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Nonlinear free vibration analysis of functionally graded third-order shear deformable microbeams based on the modified strain gradient elasticity theory

Nonlinear ElasticityEngineeringMultiscale MechanicsMicromechanicsMechanicsMechanical EngineeringMaterial NonlinearitiesSolid MechanicsStructural MechanicsMechanical DeformationMechanics Of MaterialsNonlinear Vibration