Closed form analytical solution for dispersion of Lamb waves in functionally graded plates

Wave Motion ◽  
2019 ◽  
Vol 88 ◽  
pp. 196-204 ◽  
Author(s):  
Sergey V. Kuznetsov
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Closed Form Analytical Solution

scholarly journals Lamb Waves in Anisotropic Functionally Graded Plates: A Closed Form Dispersion Solution

2019 ◽  
Vol 36 (1) ◽  
pp. 1-6
Author(s):  
S. V. Kuznetsov
Keyword(s):  
Closed Form ◽  
Dispersion Equation ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Stratified Media ◽  
Exponential Mapping ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Transverse Inhomogeneity ◽  
Dispersion Solution

ABSTRACTPropagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

2021 ◽  
pp. 1-24
Author(s):  
Liguo Jin ◽  
Liting Du ◽  
Haiyan Wang
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Half Space ◽  
Strong Interaction ◽  
Rigid Foundation ◽  
Structural Stiffness ◽  
Sh Waves ◽  
Closed Form Analytical Solution ◽  
Flexible Foundation ◽  
Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

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