Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory
Л. В. Курпа, Jan Awrejcewicz, Olga Mazur, Iryna Morachkovska
Abstract
Abstract Free vibrations of the orthotropic micro/nanoplate with nonclassical shape are investigated. The considered model is based on the nonlocal elasticity theory. The developed method uses the Ritz method as well as R-function theory for the construction of the system of coordinate functions. The linear frequencies are obtained for a rectangular plate with two cutouts on opposite sides, while the boundary conditions are considered of several types, including simply supported and clamped edges. The small-scale effects for various sizes of cutouts are discussed.
Topics & Concepts
Orthotropic materialSolid mechanicsElasticity (physics)VibrationRitz methodBoundary value problemLength scalePlate theoryVibration of platesMathematical analysisMathematicsClassical mechanicsPhysicsMechanicsMaterials scienceStructural engineeringComposite materialAcousticsEngineeringFinite element methodNonlocal and gradient elasticity in micro/nano structuresComposite Structure Analysis and OptimizationNumerical methods in engineering