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On the Dynamics of Elastic Strips
 J. Nonlinear Sci
, 1999
"... The dynamics of elastic strips, i.e. long thin rods with noncircular crosssection, is analyzed by studying the solutions of the appropriate Kirchho# equations. First, it is shown that if a naturally straight strip is deformed into a helix, the only equilibrium helical configurations are those with ..."
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Cited by 8 (4 self)
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The dynamics of elastic strips, i.e. long thin rods with noncircular crosssection, is analyzed by studying the solutions of the appropriate Kirchho# equations. First, it is shown that if a naturally straight strip is deformed into a helix, the only equilibrium helical configurations are those with no internal twist and whose principal bending direction is either along the normal or the binormal. Second, the linear stability of a straight twisted strip under tension is analyzed showing the possibility of both pitchfork and Hopf bifurcations depending on the external and geometric constraints. Third, nonlinear amplitude equations are derived describing the dynamics close to the di#erent bifurcation regimes. Finally, special analytical solutions to these equations are used to describe the buckling of strips. In particular, finitelength solutions with a variety of boundary conditions are considered. KEYWORDS: Elastic Strips, Amplitude Equations, Localized solutions RUNNING TITLE: Dynami...
Biomimetic Propulsion for a Swimming Surgical Microrobot
 Proceedings of the 2004 IEEE International Conference on Intelligent Robots and System
, 2003
"... Abstract A surgical microrobot that swims inside the human ureter is proposed to provide a novel and minimally invasive method of kidney stone destruction. Inspired by the swimming mechanisms of bacteria such as E. coli, the robot utilizes biomimetic synthetic flagella composed of multiwalled car ..."
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Cited by 4 (2 self)
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Abstract A surgical microrobot that swims inside the human ureter is proposed to provide a novel and minimally invasive method of kidney stone destruction. Inspired by the swimming mechanisms of bacteria such as E. coli, the robot utilizes biomimetic synthetic flagella composed of multiwalled carbon nanotubes that are driven into a rotating helical shape by a micro motor. Design aspects are discussed with the focus on locomotion. The performance of the propulsion mechanism is determined through simultaneous modeling of the viscous drag on the filaments and the stress strain behavior of the nanotubes. The effects of the synthetic flagellum geometry and frequency of rotation on efficiency and swimming speed are explored. With 1nW of power, utilizing 100 Plong filaments, swimming speeds approaching 1 mm/s are shown to be possible for a realistic design. The proposed new robot would revolutionize kidney stone destruction if implemented, yet the design of the robot and the propulsion analysis are applicable to many other possible surgical procedures. I.
Kovalevskaya rods and Kovalevskaya waves
, 2000
"... The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular crosssections. In this paper the Kirchhoff analogy is further generalized to show that the c ..."
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Cited by 2 (1 self)
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The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular crosssections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution of the Kirchhoff model for thin elastic rod with anisotropic crosssections (elastic strips). These Kovalevskaya rods are completely integrable and are part of a family of integrable traveling waves solutions for the rod (Kovalevskaya waves). The analysis of homoclinic twistless Kovalevskaya rod reveals the existence of a three parameter family of solutions corresponding to the Steklov and Bobylev integrable case of the rigid body problem. Furthermore, the existence of these integrable solutions is discussed in conjunction with recent results on the stability of strips.
Dynamics of charged molecular strands
, 2009
"... EulerPoincaré equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the equations of motion for the dynamics of such molecular strands are ..."
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EulerPoincaré equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the equations of motion for the dynamics of such molecular strands are nonlocal when the screened Coulomb interactions, or LennardJones potentials between pairs of charges are included. These nonlocal dynamical equations are derived in the convective representation of continuum motion by using modified EulerPoincaré and HamiltonPontryagin variational formulations that illuminate the various approaches within the framework of symmetry reduction of Hamilton’s principle for exact geometric rods. In the absence of nonlocal interactions, the equations recover the classical Kirchhoff theory of elastic rods in the spatial representation. The motion equations in the convective representation are shown to be affine EulerPoincaré equations relative to a certain cocycle. This property relates the geometry of the molecular strands to that of complex fluids. An
Nonlinear Euler buckling
, 2008
"... The buckling of hyperelastic incompressible cylindrical shells of arbitrary length and thickness under axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are obtained using the Stroh formalism and the exact solution of Wilkes [Q. J ..."
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The buckling of hyperelastic incompressible cylindrical shells of arbitrary length and thickness under axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are obtained using the Stroh formalism and the exact solution of Wilkes [Q. J. Mech. Appl. Math. 8:88–100, 1955] for the linearized problem. The main focus of this paper is the range of validity of the Euler buckling formula and its first nonlinear corrections that are obtained for thirdorder elasticity. 1