Nonlinear Dynamic Analysis Of Micro-structure With Damage

Pie zoelectr ic mater ia l, as a new type of materia ls, has been applied to all kindsof industr y. The common use of piezoe lectr ic units and devices promote the mature ofprocess technolo gy. As the degree of the batch process higher, the price of singledevice cheaper, the superior ity more obvious when compare to the traditiona l devices.But on the other hand, as wide ly used, more proble ms e xposed to be solved. With thegeometr y size sma ller，the mechanica l properties of pie zoelectr ic units and devicesnot scale reductio n as we ima gine, but gives out some re lations to size-dependent.Damage caused by productio n process and service wear is una voidably, It is not area listic that we change a new devices as the damage happened. it has greatsignifica nce for study on damage. A lot of pie zoelectr ic units and devices cansimp lified to beam model, the research is carr ied out according to p iezoe lectriclaminated beams from aspects as follows:We study the nonlinear defor mations o f cantilever pie zoelectr ic la minated bea mswith damage under electr ic fie ld and mecha nical force. A unifor m constitutive relationcan be used to describe nonlinear vibration ana lys is of the piezoe lectric la minatedbeam when we considered size effect and damage effect. Based on the theory o fcontinuum mec hanics and the Euler-bernoulli theory, the dyna mic contro l equationexpress ion of the cantilever piezoe lectr ic la minated beams was deduced. By us ingGalerkin’s method， we trans late the contro l equation into no nlinear ordinarydifferential equations, the responses of the system are obtained through numerica lintegration method. The n we discuss the results between when the effect of geometr icnonlinearity is considered and been neglected, the results between different contro lvolta ge. We obtain a series o f cr itical p ull-in vo lta ge as we set the different le ngth orthe different dama ge parameter. Next we use finite ele ment method for solving andcompared the results of the two groups. Through compar ing, it is found that as thecontro l vo ltage increase or the damage increase the critica l pull-in vo lta ge decrease.When co mpare to the Nor mal beam, the pull-in volta ge is low. F ina lly, somechalle nges are pointed out. Whe n compared the two differe nt Methods, the ansysresults is low under the same condition.The har monic ba lance techniq ue is used for solution vibratio n feature of thecantile ver beam. Discussed the no nlinear responses of the system on free vibration and forced vibration respectively. Then we disc uss the results o f amp litude-freque ncycharacteristic between d ifferent control vo ltages, different load volta ges and differentdamping coefficients.