Semi-analytical stability behavior of composite concrete structures via modified non-classical theories

Luxin He , Mostafa Habibi , Majid Khorami

Abstract

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotaing nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and amilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

Key Words

beam theory; bending vibration; forced vibration; rotating; stability analysis; time dependent analysis; tube theory

Address

(1) Luxin He — Beijing No. 5 Construction Engineering Group Co., Ltd.Beijing,100028, China
(2) Mostafa Habibi — Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai 600 077, India
(3) Mostafa Habibi, Majid Khorami — UTE University, Faculty of Architecture and Urbanism, Architecture Department, Calle Rumipamba S/N and Bourgeois, Quito, Ecuador
(4) Mostafa Habibi — Department of Mechanical Engineering, Faculty of Engineering, Haliç University, 34060, Istanbul, Turkey
(5) Mostafa Habibi — Institute of Research and Development, Duy Tan University, Da Nang 550000, Viet Nam.

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