Behavior of a curved 2D sheet and a curved 1D wire under acoustic wave

[Seanskahn]

TL;DR

How do complex shapes respond to acoustic waves?

Good day.

We know how simple objects, such as 1D wires behave when a simple harmonic wave travels along a wire, or two wires knotted togethe.We also know what happens if you excite a circular thin disc with a single frequency.

Are there some material I can read on, that considers the effect of exciting a stiff wire given by y = f(x) , for a polynomial or exponential function f, excited by an acoustic wave comprising of multiple frequencies?

While we are at it how does a surface given by z = f(x,y) respond if several acoustic waves are falling on it, each at a different point, each comprising of multiple frequencies?

I understand that an analytical solution would be very complicated.

I am not requesting you to solve it for me, I just want you to direct my to some study / research material in this direction.

Thank you.

 

[Arjan82]

Sounds like you want to do a Frequency Response analysis using FEM. A surface can probably best be modeled by shell elements, so Timoshenko's canonical 'Theory of Plates & Shells' might be a good reference.

You can also model wires with FEM. So any reference on FEM theory, numerical analysis and theory of elasticity would help I guess. There are tons of books about that.

 

[Baluncore]

How do complex shapes respond to acoustic waves?

Welcome to PF.
Complex shapes respond in complex ways.
The acoustic impedance and the degree of freedom at boundaries or attachment points will be important. You have no choice but to use FEM, or to build and test a model.

 

[Seanskahn]

Welcome to PF.
Complex shapes respond in complex ways.
The acoustic impedance and the degree of freedom at boundaries or attachment points will be important. You have no choice but to use FEM, or to build and test a model.

Thank you for your answer.
I know how to proceed now.
Enjoy your weekend.