湿热条件下具脱层压电梁的非线性动力响应

Nonlinear Dynamic Response of Piezoelectric Beam with Delamination under Hygrothermal Conditions

摘要: 基于非线性梁及压电理论，建立了湿热条件下考虑接触效应的具脱层压电梁的非线性运动控制方程。通过引入假想弹簧所算得的接触力对系统的横向振动控制方程进行修正，从而有效地避免了脱层之间的相互贯穿，并且给出了假想弹簧系数的计算式。整个问题采用有限差分法进行求解，算例中，详细讨论了电压、温度、湿度、脱层长度、深度及外载荷幅值等因素对具脱层压电梁非线性动力响应的影响。结果表明：正的控制电压可使脱层压电梁的振动幅值增大，而负的控制电压可使脱层压电梁的振动幅值减小；随着温度和湿度的增加，压电梁振动幅值增大；当脱层越长、越靠近梁外表面以及横向外载荷越大时，脱层压电梁在振动过程中达到的幅值也越大。

Abstract: On the basis of the nonlinear beam and piezoelectric theory, the governing equations of motion for piezoelectric beam with arbitrary delamination were derived. The governing equation of transverse motion was modified by contact force which is calculated through introducing into the assumed spring and thus the penetration between two delaminated layers could be avoided. Moreover, the formulation for calculating the coefficient of artificial spring is presented. The whole problem was resolved by using the finite difference method. In calculation examples, the effects of piezoelectricity, hygrothermal condition, delamination length, depth and amplitude of load on the nonlinear dynamic response of the piezoelectric beam with delamination were discussed in detail. Numerical results show that the vibration amplitude of piezoelectric beam with delamination in-creases under positive control voltage and decreases under negative voltage, and it also increases with the increase of temperature, humidity, delamination length and mechanical load.