The Nonlinear Vibration Analysis Of Piezoclectric Beam And Plate Structure

In recent years,development and application of smart materials has gone deep into every corner of society,whether it is the aerospace vehicles,robots,the sophisticated weapons and high-end construction equipments,or our lives household appliances controllers.With a large number application of flexible piezoelectric structures,the nonlinear vibration has become an important problem that we have to face.It is necessary to study the nonlinear vibration of piezoelectric structures.For the nonlinear vibration problems,analytical approximate solution and numerical approximate solution are both useful,but the analytical method is that people want.Because once the analytical solution is obtained,any numerical results can be obtained.the range of solutions can be found.In this paper,analytical method is used to research the nonlinear vibration of piezoelectric beam and plate structure.The analytical equations of nonlinear vibration of piezoelectric beam and plate structure were established.The incremental harmonic balance method(IHB)is an effective quantitative analysis method,and it has been successfully extended to the nonlinear vibration fields.The incremental harmonic balance methodis extended to study the nonlinear vibration of piezoelectric field in this article.The amplitude incremental variational principleis the theoretical fundament of the incremental harmonic balance method.Based on the basic equations of nonlinear vibration of piezoelectric structure,the amplitude incremental potential energy principle and complementary energy principle were established by using the variational integral method.Also the amplitude incremental generalized potential energy principle and generalized complementary energy principle with two kinds of variables were established.And the amplitude incremental generalized potential energy principle and generalized complementary energy principle with three kinds of variables were established.Thus,the finite element formulation of the nonlinear vibration of piezoelectric structure wasfound.In this paper,based on geometric nonlinearity,the Duffing equation of simply supported piezoelectric beam was established and its vibration characteristic was analyzed.The amplitude incremental variational principle of the piezoelectric rectangular thin plate,which is simply supported on the four sides,was established.The vibration characteristic of plate structure was analyzed by using the incremental harmonic balance method.