Isogeometric Analysis of Bi-directional Functionally Graded Porous Micro-beam with Geometrical Imperfections Using Nonlocal Strain Gradient Theory.

Background: Micro structures are gaining prominence in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS). Nonetheless, numerous studies have revealed discrepancies between experimental observations of microstructure mechanical properties and simulation out comes derived from classical continuum theory. Recently, the bi-directional functionally graded microbeams have attracted wide attention from scholars as a new form of material. Purpose: A free vibration of bi-directional functionally graded porous microbeams with geometric imperfections is presented considering the influence of FG power index (n_x, n_z), boundary condition, geometric imperfection mode, nonlocal parameter and characteristic length. Method: In the present work, an isogeometric analysis formulation in the framework of nonlocal strain gradient theory is developed to investigate the free vibration characteristics of bi-directional FG porous micro-beams with geometrical imperfections. Porosity, FG power index, boundary condition, and size parameters can all be taken into account to determine the vibration behavior of a bi-directional FG porous microbeam with various geometric imperfections. Results: The non-dimensional frequencies of bi-directional functionally graded microbeam are studied based on the variations in crucial parameters such as porosity, FG power index (n_x, n_z), boundary condition, geometric imperfection mode, nonlocal parameter, and characteristic length. Conclusions: The study finds that strain gradient parameter has a greater impact on vibration than non-local parameter, and the influence of porosity distribution on vibration is more pronounced for even porosity. Geometric imperfections significantly affect vibration, with sine and G1 modes being most sensitive to imperfection amplitude. Applications: These findings demonstrate the importance of considering multiple factors for analyzing the vibration characteristics of bi-directional Functionally graded microbeams with geometrical imperfections in practical engineering applications. [ABSTRACT FROM AUTHOR]