局部主动约束阻尼开球壳的振动特性分析

Vibration characteristic analysis of opening spherical shell with local active constrained layer damping

摘要:

为了有效减小开球壳的振动,对球壳设置局部主动约束阻尼 (ACLD),根据一阶剪切变形理论和Donnell壳体理论得出应变位移关系,用Jacobian多项式和Fourier级数组合表征球壳经度和纬度方向变形关系,基于能量法和Lagrange方程建立了系统的动力学模型,研究了主动约束阻尼结构参数、阻尼层占空比和压电层激励电压对模态频率和阻尼比的影响,对不同固定幅值激励电压下球壳中点的频域响应进行了比较。结果表明:合理设置粘弹性厚度和占空比可有效耗散球壳振动能量；压电层经纬度方向尺寸增大可有效增大系统阻尼比,但会使系统引入质量和模态频率大幅增加,影响球壳的使用性能；施加激励电压能够在几乎不改变模态频率的情况下增加系统的振动能耗,但一定幅值的激励电压仅对特定方向的模态幅值能够实现有效缩减。

Abstract:

To reduce the vibration of the opening spherical shell, this paper proposes a kind of spherical shell with local active constrained layer damping (ACLD). Based on the first-order shear deformation theory and the Donnell shell theory, the strain is expressed as a function of displacement. The spherical shell deformation is represented by the expansions of Jacobian polynomials in latitude direction and Fourier functions in the longitude direction. The system dynamics model is established by use of the energy method and Lagrange equation. The effects of the structure parameters of ACLD, damping layer duty ratio and excitation voltage of piezoelectric layer on modal frequency and damping ratio are studied and the frequency response of the mid-point of the spherical shell is compared under different excitation voltages. The results show that the proper viscoelastic thickness and duty ratio can dissipate the vibration energy of spherical shell effectively. The large size of the piezoelectric layer in the latitude and longitude direction can generate big damping ratio of the system but it will make the mass and modal frequency grow so fast that the performance of the spherical shell is destroyed. The application of excitation voltage can promote the dissipation of vibration energy almost without changing the modal frequency. However, a certain excitation voltage can be effectively only for reduction of the modal amplitude in a specific direction.