波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风...波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。展开更多
This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuato...This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.展开更多
文摘波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。
文摘This study proposes a three-dimensional(3D)coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations.The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations,the 3D divergence equation for magnetic induction,and the 3D divergence equation for the electric displacement.The proposed solution involves the exponential matrix in the thickness direction and primary variables’harmonic forms in the in-plane ones.A closed-form solution is performed considering simply-supported boundary conditions.Interlaminar continuity conditions are imposed for displacements,magnetic potential,electric potential,transverse shear/normal stresses,transverse normal magnetic induction and transverse normal electric displacement.Therefore,a layerwise approach is adopted.The results section is composed of an assessment part,where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part.Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios.Tabular and graphical results are presented for displacements,stresses,magnetic potential,electric potential,transverse normal magnetic induction and transverse normal electric displacement.For each presented benchmark,magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.
