Free-Wave Dispersion Curves of a Multi-Supported String

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Benjamin A. Cray ◽  
Andrew J. Hull ◽  
Albert H. Nuttall
Keyword(s):  
Material Properties ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Viscous Damping ◽  
Free Wave ◽  
Support Set ◽  
Dispersion Formula ◽  
General Dispersion ◽  
Support Sets ◽  
Free Wave Propagation

Free-wave propagation of an infinite, tensioned string, supported along its length by repeating segments of multiple spring-mass connections, is examined. The segments can consist of an arbitrary number of different support sets and be of any overall length. Periodicity is intrinsic, since the segments repeat; the goal, though, is to examine what effect variations within the segments have on dispersion. The formulation reveals an unexpected amount of complexity for such a simply posed system. Each support set has independent mass, stiffness, and viscous damping, and the sets are allowed to be offset from one another. A free-wave dispersion formula is derived for two sets of supports (Q = 2) and compared to the well-known ideally periodic expression (Q = 1). A means to obtain general dispersion formulas, for any Q, is discussed. It is shown that the systems’ dispersion curves are primarily governed by the material properties of the string and by the location of the supports.

scholarly journals Free Wave Propagation in Plates of General Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 881-886 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
D. E. Chimenti
Keyword(s):  
Anisotropic Plate ◽  
Secular Equation ◽  
Formal Analysis ◽  
Transversely Isotropic ◽  
Wave Dispersion ◽  
Wave Mode ◽  
Higher Symmetry ◽  
Free Wave ◽  
Axis Of Symmetry ◽  
Free Wave Propagation

We develop the analysis for the propagation of free waves in a general anisotropic plate. We begin with a formal analysis of waves in a plate belonging to the triclinic symmetry group. The calculation is then carried forward for the slightly more specialized case of a monoclinic plate. We derive the secular equation for this case in closed form and isolate the mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms. Material systems of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic are contained implicitly in our analysis. We also demonstrate that the particle motions for Lamb and SH modes uncouple if propagation occurs along an in-plane axis of symmetry. We present numerical free-wave dispersion results drawn from concrete examples of materials belonging to several of these symmetry groups.

Inversion of Rayleigh wave dispersion curves via adaptive GA and nested DLS

2019 ◽  
Vol 218 (1) ◽  
pp. 547-559 ◽  
Author(s):  
Yuhang Lei ◽  
Hongyan Shen ◽  
Xinxin Li ◽  
Xin Wang ◽  
Qingchun Li
Keyword(s):  
Rayleigh Wave ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Rayleigh Wave Dispersion

P- and S-wave velocity models from surface wave dispersion curves data transform

2017 ◽  
Author(s):  
Valentina Socco ◽  
Farbod Khosro Anjom ◽  
Cesare Comina ◽  
Daniela Teodor
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Velocity Models

scholarly journals Calculation of Wave Dispersion Curves in Multilayered Composite-Metal Plates

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ameneh Maghsoodi ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Transfer Matrix ◽  
Equations Of Motion ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Metal Plate ◽  
Material Symmetry ◽  
Major Purpose ◽  
Characteristic Equations ◽  
Multilayered Composite ◽  
Metal Plates

The major purpose of this paper is the development of wave dispersion curves calculation in multilayered composite-metal plates. At first, equations of motion and characteristic equations for the free waves on a single-layered orthotropic plate are presented. Since direction of wave propagation in composite materials is effective on equations of motion and dispersion curves, two different cases are considered: propagation of wave along an axis of material symmetry and along off-axes of material symmetry. Then, presented equations are extended for a multilayered orthotropic composite-metal plate using the transfer matrix method in which a global transfer matrix may be extracted which relates stresses and displacements on the top layer to those on the bottom one. By satisfying appropriate boundary conditions on the outer boundaries, wave characteristic equations and then dispersion curves are obtained. Moreover, presented equations may be applied to other materials such as monoclinic, transversely isotropic, cubic, and isotropic materials. To verify the solution procedure, a number of numerical illustrations for a single-layered orthotropic and double-layered orthotropic-metal are presented.

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

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