Mode Shapes Calculator v1

Price: £20.00 (£20.00 Inc. VAT)
Mode shape database


A mode shape is the profile a member adopts when it is vibrated. The distance between adjacent nodes and the amplitude of the mode defines a stress cycle and range, which must be addressed for fatigue. If the vibration coincides with the beam's natural frequency the mode shape may become unstable and result in failure.

An example of what can occur if the natural frequency of a beam or structure coincides with the forces exciting the vibration is the failure of the Broughton Suspension Bridge over the River Irwell (1831) where soldiers marching 'in-step' probably induced vibrations that matched the bridge span’s natural frequency and the reason why soldiers now 'break-step' when marching over a bridge. If the bridge's support spacing or its structural stiffness were different this incident would probably not have occurred.

This problem can also occur in any pipe, beam or structure spanning a gap that is exposed to free flowing or gusty fluid (air or water), or attached to vibrating equipment. The consequences of a structural failure of this type can be at worst; devastating and at best; expensive.


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Mode Shapes calculates the deflection and natural frequency of a beam, that can be any long member such as a shaped section, a pipe, a bar, a rod etc., vibrating between guided, pinned and/or clamped (fixed) supports.

The mode shapes calculator limits the number of modes that can be computed to 1000

The mode shapes calculator can be used to ensure that a beam’s natural frequency does not coincide with:

1) a sensitive piece of vibrating equipment
(see CalQlata's Engineering Basics, Rotary Balancing, Vibration Damping, Shafts calculators), or

2) the effects of a fluid flowing across it
(see CalQlata's Vortex Shedding)

For help using this calculator see Technical Help

Mode Shapes Calculator - Options

For all of the calculation options, the input and output data are as follows:

You enter: and the mode shapes calculator will provide:
  • Number of modes
  • Unsupported length
  • Representative dimension
  • Mass (per unit length)
  • Bending stiffness (k or EI)
  • Damping ratio
  • Induced frequency
  • Wavelengths (end and middle modes)
  • Maximum expected resonance amplitudes
  • Maximum expected static deflections
  • Natural frequencies
  • Mode shape parameters
  • Maximum dynamic bending moments
  • Maximum lift acceleration at ʄn


Both ends of the beam have fixed supports.


One end of the beam has a fixed support and the other end has a guided support.


Both ends of the beam have guided supports.

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