Higher-order isogeometric thermal vibration analysis of functionally graded porous microplates interacting with an ideal fluid
Wei Chen, Ping Xiang, Peng Shi, Zhixiang Liu, Bo Deng
Abstract
Underwater plate structures are widely employed in various marine systems and may be subjected to prolonged exposure to high-temperature in environments such as deep-sea hydrothermal fields, oil and gas extraction, and heat exchange, which can significantly affect their properties. For the first time, this study establishes a computational framework based on isogeometric analysis (IGA), incorporating the modified couple stress theory (MCST) and higher-order shear deformation theory (HSDT), to investigate the thermal vibration characteristics of functionally graded porous (FGP) microplates immersed in an ideal fluid. The fluid flow is characterized as homogeneous, incompressible, zero-viscosity, and non-rotational, while interaction mechanisms between the porous microstructure and the fluid in both horizontal and vertical orientations are established. Temperature-dependent material properties are implemented through a power-law function across the microplate's thickness direction, with systematic evaluation of even and uneven porosity configurations subjected to uniform, linear, and nonlinear temperature gradients. Fluid-induced loading on the microplate surface, modeled via the velocity potential function and Bernoulli's principle, is formulated as virtual inertial mass terms in the governing equations derived through Hamilton's variational framework. The comparison of the results from the proposed method with publicly available data validates the model's convergence and accuracy. Parameter studies systematically evaluate the boundary conditions, temperature gradient form, material length scale, structural parameters (power-law index, porosity index, geometric dimensions), and fluid environment (density, level, immersion depth), demonstrating their significant impact on the free vibration of FGP microplates.