1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Microcantilever, different resonance modes

  1. Apr 6, 2012 #1


    User Avatar

    I'm now styduing micro-cantilever used as a sensor.

    It is usually made of silicon based materials.

    In a certain condition below, the cantilever will vibrate itself when a certain external frequency is applied.

    Certain cantilevers may
    exhibit mode coupling depending on the device characteristics.
    Analytical expressions for various mode shapes can be derived
    mathematically from the corresponding equations of motion under
    the following assumptions: the aspect ratio is sufficiently large, the
    deflection is small compared to cantilever thickness, the geometry
    is of single-layer uniform rectangular cross-section, and the
    material is isotropic.

    There are four types of vibrating modes.

    Out-of plane vibrations include transverse, also called bending or flexural, and torsional motion.
    In-plane vibrations include lateral, also called in-plane bending, and longitudinal, also called extensional or axial, motion.

    Each of the four modes exhibit resonance when excited at their characteristic frequency, known as the resonant frequency or eigen frequency.

    My question is why a microcantilever has different resonant modes in different frequencies on a single material.

    And how can the torsional mode be occurred? It's very interesting.
  2. jcsd
  3. Apr 11, 2012 #2
    Do you have theoretical knowledge in how to describe any of those motions that create the resonances? Write the equations and look what is dependent of what.


  4. Apr 11, 2012 #3
    It's because of the material it is made from. The atoms are bonded together at different angles and with different bonding strengths.

    So to distort a material in one direction by a certain amount may require a fraction of the force to do so in another direction.

    Less force equals lower frequency for the same mass.

    Torsional modes can be induced in two ways. Firstly an asymmetric force or secondly a symmetric force on an crystalline structure which is asymmetric.

    Look up 'elastic tensors' to get the math behind this.


Share this great discussion with others via Reddit, Google+, Twitter, or Facebook