving the linear stability of the visco-elastic Beck's beam via piezoelectric controllers

Piezoelectric control of the Hopf bifurcation of Ziegler’s column with nonlinear damping

Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response

Postcritical behavior of a discrete Nicolai column

Stability and Hopf bifurcation in van der Pol oscillators with state-dependent delayed feedback

Global stability and Hopf-bifurcation in a zooplankton–phytoplankton model

On the failure of the ‘Similar Piezoelectric Control’ in preventing loss of stability by nonconservative positional forces

Similar Documents

Linear stability of piezoelectric-controlled discrete mechanical systems under nonconservative positional forces

Improving the linear stability of the visco-elastic Beck's beam via piezoelectric controllers

Piezoelectric control of the Hopf bifurcation of Ziegler’s column with nonlinear damping

Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response

Postcritical behavior of a discrete Nicolai column

Stability and Hopf bifurcation in van der Pol oscillators with state-dependent delayed feedback

Global stability and Hopf-bifurcation in a zooplankton–phytoplankton model

On the failure of the ‘Similar Piezoelectric Control’ in preventing loss of stability by nonconservative positional forces