Reseacrh On Nonlinear Statics And Dynamics Of Piczoclcctric Functionally Graded Beams

Functionally graded material (FGM) is a new type of nonhomogeneous composite.Different from the traditional laminated materials, the properties of the FGM change smoothlyand continuously from one surface to another according to a certain distribution law, whichinsures that the obvious stress singularity will not appear. Piezoelectric materials couplingwith direct and inverse piezoelectric effects play an increasingly important role in the fields ofactive control and intelligent detection. What is more, beams, as the generally engineeringstructure, are always receiving considerable attentions. At the same time, Owing to theflexural tendency of the structure in the engineering practices, the geometric nonlinearity hasto be considered. Therefore, it is necessary to do more extensive research on the nonlinearmechanical behavior of the piezoelectric functionally graded beams.Firstly, employing Euler–Bernoulli beam theory, first-order shear deformation beamtheory and various higher-order shear deformation beam theories, geometrical nonlinearstrain-displacement relations, Hamilton principle, the nonlinear governing equation for theFGM beam with two clamped ends and surface-bonded piezoelectric actuators is divided. Byintroducing some novel methods, the closed-form solution for the piezoelectric FGM beamssubjected to thermo-electric loading. In the numerical examples, the good agreement betweenthe present results and existing solutions verifies the validity and accuracy of the presentanalysis and solving method, and the factors of the thermo-electric loads, the volume fractionexponent, length-to-thickness ratio, temperature-dependent (TD) or temperature-independent(TID) material properties and the different beam theories on the nonlinear stability of thepiezoelectric FGM beam are discussed.Furthermore, employing higher–order shear deformation theory, geometrically nonlinearstrain-displacement relations and Hamilton principle, a set of the nonlinear equations for theFGM beams with surface-bonded piezoelectric is divided. Then, the negative velocityfeedback algorithm coupling the direct and converse piezoelectric effect is used to activelycontrol the piezoelectric function graded laminated beams. Using finite difference method andNewmark method, the numerical solutions for the equation of piezoelectric FGM beams areobtained.Finally, considering a FGM beam with partly debonded piezoelectric actuators andsensors, and taking the nonlinear contact force and nonlinear geometric relationship of thedelaminated sections into consideration, the nonlinear dynamic equations of the piezoelectricFGM beams with delamination are derived. Then, the negative velocity feedback algorithm coupling with the direct and inverse piezoelectric effect is used to control the FGM beamswith delaminated piezoelectric actuators and sensors actively. Using the finite differencemethod and Newmark method synthetically, the numerical solutions for the nonlineargoverning equations of FGM beams with delaminated piezoelectric patches are obtainediteratively. In calculation examples, the effects of the volume fraction exponent, nonlinearcontact force and the length of the inner delamiantion on the nonlinear free vibration andactive control of the beam are investigated. The effects of edge delamination and the length ofit on the active control and control stability are analyzed.Basically, at the first half part of this thesis, our attentions are focused qualitativeanalysis of nonlinear stability (thermal buckling, postbuckling and dynamic stability) for thepiezoelectric FGM beams by introducing some novel methods. In the latter half part, ourattentions are concentrated on the quantitative analysis of nonlinear free vibration and activecontrol of the piezoelectric FGM beams by using the finite difference method and Newmarkmethod synthetically. Through the above comprehensive works on the nonlinear mechanicalbehaviors of piezoelectric FGM beams, some benchmark and meaningful solutions have beendrawn. Moreover, it is hoped that this studies could be benefit for the further researches andengineering application of these intelligent beams in more complex environments.