功能梯度电活性软管中的非线性响应和轴对称波传播
Nonlinear response and axisymmetric wave propagation in functionally graded soft electro-active tubes
摘要：
软电活性（SEA）材料可以设计和制造成在其材料特性中具有梯度，以修改和潜在地改善其在使用中的机械响应。在这里，我们调查的非线性响应，和轴对称波在一个软圆管的功能梯度SEA材料制成，并受到几个偏置场，包括轴向预拉伸，内部/外部压力，和通过厚度的电压。我们取材料的能量密度函数为Mooney-Rivlin理想介电类型，材料参数沿径向线性变化。我们采用非线性电弹性的一般理论，明确地获得的非线性响应的管的外施加的电场。为了研究非均匀偏置场下的波传播，我们在状态空间形式主义中建立了增量运动方程。本文采用层合板近似方法，导出了小振幅扭转波和小振幅纵波叠加在弹性变形状态下的解析频散关系。综合的数值结果表明，材料梯度和偏置场有显着的影响的静态非线性响应和轴对称波在管中的传播。这项研究奠定了基础，设计SEA致动器具有更好的性能，定制可调SEA波导，并表征非破坏性功能梯度管状结构。
英文摘要：
Soft electro-active (SEA) materials can be designed and manufactured with gradients in their material properties, to modify and potentially improve their mechanical response in service. Here, we investigate the nonlinear response of, and axisymmetric wave propagation in a soft circular tube made of a functionally graded SEA material and subject to several biasing fields, including axial pre-stretch, internal/external pressure, and through-thickness electric voltage. We take the energy density function of the material to be of the Mooney-Rivlin ideal dielectric type, with material parameters changing linearly along the radial direction. We employ the general theory of nonlinear electro-elasticity to obtain explicitly the nonlinear response of the tube to the applied fields. To study wave propagation under inhomogeneous biasing fields, we formulate the incremental equations of motion within the state-space formalism. We adopt the approximate laminate technique to derive the analytical dispersion relations for the small-amplitude torsional and longitudinal waves superimposed on a finitely deformed state. Comprehensive numerical results then illustrate that the material gradients and biasing fields have significant influences on the static nonlinear response and on the axisymmetric wave propagation in the tube. This study lays the groundwork for designing SEA actuators with improved performance, for tailoring tunable SEA waveguides, and for characterizing non-destructively functionally graded tubular structures.
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