Vol. 14, No. 2, 2019

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Dynamic analysis of a mass traveling on a simply supported nonhomogeneous beam composed of transversely embedded periodic arrays

Yi-Ming Wang and Hung-Chieh Liu

Vol. 14 (2019), No. 2, 237–257
Abstract

Periodically embedded specified materials and laminas into the beam of a beam-mass system to form a stiffness-driven nonhomogeneous beam having the potential to shift its specific stiffness to avoid the happening of large amplitude vibration and resonance is worthy of note. However, if the arrangement of composed materials and layers of the beam is changed, the developed model generally has to be reestablished. To propose a model that can be used to analyze beams consisting of different assemblies of materials and laminas is of great importance. Another point is using specified materials and laminas, which are periodically embedded into a beam to form transversely periodic arrays, to make the beam have the capability to change its specific stiffness to satisfy designing requirement. The Fourier-series based approach is employed to take into account the periodicity of material properties and matching conditions across laminas’ interfaces. The influence produced by the arrays to the dynamics of the system is examined.

Result shows that the axial Young’s modulus and density of the proposed beam are biaxial periodic functions. Different arrangements of embedded arrays bring different stiffness shifting potential of the beam to reduce the vibration of the system. With proper choice of the stiffness and thickness ratios between the arrays and basic layers, the growth of small amplitude vibration into large motion regime can be attenuated. Meanwhile, by changing the thickness ratios in the width and height directions, there exist seven possible compositions of the beam. It discloses that despite without considering the material damping, the proposed beam still has good ability to diminish the beam vibration even after the mass left the beam.

Keywords
transversely periodic arrays, stiffness-driven beam, Fourier series, thickness ratio
Milestones
Received: 23 June 2018
Revised: 28 January 2019
Accepted: 18 April 2019
Published: 26 July 2019
Authors
Yi-Ming Wang
Department of Mechatronics Engineering
National Changhua University of Education
2 Shih-Ta Road
Changhua 500
Taiwan
Hung-Chieh Liu
Department of Mechatronics Engineering
National Changhua University of Education
2 Shih-Ta Road
Changhua 500
Taiwan