Forum Technical Discussions Re: Lamb wave dispersion curves Posted by: James Barshinger (PID_688), E-mail: Address, on August 18, 2008 at 15:34 : In Reply to: Re: Lamb wave dispersion curves posted by : Neelima Erukulla , E-mail: Address, on August 18, 2008 at 06:09 : Hi. Here are a couple of references that should help you out. 1. " Matrix techniques for modeling ultrasonic waves in multilayered media" by Mike Lowe. IEEE Trans on Ultrasonics Ferroelectrics and Frequency Control, vol 42, pp 525-542, 1995. 2. "Guided Wave Propagation in an Elastic Hollow Cylinder Coated with a Viscoelastic Material" by Barshinger and Rose. IEEE Trans on UFFC, vol. 51, pp 1547-1556, 2004. To your questions. 1. Use continuity of stress and displacement for the boundary condition at the interface. 2. The easiest method to find the roots is to use a bi-section routine. As there are multiple roots, you need to test starting values in your solution space to find a sign change, then use bisection to find the root. This method works well, but can have trouble finding all of the roots when modes are close together. As I recall, Lowe's paper describes a routine that is more robust but probably more complicated to implement. -Jim ----------- Start Original Message ----------- : -Hi, : : I am writing my own code for plotting dispersion curves for guided waves propagating in two layered cylinder. I have derived the equation of motion and also applied the relevant boundary conditions. I have two questions to ask and would appreciate if any one can answer them : 1) what boundary condition should be considered at the interface of the two layers. : Should stress continuity and displacement continuity be considered : OR : strain and displacement continuities be considere. The cylinder is composed of two layers of two different materials. : 2) I am unable to find the solution for layer matrix I derived from equation of motion. Please can anyone tell me how I can find the roots of this matrix (dispersion equation) : : Thanks. : Regards, : Neelima : ---------- Start Original Message ----------- : : : : Hi, : : You can use thids book, : : wave propagation in solids By : Achenbach : : or : : wave propagation in layered anisotropic media : : By: Adnan h. Nayfeh : : if you get answer please aware me. : : : Regards, : : : Amir ------------ End Original Message ------------ Follow Ups: Re: Lamb wave dispersion curves G.Sudheer 18:01 Sep-01-2008 (1) Post a Followup: Name: E-Mail: Subject: Comments: ----------- Start Original Message ----------- : Hi. : Here are a couple of references that should help you out. : 1. " Matrix techniques for modeling ultrasonic waves in multilayered media" by Mike Lowe. IEEE Trans on Ultrasonics Ferroelectrics and Frequency Control, vol 42, pp 525-542, 1995. : 2. "Guided Wave Propagation in an Elastic Hollow Cylinder Coated with a Viscoelastic Material" by Barshinger and Rose. IEEE Trans on UFFC, vol. 51, pp 1547-1556, 2004. : To your questions. : 1. Use continuity of stress and displacement for the boundary condition at the interface. : 2. The easiest method to find the roots is to use a bi-section routine. As there are multiple roots, you need to test starting values in your solution space to find a sign change, then use bisection to find the root. This method works well, but can have trouble finding all of the roots when modes are close together. As I recall, Lowe's paper describes a routine that is more robust but probably more complicated to implement. : : -Jim : : -Hi, : : : : I am writing my own code for plotting dispersion curves for guided waves propagating in two layered cylinder. I have derived the equation of motion and also applied the relevant boundary conditions. I have two questions to ask and would appreciate if any one can answer them : : 1) what boundary condition should be considered at the interface of the two layers. : : Should stress continuity and displacement continuity be considered : : OR : : strain and displacement continuities be considere. The cylinder is composed of two layers of two different materials. : : 2) I am unable to find the solution for layer matrix I derived from equation of motion. Please can anyone tell me how I can find the roots of this matrix (dispersion equation) : : : : Thanks. : : Regards, : : Neelima : : ---------- Start Original Message ----------- : : : : : Hi, : : : You can use thids book, : : : wave propagation in solids By : Achenbach : : : or : : : wave propagation in layered anisotropic media : : : By: Adnan h. Nayfeh : : : if you get answer please aware me. : : : : Regards, : : : : Amir ------------ End Original Message ------------ Optional Link URL: Example: "http://www....html". Alternative write "http://www.ndt.net/wshop/attach/filename.htm" if you transfered a filename.htm via FTP Page Title: is important! Optional Image URL: http://www....gif Attention! Please click the button only once. This may take a moment to process Forum Technical Discussions Help