Magnetoelastic buckling: Theory vs. experiment

Existing theoretical values and experimental values of magnetoelastic critical buckling fields for ferromagnetic beams and plates differ by a factor of two. The usual theoretical treatment assumes that the plate (a) is immersed in an infinite uniform field, (b) is infinitely wide and long, and (c) is made of a linearly magnetic material. We present an experimental investigation, combined with a simple analysis, which determines specific criteria which must be satisfied by experimental programs in order to validate the three assumptions. It is shown that experimental arrangements which validate (a) and (c) are feasible, but not (b). Hence, there is need for improved theoretical treatments which take into account the finite size of the specimens.     

Magnetoelastic buckling of tokamak superconducting toroidal field coils

Based on the perturbed vector potential theory and principle of stationary potential energy, a finite element method is applied to finding the critical current of the magnetoelastic buckling of the toroidal field coils of the fusion reactor. Stress is laid on the effects of the tremendous inplane tension induced magnetically and the perturbation history of the current vectors.     

An active high-static-low-dynamic-stiffness vibration isolator with adjustable buckling beams: theory and experiment

High-static-low-dynamic-stiffness(HSLDS) vibration isolators with buckling beams have been widely used to isolate external vibrations. An active adjustable device composed of proportion integration(PI) active controllers and piezoelectric actuators is proposed for improving the negative stiffness stroke of buckling beams. A nonlinear output frequency response function is used to analyze the effect of the vibration reduction.The prototype of the active HSLDS device is built, and the verification ...     

Magnetoelastic buckling of a rectangular block in plane strain

Of interest here is the stability of a rectangular block subjected to a uniform magnetic field perpendicular to its longitudinal axis. The two ends of the block are frictionless and kept parallel to each other. This boundary value problem is motivated by the classical problem of magnetoelastic buckling in which a cantilever beam subjected to a transverse magnetic field buckles when the applied field reaches a critical value.This work presents a finite strain continuum mechanics formulation of the stability problem of a homogeneous, compressible, magnetoelastic rectangular block in plane strain subjected to a uniform transverse magnetic field. The applied variational approach employs an unconstrained energy minimization recently proposed by the authors.The analytical solution for the critical buckling fields for both the antisymmetric and symmetric modes are obtained for three different constitutive laws. The corresponding result for thin beams is extracted asymptotically for a special material and the solution is compared to previously published results. The critical magnetic field is shown to increase monotonically with the block's aspect ratio for each material and mode type. Antisymmetric modes are always the critical buckling modes for stress saturated and neo-Hookean materials, except for a narrow range of moderate aspect ratios (about 0.25) where symmetric modes become critical. For strain-saturated solids no buckling is possible above a maximum aspect ratio.     

Magnetoelastic buckling of thin plates in a uniform transverse magnetic field

The buckling of thin soft ferromagnetic elastic plates in a uniform transverse magnetic field is discussed. Based on a linearized version of the general magnetoelastic equations, a plate equation is derived together with the pertinent boundary conditions. By searching a nontrivial solution of this homogeneous system, a buckling value can be found. As an example, the circular plate is considered. In this paper, Maxwell stresses are used, but it is shown that identical results can be obtained by using other models (especially Amperian current) for the magnetoelastic stresses.

---

Zusammenfassung In dieser Arbeit wird das Knicken dünner ferromagnetischer, elastischer Platten in uniformen magnetischen Feldern behandelt. Die Ableitung einer Plattengleichung zusammen mit den bezüglichen Randesbedingungen wird auf die linearisierten Gleichungen für weiche ferromagnetische Medien begründet. Durch Lösung dieses Systems wird eine Knicklast ermittelt. Die Methode wird anhand des Beispieles der kreisförmigen Platte illustriert. In dieser Abhandlung werden Maxwell Spannungen verwendet, aber es wird gezeigt dasz andere Modelle (insonderheit Amperesche Stromstärke) für die magnetoelastischen Spannungen das gleiche Resultat bilden.

     

Millimeter wave rheometry: theory and experiment

A novel millimeter wave (MMW) rheometry is developed to determine the viscosity of fluids based on an unsteady film flow on an inclined plane. The method measures fringes due to MMW interference between the front and back surfaces of a fluid flowing across the field of view of a ceramic wave guide coupled to a MMW receiver operating at 137 GHz. With knowledge of the dielectric constant, the interference fringe spacing is used to calculate the thickness of the fluid layer. This thickness is then transformed into the viscosity by means of a simple hydrodynamic theory. Our results show that the MMW rheometry can practically distinguish between the 30, 100, and 200 Pa·s silicone oils. The geometry of the method allows for potential industrial applications such as measuring viscosity of the flowing slag down the walls of coal gasifiers. The MMW rheometry with simple modifications can be easily extended to measure important non-Newtonian fluid characteristics such as yield stress.     

Crack tip superblunting: experiment,theory and numerical simulation

Experimental revelation ofsuperblunting along plane strain predominant crack tip segment is reported here for modified polyproplene. As elucidated by a heuristic model of progressive circumferential cold-draw, the formation of superblunting crack tip depends critically on the ratio between the cold-draw propagation speed and the loading speed, and contributes significantly to the material toughening, especially for the improvement in impact toughness. Detailed numerical calculations are conducted based on a hyperelastic-viscoplastic and anisotropic damage constitutive model at finite deformation. The simulated results recapitulate the essential features of crack tip superblunting. The project supported by the National Natural Science Foundation of China     

Dynamic buckling of simple two-bar frames using catastrophe theory

Non-linear static and dynamic elastic buckling of simple imperfect two-bar frames, treated as continuous systems, are analyzed with the aid of catastrophe theory using a comprehensive and readily employed procedure. Static catastrophes are extended to the corresponding dynamic catastrophes of undamped frames under step loading (autonomous systems) by properly determining the dynamic singularity and bifurcational sets. Attention is focused on fold and cusp catastrophes. A local analysis based on Taylor's expansion of the non-linear equilibrium equation of the frame allows us: (a) to classify the total potential energy function of the frames to the canonical form of the corresponding universal unfolding of the seven elementary Thom's catastrophes, and (b) to easily obtain static and dynamic buckling loads, critical points (singularity sets) and related imperfection sensitivities (bifurcational sets). An illustrative example associated with a static and dynamic fold catastrophe demonstrates the efficiency and reliability of the methodology proposed herein.     

Modification in the theory on flexural-torsional buckling of structures

I.IntroductionltwasuntiIl899thattheflrsttreatmentwaspub1ishedofflexural-torsionalbucklingbyMichelII1]whoconsideredthelateralbucklingofbeamsofnarrowrectangularcross-sectionandwhoseworkwasextendedin19O5byTimoshenkol2ltoincludetheeffectsofwarpingtorsioninI-s…     

Thermal buckling of nanorod based on non-local elasticity theory

The buckling of nanostructures including as a nanobeam, nanorod, and nanotube in a temperature field is investigated based on the non-local elasticity field theory with non-linear strain gradients first proposed by Eringen. New higher-order governing differential equations both in transverse and axial direction for buckling of such nanostructures are derived based on the exact variational principle approach with corresponding higher-order non-local boundary conditions. Based on these new governing equations and boundary conditions, new analytical solutions for some practical examples on buckling of nanostructures are presented and analyzed in detail. Subsequently, the effects of non-local nanoscale and temperature change on critical buckling load are analyzed and discussed. It is observed that those factors have great influence on the critical buckling load of the nanostructures. In particular, the non-local stress very much affects the stiffness of nanostructures and the critical buckling load is significantly increased in the presence of non-local stress. The paper concludes that at low and room temperature the critical buckling load of nanostructures increases with increasing temperature change, while at high temperature the critical buckling load decreases with increasing temperature change. A critical temperature change which causes buckling without external load is also derived and discussed.     

振动力学、材料力学关于压杆稳定的综合实验

振动力学、材料力学关于压杆稳定性的综合实验可以拓宽学生思维与研究的空间，改善了人力资源和物质资源的利用效率，并具有实际的工程应用价值。     

A hyperchaotic time-delayed system with single-humped nonlinearity: theory and experiment

In this paper, two different concepts of multiple task motion planning algorithm for nonholonomic systems are considered. The egalitarian approach treats all the tasks equivalently and tries to solve all the tasks simultaneously. In contrast, the prioritarian approach arranges the tasks with decreasing priorities in such a way that the solution of the lower order task should not influence the solution of the higher order task. This paper contains the derivation of the egalitarian motion planning algorithm and the prioritarian motion planning algorithm. Moreover, the definitions of the three types of basic subtasks are also included. The efficiency of the egalitarian and prioritarian algorithms is presented with the simulation of the nonholonomic model of the unmanned surface vessel. The simulation results provide the data to perform a comparison of the egalitarian versus the prioritarian approach.     

Dynamic buckling of partially-sway frames with varying stiffness using catastrophe theory

This work deals with the static and dynamic stability analysis of imperfect partially-sway frames with non-uniform columns. The examined two-bar frames are elastically supported and subjected to an eccentrically vertical load at their joint. Through a linear stability analysis, the effect of the taper ratio of the column cross-section on the buckling capacity of the partially-sway frame is thoroughly discussed. Using a non-linear method an accurate formula has been established for determining the exact asymmetric bifurcation point associated with the maximum load carrying capacity. These findings have been re-derived more readily using Catastrophe Theory (CT) and considering the frame as a one degree-of-freedom (1-DOF) system through an efficient technique. A local analysis allows us to classify, after reduction, the total potential energy (TPE) function of the system to one of the seven elementary Thom׳s catastrophes (with known properties) and to obtain static and dynamic singularity as well as bifurcational sets. It has been found that geometrical and loading imperfections, which are always present in structural engineering problems, have a significant effect on the dynamic buckling loads. The efficiency of the present approach is illustrated via several examples, while results from finite element analyses are in good agreement with the analytical solution presented herein.     

Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory

This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic (MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate (SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO₃/CoFe₂O₄. The refined zigzag theory (RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton’s principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.     

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams.     

Comparisons of test and theory for nonsymmetric elastic-plastic buckling of shells of revolution

Experimental and analytical buckling pressures are presented for very carefully fabricated thin cylindrical shells with 45, 60 and 75° conical heads and for cylindrical shells with torispherical heads pierced by axisymmetric cylindrical nozzles of various thicknesses and diameters. Nonsymmetric buckling occurs at pressures for which some of the material is loading plastically in the neighborhoods of stress concentrations caused by meridional slope discontinuities. The buckling pressures for the cone-cylinder vessels are predicted within 2.6 per cent and for the pierced torispherical vessels within 4.4 per cent with use of BOSOR5, a computer program based on the finite difference energy method in which axisymmetric large deflections, nonlinear material properties and nonsymmetric bifurcation buckling are accounted for. The predicted buckling pressures of the pierced torispherical specimens are rather sensitive to details of the analytical model in the neighborhood of the juncture between the nozzle and the head. The buckling pressures of the cone-cylinder vessels can be accurately predicted by treatment of the wall material as elastic, enforcement of the full compatibility conditions at the juncture in the prebuckling analysis, and release of the rotation compatibility condition in the bifurcation (eigenvalue) analysis.     

Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory

Variational principles for the buckling and vibration of multi-walled carbon nanotubes （MWCNTs） are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary conditions coupled by small scale parameters. Hamilton＇s principle and Rayleigh＇s quotient for the buckling and vibration of the MWCNTs are given. The Rayleigh-Ritz method is used to study the buckling and vibration of the single-walled carbon nanotubes （SWCNTs） and double-walled carbon nanotubes （DWCNTs） with three typical boundary conditions. The numerical results reveal that the small scale parameter, aspect ratio, and boundary conditions have a profound effect on the buckling and vibration of the SWCNTs and DWCNTs.