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81.
Shamim I. Ansari 《Proceedings of the American Mathematical Society》2002,130(10):2905-2909
In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.
82.
D. Kocheva G. Rainovski J. Jolie N. Pietralla A. Blazhev A. Astier R. Altenkirch S. Ansari Th. Braunroth M. L. Cortés A. Dewald F. Diel M. Djongolov C. Fransen K. Gladnishki A. Hennig V. Karayonchev J. M. Keatings E. Kluge J. Litzinger C. Müller-Gatermann P. Petkov M. Rudigier M. Scheck Ph. Scholz P. Spagnoletti M. Spieker C. Stahl R. Stegmann M. Stoyanova P. Thöle N. Warr V. Werner W. Witt D. Wölk K. O. Zell P. Van Isacker V. Yu. Ponomarev 《The European Physical Journal A - Hadrons and Nuclei》2017,53(9):175
83.
Eringen’s nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler–Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature. 相似文献
84.
Nowadays, the eye-catching characteristics of boron nitride nanotubes, in particular, the capability of sensing nano-objects, have opened up new prospects to develop the bio-/nano-sensing technologies. This research deals with physically affected single-walled boron nitride nanotubes (SWBNNT) as nano-sensors for sensing attached nanoscale objects. Three different boundary conditions including simply supported at both ends, clamped-free and clamped-clamped are considered to illustrate the vibrational behaviour of SWBNNTs as nano-sensor. The Rayleigh and Timoshenko beam theories are employed to model the SWBNNT. Also, the nonlocal strain gradient model is utilized to capture the size-dependent effects. One of the major factors in the scrutiny of mass nano-sensors is pertinent to the variation in frequency shift magnitudes against the number and mass weight values of attached nanoparticles. Herein, the effects of the nonlocal and material length scale parameters, the number and location of nano-objects, the rotary inertia and mass weight magnitudes of attached nanoparticles, the aspect ratio of SWBNNT, electrical potential and different boundary conditions on the variation in frequency shift and resonant frequency are analysed. 相似文献
85.
Kohansal-Vajargah M. Ansari R. Faraji-Oskouie M. Bazdid-Vahdati M. 《应用数学和力学(英文版)》2021,42(7):999-1012
Based on the micropolar theory(MPT), a two-dimensional(2 D) element is proposed to describe the free vibration response of structures. In the context of the MPT, a 2 D formulation is developed within the ABAQUS finite element software. The user-defined element(UEL) subroutine is used to implement a micropolar element. The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied. The effect of micro-inertia becomes dominant, and by considering the micropolar effects, the frequencies decrease. Also, there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales, and this difference decreases when the side length-to-length scale ratio becomes large. 相似文献
86.
V. Mohammadi R. Ansari M. Faghih Shojaei R. Gholami S. Sahmani 《Nonlinear dynamics》2013,73(3):1515-1526
In the present study, the dynamic pull-in instability and free vibration of circular microplates subjected to combined hydrostatic and electrostatic forces are investigated. To take size effects into account, the strain gradient elasticity theory is incorporated into the Kirchhoff plate theory to develop a nonclassical plate model including three internal material length scale parameters. By using Hamilton’s principle, the higher-order governing equation and the corresponding boundary conditions are obtained. Afterward, a generalized differential quadrature (GDQ) method is employed to discritize the governing differential equations along with simply supported and clamped edge supports. To evaluate the pull-in voltage and vibration frequencies of actuated microplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. Also, a comparison between the pull-in voltages predicted by the strain gradient theory and the degenerated ones is presented. It is revealed that increasing the dimensionless internal length scale parameter or decreasing the applied hydrostatic pressures leads to higher values of the pull-in voltage. Moreover, it is found that the value of pull-in hydrostatic pressure decreases corresponding to higher dimensionless internal length scale parameters and applied voltages. 相似文献
87.
88.
Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form. 相似文献
89.
In this paper, a size-dependent first-order shear deformable shell model is developed based upon the modified strain gradient theory (MSGT) for the axial buckling analysis of functionally graded (FG) circular cylindrical microshells. It is assumed that the material properties of FG materials, which obey a simple power-law distribution, vary through the thickness direction. The principle of virtual work is utilized to formulate the governing equations and corresponding boundary conditions. Numerical results are presented for the axial buckling of FG circular cylindrical microshells subject to simply-supported end conditions and the effects of material length scale parameter, material property gradient index, length-to-radius ratio and circumferential mode number on the size-dependent critical buckling load are extensively studied. For comparison purpose, the critical buckling loads predicted by modified couple stress theory (MCST) and classical theory (CT) are also presented. Results show that the size effect plays an important role for lower values of dimensionless length scale parameter. Moreover, it is observed that the critical buckling loads obtained based on MSGT are greater than those obtained based on MCST and CT. 相似文献
90.
Multimode generalization of Schrödinger cat states of light is discussed. Two-mode Schrödinger cat states are considered as an example. Squeezing in even and odd coherent states of a two-mode field is studied. 相似文献