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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Solutions to the undamped forced problem have unbounded displacements when the driving frequency matches a natural frequency , i.e., the beam can resonate. The natural frequencies of a beam therefore correspond to the frequencies at which resonance can occur.

  3. Natural frequency - Wikipedia

    en.wikipedia.org/wiki/Natural_frequency

    Natural frequency, measured in terms of eigenfrequency, is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency.

  4. Cantilever - Wikipedia

    en.wikipedia.org/wiki/Cantilever

    Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab. When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment. [1] Cantilever construction allows overhanging structures without additional support.

  5. Vibration fatigue - Wikipedia

    en.wikipedia.org/wiki/Vibration_fatigue

    First natural mode of a cantilever beam. Random excitation of the structure produces different responses, depending on the natural dynamics of the structure in question. Different natural modes get excited and each greatly affects the stress distribution in material.

  6. Structural engineering theory - Wikipedia

    en.wikipedia.org/wiki/Structural_engineering_theory

    The dynamic response of a structure to dynamic loads (the natural frequency of a structure) is also dependent on its stiffness. In a structure made up of multiple structural elements where the surface distributing the forces to the elements is rigid, the elements will carry loads in proportion to their relative stiffness - the stiffer an ...

  7. Modal analysis using FEM - Wikipedia

    en.wikipedia.org/wiki/Modal_analysis_using_FEM

    The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration.It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the calculations are acceptable.

  8. Normal mode - Wikipedia

    en.wikipedia.org/wiki/Normal_mode

    A mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of half waves in the vibration. For example, if a vibrating beam with both ends pinned displayed a mode shape of half of a sine wave (one peak on the vibrating beam) it would be vibrating in mode 1.

  9. Unified framework - Wikipedia

    en.wikipedia.org/wiki/Unified_Framework

    Unified framework is a general formulation which yields n th - order expressions giving mode shapes and natural frequencies for damaged elastic structures such as rods, beams, plates, and shells. The formulation is applicable to structures with any shape of damage or those having more than one area of damage.