Estimate of the applicability limits of a linear theory of internal waves

Using a perturbation method, the applicability limits of a linear theory of internal gravity waves are estimated. It is shown that over a wide range of wavelengths, typical of a real ocean, in studying the dynamics of internal gravity waves it is possible to use a linear approximation, which confirms the validity and adequacy of this approximation for the corresponding spatial and temporal scales of the linear model of wave dynamics.     

Atomistic viewpoint of the applicability of microcontinuum theories

Microcontinuum field theories, including Micromorphic theory, Microstructure theory, Micropolar theory, Cosserat theory, nonlocal theory and couple stress theory, are the extensions of the classical field theories for the applications in microscopic space and time scales. They have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale. This work provides an atomic viewpoint to examine the physical foundations of those well-established microcontinuum theories, and to justify their applicability through lattice dynamics and molecular dynamics.     

On the dynamic bending of layered plates

The dynamic bending of layered metallic plates is studied. Their layers are reinforced with wires, and there are interfacial layers between the contact surfaces. A general approach to solving the corresponding dynamic problems is proposed. It is the principle of virtual work. A system of ordinary differential constitutive equations is obtained and used to determine the amplitude coefficients of the series of coordinate functions that approximates the deflections. The constitutive equations are reduced to Volterra equations of the second kind. Algorithms are developed to calculate the coefficients of the constitutive equations depending on the coordinate functions and on the reinforcement pattern. Possible methods to set up coordinate functions and solve integral equations are indicated     

On the applicability of some approximate similitude laws in hypersonic aerodynamics

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–130, March–April, 1994.     

Design and layout of layered plates

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 152–161, July–August, 1989.     

Higher order approximate dynamic models for layered composites

Based on a higher order dynamic approximate theory developed in the present study for anisotropic elastic plates, two dynamic models, discrete and continuum models (DM and CM), are proposed for layered composites. Of the two models, CM is more important, which is established in the study of periodic layered composites using smoothing operations. CM has the properties: it contains inherently the interface and Floquet conditions and facilitates the analysis of the composite, in particular, when the number of laminae in the composite is large; it contains all kinds of deformation modes of the layered composite; its validity range for frequencies and wave numbers may be enlarged by increasing, respectively, the orders of the theory and interface conditions. CM is assessed by comparing its prediction with the exact for the spectra of harmonic waves propagating in various directions of a two-phase periodic layered composite, as well as, for transient dynamic response of a composite slab induced by waves propagating perpendicular and parallel to layering. A good comparison is observed in the results and it is found that the model predicts very well the periodic structure of spectra with passing and stopping bands for harmonic waves propagating perpendicular to layering. In view of the results, the physical significance of Floquet wave number is also discussed in the study.     

Stress-resultant plasticity theories for composite laminated plates

Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.     

Nonlinear bendings of symmetrically layered anisotropic rectangular plates

This paper has studied the nonlinear bending of symmetrically layered anisotropic rectangular plates under various supports. The uniformlys valid N-order asymptotic solutions of the deflection and stress function are derived by the singular perturbation methods offered in [1]. The analysis and calculations are given for simply and clamped supported, rectangular plates subjected to combined edge tensions and lateral loading in conjunction with the modified Galerkin procedure (a method of weighted residuals).     

Nonlinear bendings of unsymmetrically layered anisotropic rectangular plates

An analysis for the nonlinear bendings of unsymmetrically layered anisotropic rectangular plates subjected to combined edge tensions and lateral loading under verious supports is presented. The uniformly valid N-order asymptotic solutions of the transverse deflection and stress function are derived by the singular perturbation method offered in [1]. The present investigation may provide a simple and convenient method for such a complex problem.     

A comparison of approximate theories for scattering from rough surfaces

Scattering from a perfectly conducting rough interface is developed in terms of a generalized angular spectrum of plane waves which includes both upward and downward traveling waves. This spectral formulation is used to examine the interrelationships between three classical approximate techniques in rough surface scattering, i.e., physical optics, boundary perturbation, and extinction theorem. These methods are also traced to conventional deterministic scattering analysis techniques. In particular, physical optics is related to the Magnetic Field Integral Equation, boundary perturbation is shown to result from the Electric Field Integral Equation subsequent to invoking the Rayleigh Hypothesis, and the extinction theorem is equivalent to the Extended Boundary Condition Method. The capabilities and limitations of these rough surface approximate techniques are developed using the angular spectrum approach, and they are discussed in detail.     

Viscoelastic shear horizontal wave in graded and layered plates

In this paper, viscoelastic shear horizontal (SH) wave propagation in functionally graded material (FGM) plates and laminated plates are investigated. The controlling differential equation in terms of displacements is deduced based on the Kelvin–Voigt viscoelastic theory. The SH wave characteristics is controlled by two elastic constants and their corresponding viscous coefficients. By the Legendre polynomial series method, the asymptotic solutions are obtained. In order to verify the validity of the method, a homogeneous plate is calculated to make a comparison with available data. Through three different graded plates, the influences of gradient shapes on dispersion and attenuation are discussed. The viscous effects on the displacement and stress shapes are illustrated. The different boundary conditions are analyzed. The influential factors of the viscous effect are analyzed. Finally, two multilayered (two layer and five layer) viscoelastic plates that are composed of the same material volume fraction are calculated to show their differences from the graded plate.     

Crack propagation in layered plates—an experimental study

The effects of the layer height and the material properties of a layered medium on the propagation mode of a crack are discussed. Crack-propagation velocities and dynamic stress-intensity factors were evaluated during fracture and the corresponding curves were plotted. The medium consisted of two identical external layers and a middle layer of softer or harder material. This layer contained an initial crack which ran parallel to the interfaces of the layers. All phases of the specimens were fabricated from epoxy polymers. After the preparation of the middle layer, the surrounding layers were successively cast along the middle layer's straight boundaries without applying any kind of adhesive. High-speed photography and dynamic caustics were utilized to establish the changes in crack speeds and intensities of the stress field. The influence of geometry and especially of the height of the middle layer and the mechanical properties of the layered material was studied; interesting results were derived.     

Generalisations of long wave theories for pre-stressed compressible elastic plates

Generalisations of classical bending and extension are established for pre-stressed compressible elastic plates. In respect of the analogue of extension, the associated quasi-front is shown to be either advancing or receding, contrasting with the classical case. For the generalisation of bending, the long wave limit of the fundamental mode is non-zero; thus, unlike its classical counterpart, an associated quasi-front can, therefore, exist and is again noted to be either advancing or receding. In both cases appropriate leading order and higher order corrected governing equations are obtained. The ideas are illustrated through investigation of a model problem involving impact edge loading. For the generalised theory of bending, the leading order governing equation for the mid-surface deflection is used to establish the classical equation for wave propagation along an infinite string, with its second order refinement providing a second order correction. Motion within the vicinity of the thickness shear and thickness stretch resonance frequencies is also investigated. Special cases, in which either a stretch resonance and shear resonance frequency are very close, or the speeds of longitudinal and shear waves are very close, are also discussed.     

Insights on the continuous representations of piecewise-smooth nonlinear systems: limits of applicability and effectiveness

Nonlinear Dynamics - It is known that three-parameter representations of spatial rotation suffer from kinematic singularities. Euler parameters (unit quaternions) are a four-parameter solution for...