Highest frequency before mechanical failure

[jeberd]

I am wondering what property of a material would be of interest (or better yet if you knew some formulas that describe this property) if I want to know what frequencies different materials could handle.

I am thinking along the lines of "the fat lady singing" and reaching that high note that breaks all of the crystal in the room. I imagine that this is a property of both frequency and amplitude and has to do with the elasticity of the material.

I am working on a project wherein I propose using high frequency vibrations to move particles across the surface of a substrate, and I predict getting questions along the line of "but won't that just cause it to break"

 

[f95toli]

Most materials won't break no matter what the frequency is (I am assuming now that the material is simply vibrating, not shearing etc). And even objects that are made from materials that DO break (such as glas) will do so at a frequency that will depend on the particular properties of that object: the shape (which will determine the resonance frequencies), size, defects, cracks etc

 

[jeberd]

I am primarily thinking about silicon wafers (which are only 500 microns thick and crystalline silicon is brittle).

Also, do you know where I would find the equations for resonant frequencies of shapes?

 

[Dale]

Also, do you know where I would find the equations for resonant frequencies of shapes?

This is closely related to the https://www.physicsforums.com/showthread.php?t=276617" earlier this week.

 

[jeberd]

This is closely related to the https://www.physicsforums.com/showthread.php?t=276617" earlier this week.

Yes, but I am interested in simple 2-d shapes. I imagined that these equations exist as a standard set for basic shapes but it may not be the case.

Possibly of interest is this video: http://www.coolestone.com/media/124/Seeing_Sound_Waves_-_Awesome/" which illustrates what I would like to calculate. If there is a way to do it, I would like to determine the locations of the lines mathematically, by numerical methods if required.

 

[timmay]

For simple structures this is reasonably straight forward. For a variety of simple shapes (columns, beams, plates) one can estimate the mode shapes and associated natural frequencies. These are related to, amongst other things, boundary conditions, structure material properties, and geometry. A good place to start would be Blevins' 'Formulas for Natural Frequency and Mode Shape'.

For more complicated structures you would generally carry out this analysis using Finite Element Analysis. By generating a computer model of the problem and sub-dividing the structure into many smaller elements (by generating what is known as a mesh), it is possible to estimate with varying degrees of accuracy what will happen. Depending on your abilities or resources available to you though, this probably will not be an easy thing to teach yourself to do.

As I said, if it's just a simple case such as an edge clamped or simply supported symmetrical plate, Blevins will give you the tools with which to predict what you are after.