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Beam & VibrationAll functions are free

Beam & Vibration

View deflections, bending moments, and foundation natural frequencies under concentrated loads.

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Euler–Bernoulli homogeneous rectangular beam with small deflection; simply supported central load or cantilever end load; no shear deformation. Analytical solution of

Beam & Vibration: uses and methods

View deflections, bending moments, and foundation natural frequencies under concentrated loads.

Applicable scope and calculation boundary

Euler–Bernoulli homogeneous rectangular beam with small deflection; simply supported central load or cantilever end load; no shear deformation. Analytical solution of

model and reference method

Euler–Bernoulli beam.

model version: 1.0.0. The results are used for scientific research, exploration and teaching, please interpret according to the model conditions.

input parameters

support and loading
simply supported · central load / Cantilever · End load
span(m)
Value range: 0.1 – 30
Section width(m)
Value range: 0.001 – 2
Section height(m)
Value range: 0.001 – 2
Young's modulus(GPa)
Value range: 0.01 – 1000
Density(kg/m³)
Value range: 1 – 25000
concentrated load(N)
Value range: 0 – 10000000

How to use

  1. Load the example or enter data that matches the field description.
  2. Confirm units and models, run calculations and check diagnostics.
  3. Export charts, tables or results packages and record model versions.

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FROM SCIENCE TO PRACTICE

commercial application case

Industry Application · Independent Reproduction Example

equipment bracket The

equipment design team compared the effects of beam span, load, and section stiffness on deflection.

Public industry reference: Ansys · Structural Analysis

Ansys structural analysis products are used for stress, deformation, and structural engineering verification.

View product or organization original information

on this site

  1. Confirm support boundary
  2. input E, I and load
  3. Compare bending moment and deflection

Deliverables

beam deflection and internal force diagram, used for preliminary screening of plans

needs to be checked before landing

does not cover connections, fatigue, buckling and three-dimensional local stresses。

case is compiled for public industry purposes, and the reproduction steps are independent examples of this site; it does not mean that the above-mentioned institutions use or endorse this site, nor does it cite customer benefits that have not been publicly verified. The

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recommended by universities and research institutions

Mechanical Engineering

The following is the recommended reading order of this website organized by direction relevance, public research resources and learning portals. The number is the serial number recommended by the editor, not QS, THE or paper measurement ranking; it does not represent the overall strength of the institution.

  1. 01

    MIT · Department of Mechanical Engineering

    United States The

    Mechanism design, robotics, mechanics and manufacturing。

    official website link accessibility check: 2026-10-03
  2. 02

    ETH Zürich · Department of Mechanical and Process Engineering

    Switzerland

    Robots, Mechanical Systems and Computational Mechanics。

    official website link accessibility check: 2026-10-03
  3. 03

    Fraunhofer IPA

    Germany

    Industrial automation, production engineering and robot transformation The。

    official website link accessibility check: 2026-10-03

catalog compiled on 2026-10-03. Link accessibility does not equate to verification of the latest papers, admissions, or program status; please check the institution's official website for specific research teams and opportunities.

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