Vibration of elastically supported bidirectional functionally graded sandwich Timoshenko beams on an elastic foundation

Wei-Ren Chen, Liu-Ho Chiu and Chien-Hung Lin

Abstract

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

Key Words

BDFG sandwich beams; Chebyshev collocation method; foundation; gradient index; natural frequency; support spring; thickness ratio

Address

Wei-Ren Chen: Department of Mechanical Engineering, Chinese Culture University, Taipei 11114, Taiwan Liu-Ho Chiu: Department of Mechanical and Materials Engineering, Tatung University, Taipei 104, Taiwan Chien-Hung Lin: Department of Mechanical Engineering, Chinese Culture University, Taipei 11114, Taiwan

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