Research On Nonlinear Static-dynamic Characteristics Of Piezoelectric Cylindrical Shells With Delamination Under Hygrothermal Conditions

Because the positive and inverse piezoelectric effect of piezoelectric materials has many important advantages,such as light weight,wide frequency response range,low cost and convenient application,has been widely used in aerospace,civil engineering,sports,medicine,daily supplies and so on.As a new type of material,due to the limited of the manufacturing technology,delamination damage will emerge in piezoelectric materials when affected by external factors.And also it is often in the condition of hygrothermal environment,the stiffness and strength of piezoelectric cylindrical shell reduced by the residual stress.Throughout,considering piezoelectric cylindrical shell with throughout circumference delamination as the subjects investigated,the buckling,nonlinear dynamic response and dynamic stability are studied.Use the Rayleigh-Ritz method,derived the buckling eigenvalue equation of the piezoelectric cylindrical shell with delamination.Firstly,supposing a displacement mode suitable for delaminated cylindrical shell by the Heaviside unit step function,analysis the internal force and derived the total energy equation.Then,based on the Hamilton variational principle,applying the Rayleigh-Ritz method,the control equation of the system static buckling under axial loading are obtained.Finally,through the calculation examples,the effects of various parameters of delamination and mateaial,hygrothermal condition and piezoelectricity on the buckling of the piezoelectric cylindrical shell with delamination are discussed.Based on the nonlinear elastic shell theory and piezoelectric theory,considering the effects of the contact force,hygrothermal condition and piezoelectric effect,establish the control equation of the piezoelectric cylindrical shell with symmetrical delamination.Using the finite difference method and Newton-Newmark method to control the partial derivative in nonlinear differential equations and definite condition are dispersed,and then to find the solution by iterative method.Then discuss the influences of the delaminating parameters,hygrothermal condition,piezoelectric effect and external load on the nonlinear dynamic response of piezoelectric cylindrical shell with delamination under hygrothermal condition.Based on Rayleigh-Ritz method,the effects of the geometric nonlinearity and the piezoelectric on dynamic stability of piezoelectric cylindrical shell with delamination are studied.Firstly,using Heaviside unit step function to supposing a displacement model,then,internal force analysis and energy analysis,applying Rayleigh-Ritz method,the Mathieu-type parameter vibrating equations of the piezoelectric cylindrical shell are obtained.And the parameter equation is solved by harmonic balance method.Finally,through the calculation examples,the effects of amplitude of the external excitation,the size and depth of delamination,the geometrical parameters and piezoelectric materials on the dynamic instability regions of the piezoelectric cylindrical shell are discussed.