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Formulation of Geometrically Nonlinear Microbeams Based on the Second Strain Gradient Theory

Karparvarfard, Mohammad Hassan | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46621 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen; Vatankhah, Ramin
  7. Abstract:
  8. Nowadays, the usage of beam-shaped structures has widely spread in micro- and nano-electromechanical systems; consequently, scholars are extremely interested in precise modeling of static and dynamic behaviors of them. As the beams utilized in MEMS and NEMS structures have thicknesses in the order of microns and sub-microns, the experimentally validated small scale effects would be considerable in their behavior. In fact, experiments manifest that the size-dependent behavior is an intrinsic feature of materials when they are used in small-scale structures. In the classical continuum mechanics, there exists no material length scale parameter. Thus, the classical theory is unable to capture the size-dependency of small-scale structures. Therefore, some non-classical continuum theories such as the higher order gradient theories have been proposed to validly predict the size-dependent mechanical behavior of small-scale structures. In this study, the geometrically nonlinear governing differential equation of motion and corresponding boundary conditions of small-scale Euler-Bernoulli beams are achieved using the second strain gradient theory. This theory is the most advanced non-classical continuum theory capable of capturing the size effects. The appearance of many higher-order material constants in the formulation can certify that it appropriately assesses the behavior of extremely small-scale structures. Applying the Hamilton principle, the governing equation of motion and the corresponding boundary conditions have been gained. Subsequently, the practical case of hinged-hinged beams has been focused to lay out the nonlinear size-dependent static bending and free vibration behaviors of the derived formulation. The attained results have been compared with those of linear second strain gradient as well as linear and nonlinear strain gradient theories, and linear and nonlinear classical theories
  9. Keywords:
  10. Microbeam ; Euler-Bernoulli Beam ; Nonlinear Behavior ; Strain Second Gradient ; Nonclassical Microbeams ; Continuum Mechanics

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