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Research Papers

Ultraviolet-Activated Frequency Control of Beams and Plates Based on Isogeometric Analysis

[+] Author and Article Information
Yujie Guo

Interdisciplinary Research Institute of Aeronautics and
Astronautics,
College of Aerospace Engineering,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: yujieguo@nuaa.edu.cn

Hornsen Tzou

Fellow ASME
Interdisciplinary Research Institute of Aeronautics
and Astronautics,
College of Aerospace Engineering,
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: hstzou@nuaa.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 28, 2017; final manuscript received December 18, 2017; published online February 9, 2018. Assoc. Editor: Matthew Brake.

J. Vib. Acoust 140(3), 031013 (Feb 09, 2018) (11 pages) Paper No: VIB-17-1285; doi: 10.1115/1.4038948 History: Received June 28, 2017; Revised December 18, 2017

A new light-activated shape memory polymer (LaSMP) smart material exhibits shape memory behaviors and stiffness variation via ultraviolet (UV) light exposures. This dynamic stiffness provides a new noncontact actuation mechanism for engineering structures. Isogeometric analysis (IGA) utilizes high order and high continuity nonuniform rational B-spline (NURBS) as basis functions which naturally fulfills C1-continuity requirement of Euler–Bernoulli beam and Kirchhoff plate theories. Compared with the traditional finite elements of beams and plates, IGA does not need extra rotational degrees-of-freedom while providing accurate results. The UV light-activated frequency control of LaSMP fully and partially laminated beam and plate structures based on the IGA is presented in this study. For the analysis of LaSMP partially laminated plates, the finite cell approach in the framework of IGA is proposed to handle NURBS geometries containing trimming features. The accuracy and efficiency of the proposed isogeometric approach are demonstrated via several numerical examples in frequency control. The results show that, with LaSMPs, broadband frequency control of beam and plate structures can be realized. Furthermore, changing LaSMP patch sizes on beams and plates further broadens its frequency control ranges. Studies suggest that: (1) the newly developed IGA combining finite cell approach is an effective numerical tool and (2) the maximum frequency manipulation ratios of beam and plate structures, respectively, reach 24.30% and 16.75%, which demonstrates the feasibility of LaSMPs-induced vibration control of structures.

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Figures

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Fig. 1

One-dimensional cubic B-spline shape functions Ni,3(i = 1,…,7) across an open knot vector of four knot-span elements

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Fig. 2

Beam cross section with LaSMP layers

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Fig. 3

A stepped LaSMP laminated beam

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Fig. 4

Coupling constraints between LaSMP and elastic beams

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Fig. 5

Plate illustration, (a) plate partially covered with LaSMP patches and (b) stacking sequence in the thickness direction

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Fig. 6

Two patches model of LaSMP partially laminated plate in the framework of IGA

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Fig. 7

The concept of trimming in CAD, (a) NURBS surface patch with trimming curve and (b) corresponding trimming curve defined in the parametric space of the NURBS surface, leaving the trimmed area untouched

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Fig. 8

Principle of the finite cell method for trimmed domains, (a) trimmed, discretized NURBS structure, (b) true physical analysis domain with boundary conditions along the domain boundary Γand(c)fictitiousextensiondomainwithzeroNeumannboundaryconditions∂Ω=0

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Fig. 9

The finite cell approach for a trimmed element: subcells aggregate quadrature points along the trimming curve in the parameter space

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Fig. 10

Segmentwise integration of coupling constraints between two trimmed patches

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Fig. 11

Convergence of the LaSMP laminated beam before laser exposure, (a) quadratic NURBS basis (p = 2) and (b) cubic NURBS basis (p = 3)

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Fig. 12

Variations of natural frequencies of the beam with various LaSMP lengths (L/5, 2L/5, 3L/5, 4L/5, and L) during exposures: (a) mode 1, (b) mode 2, and (c) mode 3

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Fig. 13

Variations of natural frequencies of the beam with different LaSMP patch length before and after light exposures: (a) mode 1, (b) mode 2, and (c) mode 3

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Fig. 14

Convergence of the LaSMP laminated plate before laser exposure: (a) quadratic NURBS basis and (b) cubic NURBS basis

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Fig. 15

Variations of natural frequencies of the plate with various LaSMP sizes (L1/L = W1/W = 2/7, 3/7, 4/7, 5/7, and 1) during exposures: (a) mode (1,1), (b) mode (2,1), (c) mode (3,1), and (d) mode (1,2)

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Fig. 16

Variations of natural frequencies of the plate with different LaSMP patch size before and after light exposures: (a) mode (1,1), (b) mode (2,1), (c) mode (3,1), and (d) mode (1,2)

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