Free Vibration of FGSW Plates Partially Supported by Pasternak Foundation Based on Refined Shear Deformation Theories

A refined third-order shear deformation theory (RTSDT), in which the transverse displacement is split into bending and shear parts, is employed to formulate a four-node quadrilateral finite element for free vibration analysis of functionally graded sandwich (FGSW) plates partially supported by a Pasternak foundation. An element based on the refined first-order shear deformation theory (RFSDT) which requires a shear correction factor is also derived for comparison purpose. The plates consist of a fully ceramic core and two functionally graded skin layers with material properties varying in the thickness direction by a power gradation law. The Mori–Tanaka scheme is employed to evaluate the effective moduli. The elements are derived using Lagrangian and Hermitian polynomials to interpolate the in-plane and transverse displacements, respectively. The numerical result reveals that the frequencies obtained by the RTSDT element are slightly higher than the ones using the RFSDT element. It is also shown that the foundation supporting area plays an important role on the vibration of the plates, and the effect of the material distribution on the frequencies is dependent on this parameter. A parametric study is carried out to highlight the effects of the material inhomogeneity, the foundation stiffness parameters, and the foundation supporting area on the frequencies and vibration modes. The influence of the layer thickness and aspect ratios on the frequencies is also examined and highlighted.

Nonuniversality of fluctuations of outliers for Hermitian polynomials in a complex Wigner matrix and a spiked diagonal matrix

We study the fluctuations associated to the a.s. convergence of the outliers established by Belinschi–Bercovici–Capitaine of an Hermitian polynomial in a complex Wigner matrix and a spiked deterministic real diagonal matrix. Thus, we extend the nonuniversality phenomenon established by Capitaine–Donati-Martin–Féral for additive deformations of complex Wigner matrices, to any Hermitian polynomial. The result is described using the operator-valued subordination functions of free probability theory.

Adaptive Surrogate-Model Fitting Using Error Monotonicity

Surrogate models are useful in a wide variety of engineering applications. The employment of these computationally efficient surrogates for complex physical models offers a dramatic reduction in the computational effort required to conduct analyses for the purpose of engineering design. In order to realize this advantage, it is necessary to “fit” the surrogate model to the underlying physical model. This is a considerable challenge as the physical model may consist of many design variables and performance indices, exhibit nonlinear and/or mixed-discrete behaviors, and is typically expensive to evaluate. As a result adaptive sequential sampling techniques, where previous evaluations of the physical model dictate subsequent sample locations, are widely used. In this work, we develop and demonstrate a novel adaptive sequential sampling algorithm for fitting surrogate models of any type, with a focus on large data sets. By examining the monotonicity of an error function the design space is repeatedly partitioned in order to compute a set of “key points.” The key points reduce the problem of fitting to one of precise interpolation, which can be accomplished using well-known methods. We demonstrate the use of this technique to fit several surrogate model types, including blended Hermitian polynomials and Non-Uniform Rational B-splines (NURBs), to nonlinear noisy data. We conclude with our observations as to the effectiveness of this fitting technique, its strengths and limitations, as well as a discussion of further work in this vein.

SIGNATURE PAIRS FOR GROUP-INVARIANT HERMITIAN POLYNOMIALS

We study the signature pair for certain group-invariant Hermitian polynomials arising in CR geometry. In particular, we determine the signature pair for the finite subgroups of SU(2). We introduce the asymptotic positivity ratio and compute it for cyclic subgroups of U(2). We calculate the signature pair for dihedral subgroups of U(2).

On impulse excitation of the global poloidal modes in the magnetosphere

Through the combined action of the field line curvature and finite plasma pressure in some regions of the magnetosphere (plasmapause, ring current) there can exist global poloidal Alfvén modes standing both along field lines and across magnetic shells and propagating along azimuth. In this paper we investigate the spatio-temporal structure of such waves generated by an impulsive source. In general, the mode is the sum of radial harmonics whose structure is described by Hermitian polynomials. For the usually observed second harmonic structure along the background field, frequencies of these radial harmonics are very close to each other; therefore, the generated wave is almost a monochromatic oscillation. But mixing of the harmonics with different radial structure causes the evolution of the initially poloidal wave into the toroidal one. This casts some doubts upon the interpretation of observed high-m poloidal waves as global poloidal modes.

Dynamic analysis of prestressed Bernoulli beams resting on two-parameter foundation under moving harmonic load

This paper describes the dynamic analysis of prestressed Bernoulli beams resting on a two-parameter elastic foundation under a moving harmonic load by the finite element method. Using the cubic Hermitian polynomials as interpolation functions for the deflection, the stiffness of the Bernoulli beam element augmented by that of the foundation support and prestress is formulated. The nodal load vector is derived using the polynomials with the abscissa measured from the left-hand node of the current loading element to the position of the moving load. Using the formulated element, the dynamic response of the beams is computed with the aid of the direct integration Newmark method. The effects of the foundation support, prestress as well as excitation frequency, velocity and acceleration on the dynamic characteristics of the beams are investigated in detail and highlighted.