# Microcantilever, different resonance modes

1. Apr 6, 2012

### Tah

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.

<condition>
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. Apr 11, 2012

### gomunkul51

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.

Cheers.

Roman.

3. Apr 11, 2012

### sambristol

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.

Regards

Sam