Rayleigh waves obtained by the indeterminate couple-stress theory

✍ Scribed by Niels Saabye Ottosen; Matti Ristinmaa; Christer Ljung

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 201 KB
• Volume: 19
• Category: Article
• ISSN: 0997-7538
• DOI: 10.1016/s0997-7538(00)00201-1

✦ Synopsis

Rayleigh waves in a linear elastic couple-stress medium are investigated; the constitutive equations involve a length parameter l that characterizes the microstructure of the material. With cR = Rayleigh speed, c T = conventional transversal speed and q = wave number, an explicit expression is derived for the relation between cR /c T , lq and Poisson's ratio ν. The Rayleigh speed turns out to be dispersive and always larger than the conventional Rayleigh speed. It is of interest that when lq = 1 and ν 0, it always holds that cR /c T = √ 2. The displacement field is investigated and it is shown that no Rayleigh wave motions exist when lq → ∞ and when lq = 1, ν 0. Moreover, a principal change of the displacement field occurs when lq passes unity. The peculiarity that no Rayleigh wave motions exist when lq = 1, ν 0 may support the criticism by Eringen (1968) against the couple-stress theory adopted here as well as in much recent literature.