Normal Form;
Hopf Bifurcation;
European Physical Journal Special Topic;
Cantilever Beam;
Load Resistance;
D O I:
10.1140/epjst/e2013-01940-x
中图分类号:
O4 [物理学];
学科分类号:
0702 ;
摘要:
The normal form is proposed as a tool to analyze the performance and reliability of galloping-based piezoaeroelastic energy harvesters. Two different harvesting systems are considered. The first system consists of a tip mass prismatic structure (isosceles 30A degrees or square cross-section geometry) attached to a multilayered cantilever beam. The only source of nonlinearity in this system is the aerodynamic nonlinearity. The second system consists of an equilateral triangle cross-section bar attached to two cantilever beams. This system is designed to have structural and aerodynamic nonlinearities. The coupled governing equations for the structure's transverse displacement and the generated voltage are derived and analyzed for both systems. The effects of the electrical load resistance and the type of harvester on the onset speed of galloping are quantified. The results show that the onset speed of galloping is strongly affected by the load resistance for both types of harvesters. The normal form of the dynamic system near the onset of galloping (Hopf bifurcation) is then derived. Based on the nonlinear normal form, it is demonstrated that smaller levels of generated voltage or power are obtained for higher absolute values of the effective nonlinearity. For the first harvesting system, the results show a supercritical Hopf bifurcation for both isosceles 30A degrees or square cross-section geometries. The nonlinear normal form shows that the isosceles triangle section (30A degrees) is more efficient than the square section. For the second harvesting system, the normal form is used to identify the values of the nonlinear torsional spring which changes the harvester's instability. It is demonstrated that this critical value of the nonlinear torsional spring depends strongly on the load resistance.
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, A.
;
Hajj, M. R.
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机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Hajj, M. R.
;
Nayfeh, A. H.
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h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, A.
;
Nayfeh, A. H.
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h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Nayfeh, A. H.
;
Hajj, M. R.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, Abdessattar
;
Hajj, Muhammad R.
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h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Hajj, Muhammad R.
;
Nayfeh, Ali H.
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h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, A.
;
Hajj, M. R.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Hajj, M. R.
;
Nayfeh, A. H.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, A.
;
Nayfeh, A. H.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Nayfeh, A. H.
;
Hajj, M. R.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Abdelkefi, Abdessattar
;
Hajj, Muhammad R.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA
Hajj, Muhammad R.
;
Nayfeh, Ali H.
论文数: 0引用数: 0
h-index: 0
机构:
Virginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USAVirginia Polytech Inst & State Univ, Dept Engn Sci & Mech, Blacksburg, VA 24061 USA