Since 1963
ARTICLE
The 1/3rd subharmonic and 3rd superharmonic resonance of a shape memory alloy (SMA) laminated beam
1
Department of Civil Engineering, Hebei Jiaotong Vocational and Technical College, Shijiazhuang, China
2
College of Mechanical and Electronical Engineering, Shandong Agriculture University, Taian, China
3
Tianjin Key Laboratory of Microgravity and Hypogravity Environment Simulation Technology, Tianjin, China
4
College of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China
Submission date: 2019-05-21
Final revision date: 2020-01-06
Acceptance date: 2020-08-20
Online publication date: 2020-11-06
Publication date: 2021-01-15
Corresponding author
Journal of Theoretical and Applied Mechanics 2021;59(1):27-41
KEYWORDS
TOPICS
stability and vibrations systemsdynamics of machines, vehicles and flying structuresmechanics of composites
ABSTRACT
This paper examines the 1/3rd subharmonic resonance and the 3rd superharmonic resonance
of simply-supported shape memory alloy (SMA) laminated beams. First, the dynamic equation
for SMA laminated beams under transverse load is established using physical equations,
force equilibrium conditions, the compatibility equation of deformation, and a constitutive
model of SMA polynomial functions. Then, a differential equation for transverse vibration
of the SMA laminated beams is derived by the Galerkin process assuming the boundary
conditions for simply-supported beams. Next, the amplitude-frequency response equations
for the 1/3rd subharmonic resonance and the 3rd superharmonic resonance of these beams
are derived by an averaging method before their respective transition sets are calculated,
and their amplitude-frequency response diagrams were plotted using singularity theory. The
results show two different types of amplitude-frequency responses to nonlinear vibration
under the 1/3rd subharmonic resonance and the 3rd superharmonic resonance: quasi-linear
and hard characteristic. In the quasi-linear area, SMA thickness A does not make much
difference to the response of the system, whereas in the hard-characteristics area, under the
same excitation amplitude f, the resonance frequency increases with A. In the nonlinear
area, SMA can obviously reduce vibration amplitude, but it is not obvious for the 1/3rd
subharmonic resonance. The nonlinear solution of both the 1/3rd subharmonic resonance
and 3rd superharmonic resonance are stable.
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| eISSN: | 2543-6309 |
| ISSN: | 1429-2955 |
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