Journal of Engineering Mechanics

The wave propagation in sandwich plate rows with cellular core is analyzed and controlled. Honeycomb core materials of different geometry placed periodically along the structure introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands (stop bands). The location and the extension of the stop bands can be optimized by proper selection of the geometrical and physical properties of the core. An optimal configuration of the core can be identified to design passive sandwich structures, which are stable and quiet over desired frequency bands. A theoretical model is developed to describe the wave propagation characteristics and the vibrations of a three-layered sandwich plate simply supported along its longitudinal edges. The core properties of the plate change periodically along the plate length. The wave propagation characteristics are estimated by analyzing the transfer matrix of each cell of the resulting periodic structure. The transfer matrix is also properly recast to obtain the cell’s dynamic stiffness matrix and to formulate a spectral finite element model for the periodic sandwich plate. The spectral finite element model allows predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared to conventional finite elements. The numerical model is used to predict the dynamic response of the considered class of plates and to study their propagation and attenuation characteristics for various core configurations. The presented numerical results demonstrate the simplicity and the effectiveness of the proposed treatment, which reduces the transmission of waves and the plate vibrations over specified frequency bands without the need of additional passive or active control devices. Such unique characteristics can be employed to design lightweight composite panels behaving as mechanical filters. The filtering capabilities of such passive composite panels can be properly modified and optimized to fit required transmissibility levels over desired frequencies without compromising the size and the weight of the structure.

Some fundamental dynamic characteristics of a railway subjected to a harmonic or constant moving load are established and presented in this paper. The railway is modeled as an infinite or finite Timoshenko beam on viscoelastic foundation. The dynamic-stiffness matrices characterized by the complex wave numbers are employed to deal with this problem. The relationship between the forced frequency and the resonant velocity of the moving load, and the resonant frequency of the railway are especially emphasized and intensively discussed. The fundamental dynamic characteristics of a railway modeled as a Bernoulli-Euler Beam on viscoelastic foundation are also included for comparison.

This paper presents the development of an orthotropic material model for the mechanical analysis of wood in the plane perpendicular to the growth direction. It is based on an earlier uniaxial development and experimental verification. The novel features are the biaxial extension and the description of partially irrecoverable creep deformation by enhancing a viscoelastic-mechanosorptive creep model by coupling it with orthotropic plasticity. The mathematical description of both the equations of state and the evolution laws are formulated on a thermodynamical basis. A semianalytical solution algorithm is derived for the obtained nonlinear system of differential equations. The model is applicable over a wide range of temperature as well as moisture content (20–120°C; nearly 0% moisture content to fiber saturation), which is achieved through application of the time-temperature-moisture superposition principle and the introduction of a moisture-change-temperature superposition principle. A set of material parameters suitable for this range of conditions is given for Pinus silvestris.

This paper describes the development of an efficient numerical integration algorithm for an orthotropic viscoelastic-mechanosorptive-plastic material model for wood, which was presented in Part I of this serial. This development utilizes both a semianalytical algorithm for the viscoelastic parts, and the return-mapping algorithm known from plasticity for the mechanosorptive-plastic part of the model. This yields an easily computed, closed form expression for the consistent tangent operator, and, as a consequence, a quadratic rate of asymptotic convergence on the global level of the incremental-iterative analysis by means of the FEM. To prove the practical applicability of the presented formulation, a numerical study of the so-called case-hardening phenomenon as observed on fast dried pine wood was performed. Selected results are presented and discussed.

This paper presents a novel probabilistic model of random uncertainties for dynamical system in the medium-frequency (MF) range. This approach combines a nonparametric probabilistic model of random uncertainties for the reduced matrix models in structural dynamics with a reduced matrix model adapted to the MF range. The theory is presented and the random energy matrix relating to a given MF band, its random trace, and its random eigenvalues are studied. A numerical example is presented allowing convergence properties and stability of random responses with respect to the bandwidth to be analyzed.

A new retrofitting technique based on a material [Cardiff Fiber Reinforced Concrete (CARDIFRC)] compatible with concrete has been developed at Cardiff University. It overcomes some of the problems associated with the current techniques based on externally bonded steel plates and fiber-reinforced plastic laminates which are due to the mismatch of their tensile strength and stiffness with that of the concrete structure being retrofitted. CARDIFRC is characterized by high tensile/flexural strength and high energy-absorption capacity (i.e., ductility). The special characteristics of CARDIFRC make it particularly suitable for repair, remedial and upgrading activities (i.e., retrofitting) of existing concrete structures. It has been shown that damaged reinforced concrete beams can be successfully strengthened and rehabilitated in a variety of different retrofit configurations using precast CARDIFRC strips adhesively bonded to the prepared surfaces of the damaged beams. To predict the moment resistance of the beams retrofitted in this manner an analytical model is introduced in the present paper. This model takes a fracture mechanics approach and follows the initiation and growth of the flexural crack that eventually leads to the failure of the retrofitted beams. The results of this analytical model are found to be in very good agreement with the test results.

In this paper we derive Newton’s 2nd Law of Motion from the constitutive equation of elasticity of a space-time continuum in four dimensions. This we do by introducing a four-dimensional material continuum with a Minkowskian metric, in analogy with Einstein’s general theory of relativity. The four-continuum is deformable in both space and time. The physics of the deformation is embedded in a variational principle, which is a form-invariant extension of its classical mechanical counterpart in three dimensions, but with the acceleration term absent. General dynamic equations of elasticity in four dimensions are thereby derived. When the constraint of temporal inextensibility (universal time) is introduced, these equations yield readily the dynamic equations of elasticity in three dimensions. The presence of the inertia term in these equations, is a direct consequence of the temporal curvature induced by the deformation of the four-continuum. Newton’s law of motion for rigid bodies follows when the additional constraint of spatial inextensibility is introduced.

The imperfection sensitivity of laminated cylindrical shells is considered—via the initial postbuckling analysis—on the basis of three different shell theories: Donnell in 1933; Sanders in 1963; and Timoshenko in 1961. The procedure involves nonlinear partial differential equations, which are converted into a sequence of three linear sets. The equations are solved with the variables expanded in Fourier series in the circumferential direction and in finite differences in the axial directions. A general code is developed and used in studying the effect of higher exactness of the shell theory on the sensitivity behavior, and in a parametric study of the sensitivity of anisotropic angle-ply cylindrical shells.

Moving-window micromechanics techniques are emerging as a useful tool for characterizing random composites, i.e., those with spatially random microstructures, in terms of local material property fields. These material property fields represent an approximate constitutive model for local material response. In this work, elastic property fields for randomly generated composite materials are estimated using a moving-window technique in combination with three micromechanical models, Mori-Tanaka, the generalized method of cells, and a brute-force finite element analysis. The first two methods make predictions of local properties based on small areas of the full sample. The brute-force finite element method performs its initial analysis on the full microstructure. Using the finite element results as the baseline solution, the fields developed from the methods are compared. Results illustrate the differences between the three methods and highlight the strong influence of window size on the analysis. Two criteria are suggested for further study of appropriate window size: A comparison of the correlation areas of the fields, which suggests an upper bound, and the analysis of a single fiber problem with known elasticity solution, which examines a potential lower bound. All of the techniques are demonstrated by application to numerically generated composite microstructures.

An isotropic model for creep damage of concrete under uniaxial compression is proposed, where the combined effect of nonlinear viscous strain evolution and crack nucleation and propagation at high stress levels is considered. Strain splitting assumption is used for creep and damage contributions. Creep is modeled by a modified version of solidification theory. As usual in the modeling of damage of concrete, a damage index based on positive strains is introduced. As particular cases, the proposed model reduces to linear viscoelasticity for long time low stress levels whereas, for very high stresses, tertiary creep causing failure at a finite time can be described. The effect of strength variation with time is also included. The model is numerically implemented to perform time integration of nonlinear equations by means of a modified version of exponential algorithm. The model is validated through comparison with experimental results. Some numerical examples are also presented, where the roles of concrete ageing and strength variation with time are investigated.

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train.

The perforation of a concrete target subjected to a rigid projectile impact is studied in this paper. Based on the dynamic cavity expansion theory and a plug formation model, semianalytical formulas for the perforation thickness and the perforation ballistic limit of concrete target are developed. The proposed formulas are consistent with other empirical formulas and correlate well with the experimental data.

Dynamics of a class of horizontal setback buildings with flexible floor diaphragms has been studied by developing a “separable model.” A rectangular plan building, with flexible floor diaphragms, is a particular case of the horizontal setback building. The mass and stiffness matrices have been written in terms of direct products of matrices. The separable buildings have two types of natural modes of vibration: (a) those which involve in-plane floor deformation, and (b) those in which the floors do not undergo in-plane deformation. Further, spatially uniform ground motion does not excite the modes involving in-plane floor deformation. Therefore, the problems associated with diaphragm flexibility, e.g., stress concentration at the re-entrant corners, are avoided in separable buildings. General conditions for a building to be separable have been obtained. In simplistic terms, these conditions imply that (a) all wings of the building should have identical value of lateral stiffness per unit plan area divided by mass per unit plan area in either of the principal directions of the wings, and (b) all of the floor diaphragms should have same ratio of lateral stiffness to mass. In other words, the building should be configured so that the fundamental period of vibration of each wing in either direction is the same, and that of all the floors for in-plane vibrations is the same.