Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

Effects of surface and flexoelectricity on a piezoelectric nanobeam

Abstract: The effects of surface and flexoelectricity have been found in the presence of strong size dependence and should be technically taken into account for nano-scaled dielectric structures. This paper proposes a Bernoulli–Euler beam model to investigate the electromechanical coupling response of piezoelectric nanostructures, in which the effects of surface elasticity, dielectricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations with non-classical boundary conditions are naturally derived from a variational principle. Then the present beam model is directly applied to solve the static bending problems of cantilever beams. Without considering the residual surface stresses, the bending rigidity can be defined the same as that in classical piezoelectricity theory. The bending rigidity is found to increase for silicon nanowires and decrease for silver nanowires. Also the flexoelectric effect in piezoelectric nanowires has a momentous influence on the bending rigidity. The residual surface stresses which are usually neglected are found to be more important than the surface elasticity for the bending of nanowires. However, this has no influence on the effective electromechanical coupling coefficient. The deflections reveal the significance of the residual surface stresses and the bulk flexoelectric effects. The effective electromechanical coupling coefficient for piezoelectric nanowires is dramatically enhanced, which demonstrates the significant effects of the bulk flexoelectricity and surface piezoelectricity. The effects of surface and flexoelectricity decrease with the increase of the beam thickness, and therefore these effects can be ignored for large-scale structures. This work is very helpful in designing cantilever-beam-based nano-electro-devices.

A General Solution for the Bending of Beams on an Elastic Foundation of Arbitrary Continuity

Abstract: In the analysis of beams which are supported elastically along their entire length, it is usually assumed that the elastic support is provided either by a series of independent springs, or by a completely continuous elastic medium.The present paper proposes a method of solution for the intermediate cases, that is, for foundations of partial continuity, by assuming that such foundations may be represented by beams imbedded into an otherwise discontinuous supporting material. In a foundation of this type, there are three independent elastic constants, the resilience of the discontinuous spring layers above and below the beam that is within the foundation, and the flexural rigidity of the foundation beam itself. By changing the values of these three constants, elastic foundations of a wide variety may be produced or, conversely, the constants may be adjusted in such a manner as to represent approximately the characteristics of any given elastic supporting medium.In the paper a general procedure is presented ...

A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers

Abstract: The tensile force along a cylindrical lipid bilayer tube is proportional to the membrane’s bending modulus and inversely proportional to the tube radius. We show that this relation, which is experimentally exploited to measure bending rigidities, can be applied with even greater ease in computer simulations. Using a coarse-grained bilayer model we efficiently obtain bending rigidities that compare very well with complementary measurements based on an analysis of thermal undulation modes. We furthermore illustrate that no deviations from simple quadratic continuum theory occur up to a radius of curvature comparable to the bilayer thickness.