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Related Concept Videos

Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

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The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
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Beams with Unsymmetric Loadings01:17

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Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
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Design of Prismatic Beams for Bending01:23

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

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A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by...
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Saint-Venant's Principle01:18

Saint-Venant's Principle

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The principle of Saint-Venant postulates that the stress distribution within a structural member does not rely on the precise method of load application except in the vicinity of the load application points. Consider a scenario where loads are centrally applied on two plates. In this case, the plates move toward each other without any rotation. This movement causes the member to contract in length and expand in width and thickness. Uniform deformation across all elements and maintaining...
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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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Updated: Jul 11, 2025

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
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Variational iteration method for the nanobeams-based N/MEMS system.

Wei Tang1, Naveed Anjum2, Ji-Huan He3

  • 1Suzhou International Foreign Language School, Suzhou 215131, China.

Methodsx
|November 13, 2023
PubMed
Summary
This summary is machine-generated.

The variational iteration method accurately predicts nano/microelectromechanical system (N/MEMS) dynamic behavior. This method offers a new way to optimize N/MEMS by understanding their periodic motion and preventing pull-in instability.

Keywords:
Amplitude-frequency relationshipElzaki transformElzaki transform-based variational iteration methodN/MEMSNonlinear oscillatorVariational iteration method

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Area of Science:

  • Mechanical Engineering
  • Nanotechnology
  • Applied Physics

Background:

  • Nano/microelectromechanical systems (N/MEMS) are crucial in advanced technologies like sensors and aerospace.
  • Pull-in instability limits N/MEMS reliability under large forces.
  • Accurate prediction of periodic motion is essential for N/MEMS operation.

Purpose of the Study:

  • To demonstrate the variational iteration method's (VIM) applicability for predicting N/MEMS dynamic behavior.
  • To analyze the periodic properties of a nanobeam-based N/MEMS with van der Waals forces.
  • To provide a method for fast and accurate N/MEMS property prediction.

Main Methods:

  • Euler-Bernoulli beam principle used to derive the governing equation, including midplane stretching.
  • Galerkin technique applied to convert the partial differential equation into a nonlinear ordinary differential equation.
  • Variational iteration method (VIM) employed for solving the nonlinear equation and analyzing system properties.

Main Results:

  • The VIM accurately elucidates the dynamic and periodic properties of the N/MEMS.
  • The study successfully applied VIM to a nonlinear N/MEMS model derived from fundamental principles.
  • The results demonstrate VIM's effectiveness for complex N/MEMS dynamics.

Conclusions:

  • The variational iteration method provides an effective approach for analyzing N/MEMS.
  • This study offers a pathway for optimizing N/MEMS design and performance.
  • The findings are valuable for ensuring reliable operation of N/MEMS devices.