A new technique is developed to determine the dispersion relation and the propagational speeds of waves in dispersive solids. The phase spectrum of a broadband pulse is linearly related to the dispersion relation of the dispersive medium. The method is simpler than the continuous‐wave phase comparison technique. Application is made to measure the phase and group velocities of waves in fiber‐reinforced composite materials and in thin wires. This technique is expected to be applicable to measurements of acoustic or electromagnetic wave speeds in other dispersive media.

On the determination of phase and group velocities of dispersive waves in solids

A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.

Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation

Group velocity and characteristic wave curves of Lamb waves in composites: Modeling and experiments

We present a review, through selected illustra- tive examples, of the physics of classical vibrational modes in phononic lattices, which elaborates on the theo- ry, the formalism, the methods, and mainly on the numer- ical and experimental results related to phononic crystals. Most of the topics addressed here, are written in a self- consistent way and they can be read as independent indi- vidual parts.

http://esperia.iesl.forth.gr/~ppm/PUBLICATIONS/ZfKv220p765_2005.pdf

Classical vibrational modes in phononic lattices: theory and experiment

A method with which standard finite element programs can be used to compute dispersion relations in periodic composites is proposed. The method is applied to two composite microstructures: a two-phase laminate and a fiber composite. The dispersion relations computed for the laminate are compared with a known analytical solution and the agreement is very good. The dispersion relations computed for the fibrous composite are compared with an existing approximate model and experimental results from the literature. The agreement between the approximate model, the experiments, and the computations is very good in the wave guide case and satisfactory for the wave reflect case.

The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure

An Experimental Study of Dispersion of Stress Waves in a Fiber-Reinforced Composite

Thermal Stresses in an Orthotropic Elastic Slab Due to Prescribed Surface Temperatures

Thermal Stresses in an Orthotropic Elastic Semispace

Stationary Temperature and Stress Fields in an Anisotropic Elastic Slab

Stationary two-dimensional temperature and stress distributions are examined for an orthotropic elastic body having a rectangular boundary. Temperature fields are determined for situations in which one edge of the rectangle experiences an arbitrary variation of temperature, heat flow or convection, while each of the remaining edges is either insulated or maintained at the initial temperature. Displacement potentials are then used to find the thermal stresses for those cases in which the temperature remains constant over two opposite ends of the rectangle. As an illustrative example, the temperature and stresses resulting from a uniform temperature rise over a portion of one edge of the rectangle are computed; numerical results are given for a fibre-reinforced composite material.

T. R. Tauchert

Papers

An Experimental Study of Dispersion of Stress Waves in a Fiber-Reinforced Composite

Thermal Stresses in an Orthotropic Elastic Slab Due to Prescribed Surface Temperatures

Thermal Stresses in an Orthotropic Elastic Semispace

Stationary Temperature and Stress Fields in an Anisotropic Elastic Slab

Thermoelastic Analysis of a Finite Orthotropic Slab