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Related Concept Videos

Angle of Twist: Problem Solving01:13

Angle of Twist: Problem Solving

266
An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
266
Angle of Twist - Elastic Range01:13

Angle of Twist - Elastic Range

278
Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
278
Unsymmetric Bending01:18

Unsymmetric Bending

319
Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
319
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

283
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
283
Torsion of Noncircular Members01:16

Torsion of Noncircular Members

129
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
129
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

163
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Related Experiment Video

Updated: Jun 12, 2025

Magnetic Tweezers for the Measurement of Twist and Torque
11:41

Magnetic Tweezers for the Measurement of Twist and Torque

Published on: May 19, 2014

23.2K

Isochronous bifurcations in a two-parameter twist map.

Michele Mugnaine1, Bruno B Leal1, Iberê L Caldas1

  • 1<a href="https://ror.org/036rp1748">Institute of Physics</a>, <a href="https://ror.org/036rp1748">University of São Paulo</a>, São Paulo, SP, Brazil.

Physical Review. E
|September 19, 2024
PubMed
Summary
This summary is machine-generated.

Isochronous islands in Hamiltonian systems change with perturbation amplitude. Transitions between island chains occur via pitchfork and saddle-node bifurcations, with destruction always happening through pitchfork bifurcations.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Mathematical physics

Background:

  • Isochronous islands arise in phase space of twist Hamiltonian systems due to multiple resonant perturbations.
  • The Poincaré-Birkhoff theorem dictates island number based on system and perturbation characteristics.

Purpose of the Study:

  • To analyze modifications in island chains of the two-parameter standard map (two-harmonic standard map) as perturbation amplitude increases.
  • To identify transition routes between island chains associated with different harmonics.

Main Methods:

  • Analysis of the two-parameter standard map.
  • Investigation of island chain evolution with increasing perturbation amplitude.
  • Identification of bifurcation routes (pitchfork and saddle-node).

Main Results:

  • Three distinct routes for transitions between harmonic-associated island chains were identified.
  • Intermediate island chain configurations were observed during these transitions.
  • Island destruction consistently occurs via pitchfork bifurcation.

Conclusions:

  • The study elucidates the complex dynamics of isochronous islands in the two-parameter standard map.
  • Bifurcation analysis reveals specific pathways for island chain evolution and destruction.
  • Findings contribute to understanding phase space structure in perturbed Hamiltonian systems.