Active vibration control of a smart plate using a piezoelectric sensor–actuator pair at elevated temperatures

A new scheme for active structural vibration control using piezoelectric patches at elevated temperatures is analytically derived and experimentally verified. A control law is derived using augmented piezoelectric constitutive equations which include the temperature dependence of piezoelectric stress coefficient (e31) and permittivity . Since the temperature dependence of 'e31' and '' is not analytically known, their experimental values measured at elevated temperatures are used. Using augmented constitutive equations, a finite element model of a smart two-dimensional isotropic plate instrumented with a collocated piezoelectric sensor?actuator pair is derived. A control law for active vibration control of the first mode of the smart cantilevered plate is derived using negative velocity feedback. Active vibration control of the first mode of a smart cantilevered plate is experimentally achieved at elevated temperatures ranging from 25 to 75??C under two cases: (i)?using a control law which ignores the temperature dependence of 'e31' and '' and (ii)?using a control law which includes the temperature dependence of 'e31' and ''. A comparison between these two control laws shows that: (i)?active vibration control (AVC) performance is not maintained at elevated temperatures using a control law which ignores the temperature dependence of 'e31' and '' and (ii)?AVC performance is maintained at elevated temperatures when we use a control law which includes the temperature dependence of 'e31' and ''.

[1]  Horn-Sen Tzou,et al.  Nonlinear piezothermoelasticity and multi-field actuations, part 1: Nonlinear anisotropic piezothermoelastic shell laminates , 1997 .

[2]  Horn-Sen Tzou,et al.  A theory on anisotropic piezothermoelastic shell laminates with sensor/actuator applications , 1995 .

[3]  W. Nowacki,et al.  SOME GENERAL THEOREMS OF THERMOPIEZOELECTRICITY , 1978 .

[4]  W. Hwang,et al.  Finite Element Modeling of Piezoelectric Sensors and Actuators , 1993 .

[5]  Mark J. Schulz,et al.  Piezoelectric Materials at Elevated Temperature , 2003 .

[6]  Manu Sharma,et al.  Mathematical modeling of actively controlled piezo smart structures: a review , 2011 .

[7]  Rajamohan Ganesan,et al.  Active vibration suppression of smart laminated beams using layerwise theory and an optimal control strategy , 2007 .

[8]  D. Saravanos,et al.  Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells , 1999 .

[9]  Abhijit Mukherjee,et al.  Numerical characterization of functionally graded active materials under electrical and thermal fields , 2003 .

[10]  V Balamurugan,et al.  Active vibration control of smart shells using distributed piezoelectric sensors and actuators , 2001 .

[11]  Horn-Sen Tzou,et al.  CONTROL OF ADAPTIVE SHELLS WITH THERMAL AND MECHANICAL EXCITATIONS , 2000 .

[12]  U. Gabbert,et al.  Finite element analysis of thermopiezoelectric smart structures , 2002 .

[13]  S. Poh,et al.  Performance of an active control system with piezoelectric actuators , 1988 .

[14]  Franck Massa,et al.  A complete method for efficient fuzzy modal analysis , 2008 .

[15]  Ranjan Ganguli,et al.  Influence of Temperature and High Electric Field on Power Consumption by Piezoelectric Actuated Integrated Structure , 2009 .

[16]  Y. Fotinich,et al.  Influence of temperature on the electromechanical and fatigue behavior of piezoelectric ceramics , 1998 .

[17]  H. F. Tiersten,et al.  On the nonlinear equations of thermo-electroelasticity , 1971 .

[18]  J. P. Nowacki,et al.  STEADY-STATE PROBLEMS OF THERMOPIEZOELECTRICITY , 1982 .

[19]  M. Sunar,et al.  Distributed thermopiezoelectric sensors and actuators in structural design , 1992 .

[20]  S. Yang,et al.  Modal Analysis Of Stepped Beams With Piezoelectric Materials , 1994 .

[21]  Singiresu S Rao,et al.  Thermopiezoelectric Control Design , 1997 .

[22]  Horn-Sen Tzou,et al.  A Piezothermoelastic Thin Shell Theory Applied to Active Structures , 1994 .

[23]  Maurice Petyt,et al.  Introduction to finite element vibration analysis , 1990 .

[24]  Sarp Adali,et al.  Developments in thermopiezoelasticity with relevance to smart composite structures , 2000 .

[25]  Daniel G. Cole,et al.  Experiments in piezostructure modal analysis for MIMO feedback control , 1994 .

[26]  Singiresu S Rao,et al.  Analysis of distributed thermopiezoelectric sensors and actuators in advanced intelligent structures , 1993 .

[27]  Jun-Sik Kim,et al.  Enhanced lower-order shear deformation theory for fully coupled electro-thermo-mechanical smart laminated plates , 2007 .

[28]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[29]  K. Y. Lam,et al.  Active control of composite plates with integrated piezoelectric sensors and actuators under various dynamic loading conditions , 1999 .

[30]  Uwe Stöbener,et al.  Active Vibration Control of a Car Body Based on Experimentally Evaluated Modal Parameters , 2001 .

[31]  J Vantomme,et al.  A thermal–electrical–mechanical coupled FE formulation using discrete layer kinematics for the dynamic analysis of smart plates , 2006 .

[32]  Rajeev Kumar,et al.  Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator , 2008 .

[33]  Horn-Sen Tzou,et al.  ANALYSIS OF NON-LINEAR PIEZOTHERMOELASTIC LAMINATED BEAMS WITH ELECTRIC AND TEMPERATURE EFFECTS , 1998 .

[34]  S. M. Yang,et al.  Interaction of structure vibration and piezoelectric actuation , 1994 .

[35]  P. K. Sinha,et al.  Thermally induced vibration control of composite plates and shells with piezoelectric active damping , 2004 .

[36]  Singiresu S Rao,et al.  Recent Advances in Sensing and Control of Flexible Structures Via Piezoelectric Materials Technology , 1999 .

[37]  Raymond D. Mindlin,et al.  On the Equations of Motion of Piezoelectric Crystals , 1989 .

[38]  Singiresu S Rao,et al.  Thermopiezoelectric control design and actuator placement , 1997 .

[39]  Manu Sharma,et al.  Modal control of a plate using a fuzzy logic controller , 2007 .

[40]  Victor Birman.  Thermal Effects on Measurements of Dynamic Processes in Composite Structures Using Piezoelectric Sensors , 1996 .

[41]  V. Varadan,et al.  Finite-element modeling of a smart cantilever plate and comparison with experiments , 1996 .

[42]  M. S. Gadala,et al.  Quasi-static thermo-electro-mechanical behaviour of piezoelectric stack actuators , 2008 .

[43]  R. D. Mindlin.  Equations of high frequency vibrations of thermopiezoelectric crystal plates , 1974 .

[44]  Hongjun Xiang,et al.  Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators , 2007 .

[45]  Manu Sharma,et al.  Optimization Criteria for Optimal Placement of Piezoelectric Sensors and Actuators on a Smart Structure: A Technical Review , 2010 .

[46]  Horn-Sen Tzou,et al.  Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 2: Control of Nonlinear Deflection, Buckling and Dynamics , 1997 .

[47]  K. Chandrashekhara,et al.  Thermally induced vibration suppression of laminated plates with piezoelectric sensors and actuators , 1995 .