A THEORETICAL MODEL OF MAGNETOELASTIC BUCKLING FOR SOFT FERROMAGNETIC THIN PLATES

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.

A VARIATIONAL PRINCIPLE ON MAGNETOELASTIC INTERACTION OF FERROMAGNETIC THIN PLATES

The key to revealing the behaviors of magnetoelastic interaction is how to express the magnetic forces applying on a ferromagnetic elastic body. In this paper, a functional for a ferromagnetic thin plate in magnetic fields is proposed by taking the summation of the magnetic energy of the magnetic system and the strain energy of the elastic plates. We present a variational principle for the problem by choosing the variations of magnetic potential and deflection as independent variates each other. Based on the principle, not only are the simultaneous governing equations for magnetic fields and deformation of structures deduced, but also a general expression of magnetic force acting on the plates is gained, which makes it possible to commonly simulate the distinct two experiments of magnetoelastic interaction in a theoretical model. Thus, it can be used to theoretical prediction of the magnetoelastic interaction of ferromagnetic plates in a complex environment of applied magnetic fields.

BENDING OF RECTANGULAR THIN PLATES WITH FREE EDGES LAID ON TENSIONLESS WINKLER FOUNDATION

In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.

NONLINEAR BENDINGS FOR THE ORTHOTROPIC RECTANGULAR THIN PLATES UNDER VARIOUS SUPPORTS

In this paper, the nonlinear bandings for the orthotropic rectangular thin plates under various supports are studied.The uniformly valid asymptotic solutions of the displacement ? and stress function φ are derived by the perturbation offered in [1].

A RECTANGULAR ELEMENT OF THIN PLATES BASED UPON THE GENERALIZED VARIATIONAL PRINCIPLES

Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.

High-Efficiency Generation of 0.12 mJ, 8.6 Fs Pulses at 400 nm Based on Spectral Broadening in Solid Thin Plates

We demonstrate eftlcient generation of continuous spectrum centered at 40Ohm from solid thin plates. By frequency doubling of 0.8m J, 3Ors Ti：sapphire laser pulses with a BBO crystal, 0.2m J, 33fs laser pulses at 400nm are generated. Focusing the 400-nm pulses into 7 thin fused silica plates, we obtain 0.15mJ continuous spectrum covering 350-450 nm. After compressing by 3 pairs of chirped mirrors, 0. 12 m J, 8.6 fs pulses are achieved. To the best of our knowledge, this is the first time that sub-10-fs pulses centered at 400nm are generated by solid thin plates, which shows that spectral broadening in solid-state materials works not only at 800nm but also at different wavelengths.

Binding property of Al/Mg/Al thin plates fabricated by one-pass hot rolling with different reduction ratios,temperatures and annealing treatments

In this study, Al-Mg-Al trilaminated thin plates were fabricated by one-pass hot rolling to improve the processing capacity and bonding strength of magne- sium alloy plates. The effects of processing parameters were investigated. The results show that the optimal bonding strength is up to 20 MPa with a reduction ratio of 40 % and rolling temperature of 400 ℃, superior than that in other one-pass rolling studies with regard to thin lami- nated plates. In addition, a favorable property is achieved with the annealing temperature of 250-300 ℃ or annealing time of 1.5 h. When the annealing temperature exceeds 300 ℃ or annealing time exceeds 1.5 h, respectively, the bonding strength of Al/Mg/Al plate decreases. The scan- ning electron microscopy （SEM） and energy-dispersive spectroscopy （EDS） analyses suggest that the appearance of thin diffusion layers between Al and Mg interfaces is helpful to improve the bonding strength, while the presence of thick diffusion layer would reduce the bonding strength greatly.

GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES

The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one.

Multicolored sideband generation based on cascaded four-wave mixing with the assistance of spectral broadening in multiple thin plates

The generation of multicolored sidebands with the spectrum from 377 to 970 nm in a 0.5-mm-thick N-WG280 Schott glass based on a cascaded four-wave mixing(CFWM) process is demonstrated. The experimental setup is compact and economical. A pulse with a broadened spectrum from 670 to 900 nm is generated by utilizing two 0.18-mm-thick fused silica glass plates and is used to provide two input beams for the CFWM process.The new frequency components generated from the self-phase modulation effect in the two thin glass plates contribute to the broadening of the total spectral range of the generated multicolored sidebands.

Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation

A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.

Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.

ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions.