The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.

Issue Section:
Technical Papers
Topics:
Construction, Corners (Structural elements), Manifolds, Nonlinear dynamics, Simulation results, Stability
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3.
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4.
Hogan
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1071
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Hogan
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The Effect of Damping on Rigid Block Motion under Harmonic Forcing
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7.
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, and
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,
1993
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Free Rocking of Prismatic Blocks
,”
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119
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1410
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8.
Shenton
H. W.
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1991
a, “
Base Excitation of Rigid Bodies. I. Formulation
,”
Journal of Engineering Mechanics, ASCE
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2306
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9.
Shenton
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Jones
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1991
b, “
Base Excitation of Rigid Bodies. II. Periodic Slide-rock Response
,”
Journal of Engineering Mechanics, ASCE
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2307
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2328
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10.
Spanos
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Koh
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,
1984
, “
Rocking of Rigid Blocks due to Harmonic Shaking
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Journal of Engineering Mechanics, ASCE
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110
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1627
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1642
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11.
Tso
W. K.
, and
Wong
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,
1989
a, “
Steady-state Rocking Response of Rigid Blocks, Part I
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Earthquake Engineering and Structural Dynamics
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18
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109
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12.
Tso
W. K.
, and
Wong
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,
1989
b, “
Steady-state Rocking Response of Rigid Blocks, Part II
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Earthquake Engineering and Structural Dynamics
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18
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110
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120
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13.
Wiggins
S.
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On the Detection and Dynamical Consequences of Orbits Homoclinic to Hyperbolic Periodic Orbits and Normally Hyperbolic Invariant Tori in a Class of Ordinary Differential Equations
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285
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14.
Wiggins, S., 1990, Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York.
15.
Wiggins, S., 1992, Chaotic Transport in Dynamical Systems, Springer-Verlag, New York.
16.
Yim
S. C. S.
, and
Lin
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,
1991
, “
Nonlinear Impact and Chaotic Response of Slender Rocking Objects
,”
Journal of Engineering Mechanics
, ASCE, Vol.
117
, pp.
2079
–
2100
.
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