Isogeometric analysis approach for vibration of tridirectional functionally graded porous plate in high-temperature environment taking into account initial geometrical imperfections

This research investigates the application of the isogeometric analysis (IGA) method, grounded in higher-order shear plate theory, to examine the free vibrations of a tridirectional functionally graded porous (TFGP) plate. The analysis incorporates initial geometrical imperfections and considers the effects of a high-temperature environment while the plate is supported by an elastic foundation. The distribution of symmetric and asymmetric materials adheres to a power law across the three dimensions of the Cartesian coordinate system under consideration. Transcendental functions are employed to articulate two categories of geometric imperfections: cosine-type global/localized imperfections, which are modeled using hyperbolic and cosine functions, and sine-type imperfections, characterized by global eccentricity/symmetry, represented through sine and exponential functions. The amalgamation of various materials imparts numerous essential mechanical properties to the structure, thereby facilitating its application across diverse scientific disciplines. The precision of the method is validated through numerical comparisons with other credible analytical publications or established numerical techniques. A thorough numerical investigation is presented to examine the mechanisms by which material distribution patterns, geometrical imperfection modes, and various boundary conditions affect the natural oscillations of TFGP plates, while also considering initial geometrical imperfections in high-temperature environments. In practical applications involving structures with defects, this study serves a crucial function in the referencing, examination, and computation of such structures.