a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analy...

In this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. The Timoshenko beam theory is applied instead of the classical Euler-Bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. T...

In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...

In this paper the conjugate gradient (CG) method is employed for identifying the parameters of crack in a functionally graded beam from natural frequency measurement. The crack is modeled as a massless rotational spring with sectional flexibility. By using the Euler-Bernoulli beam theory on two separate beams respectively and applying the compatibility requirements of the crack, the characteris...

not only provides an elegant formula for evaluating ζ(2n), but it also tells us of the arithmetical nature of ζ(2n). In contrast, we know very little about ζ(2n + 1). One of the major achievements in number theory in the past half-century is R. Apéry’s proof that ζ(3) is irrational [2], but for n ≥ 2, the arithmetical nature of ζ(2n+ 1) remains open. Ramanujan made many beautiful and elegant di...

In this paper, we study some supercongruences involving multiple harmonic sums by using Bernoulli numbers. Our main theorem generalizes previous results by many different authors and confirms a conjecture by the authors and their collaborators. In the proof, we will need not only the ordinary multiple harmonic sums in which the indices are ordered, but also some variant forms in which the indic...