Nonlinear　science　has　been　an　important　symbol　in　the　development　of　modern　science,　especially　the　researches　in　nonlinear　dynamics　and　nonlinear　waves　have　extraordinary　significance　in　solving　the　complex　phenomena　and　problems　encountered　in　various　fields　of　natural　science.　In　this　paper,　the　nonlinear　bending　wave　propagation　of　a　piezoelectric　laminated　beam　with　electrical　boundary　conditions　is　studied.　Firstly,　considering　the　geometric　nonlinear　effect　and　piezoelectric　coupling　effect,　the　nonlinear　equation　of　the　one-dimensional　infinite　rectangular　piezoelectric　laminated　beams　is　established　by　using　Hamiltonian　principle.　Secondly,　the　Jacobi　elliptic　function　expansion　method　is　used　to　treat　the　nonlinear　flexural　wave　equation,　and　the　corresponding　shock　wave　solution　and　solitary　wave　solution　of　the　nonlinear　flexural　wave　equation　are　obtained　in　the　approximate　case.　Last,　the　nonlinear　Schrodinger　equation　is　obtained　by　using　the　reduced　perturbation　method,　and　the　bright　and　dark　soliton　solutions　are　further　obtained.　Moreover,　the　effects　of　external　voltage　and　the　thickness　of　the　piezoelectric　layer　on　the　characteristics　of　shock　wave　and　solitary　wave　as　well　as　bright　and　dark　solitons　are　studied.　The　results　show　that　when　the　wave　velocity　is　small,　the　external　voltage　has　a　great　influence　on　the　shock　wave,　and　when　the　wave　velocity　is　large,　the　external　voltage　has　no　effect　on　the　solitary　wave.　The　bright　solitons　and　the　dark　solitons　can　be　obtained　by　adjusting　the　external　voltage　applied　to　the　piezoelectric　laminated　beam.　It　is　found　that　the　amplitudes　of　bright　and　dark　solitons　increase　with　the　increase　of　external　voltages.　©　2021,　Chinese　Journal　of　Theoretical　and　Applied　Mechanics　Press.　All　right　reserved.