Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses

Different kinematic mathematical models of nonlinear dynamics of a contact interaction of two microbeams are derived and studied. Dynamics of one of the microbeams is governed by kinematic hypotheses of the first, second, and third approximation orders. The second beam is excited through a contact interaction with the first beam and is described by the kinematic hypothesis of the second-order approximation in both geometric linear and nonlinear frameworks. The derived nonlinear partial differential equations (PDEs) are transformed to the counterpart system of nonlinear ordinary differential equations (ODEs) by the finite difference method. Nonlinear contact interaction dynamics of the microbeam structure is analyzed with the help of time series (signals), Fourier spectra, and wavelet spectra based on various mother wavelets, Morlet wavelet spectra employed to study synchronization phenomena, Poincaré maps, phase portraits, and the Lyapunov exponents estimated with the Wolf, Kantz, and Rosenstein algorithms. We have illustrated that neglecting the shear function (Euler–Bernoulli model) yields erroneous numerical results. We have shown that the geometric nonlinearity cannot be neglected in the analysis even for small two-layer microbeam deflection. In addition, we have detected that the contact between two microbeams takes place in the vicinity of x \approx 0.2 and x \approx 0.8 instead of the beams central points.

Bending Response of Composite Material Plates with Specific Properties, Case of a Typical FGM "Ceramic/Metal" in Thermal Environments

The rapid development of composite materials and structures in recent years has attracted the increased attention of many engineers and researchers. These materials are widely used in aerospace, military, mechanical, nuclear, marine, optical, electronic, chemical, biomedical, energy sources, automotive fields, ship building and structural engineering industries. In conventional laminate composite structures, homogeneous elastic plate are bonded together to obtain improved mechanical and thermal properties. However, the abrupt change in material properties across the interface between the different materials can cause strong inter-laminar stresses leading to delamination, cracking, and other damage mechanisms at the interface between the layers. To remedy these defects, functionally graded materials (FGM) are used, in which the properties of materials vary constantly. The purpose of this paper is to analyze the thermomechanical bending behavior of functionally graded thick plates (FGM) made in ceramic/metal. This work presents a model that employed a new transverse shear function. The numerical results obtained by the present analysis are presented and compared with those available in the literature (classical, first-order, and other higher-order theories). It can be concluded that this theory is effective and simple for the static analysis of composite material plates with specific properties "Case of a typical FGM (ceramic/metal)" in thermal environments.

Study on the Calculation Method of Soil-Nailing for High Soil Slope Based on the Logarithmic Spiral Slippery Fracture

This paper introduces a new failure mode pattern of soil slope – the logarithmic spiral slippery fracture. A mathematical model for the logarithmic spiral slippery fracture is established, taking the anti-shear function of the soil-nailing into consideration. The shear of soil-nailing, axial force, and the safety coefficients based on the limiting equilibrium method are derived, leading to an accurate stability analysis of the strengthening of soil slope. A case study shows that the anti-shear function of the soil-nailing can be significant and should not be ignored in engineering design.

A Modified Approach to Initialize an Idealized Extratropical Cyclone within a Mesoscale Model

A technique for initializing realistic idealized extratropical cyclones for short-term (0–72 h) numerical simulations is described. The approach modifies select methods from two previous studies to provide more control over the initial cyclone structure. Additional features added to the technique include 1) deformation functions to initialize more realistic low-level fronts, tropopause structure, and enhanced jet maximum at upper levels; 2) a barotropic shear function to help develop different cyclone and frontal geometries; and 3) damping functions to create an isolated baroclinic wave in the horizontal; therefore, the initialized cyclone is not influenced by the domain boundaries for relatively short simulations. Since this procedure allows for control of the initialized cyclone structures, it may be useful for studies of frontal and cyclone interaction with topography and mesoscale predictability. The initialization system produces a variety of basic states and synoptic disturbances, ranging from weak to explosively developing cyclones. Examples are shown to provide some insight on how to adjust selected parameters. The output is compatible with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model and the Weather Research and Forecasting model. This note describes the procedure as well as presents an example of a landfalling cyclone along the U.S. west coast with and without terrain.

A Note on a Non-Linear Theory on Bending of Orthotropic Sandwich Plates

SummaryThe derivation of a non-linear theory on bending of orthotropic sandwich plates is carried out by the principle of complementary energy from elasticity. The governing differential equations and natural boundary conditions are obtained. The assumptions used are, namely, the facings are orthotropic thin elastic plates with negligible bending rigidities and are made of the same material; the orthotropic core can take the transverse shear only; and the transverse shortening of the core may be ignored. The geometrical non-linearities are equivalent to von Kármán’s theory for single-layered plates. Through the introduction of a “shear function”, the number of differential equations is reduced to three and the equations are in rather simple form. It appears that the equations obtained here would require, comparatively, the least amount of work for analysing the finite deflection sandwich plate problems having a wide range of properties of practical interest.