In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper...

deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. the governing differential equations and c...

Strain gradient elasticity and nonlocal are two enhanced elastic theories intensively used over the last fifty years to explain static dynamic phenomena that classical fails do. The theory has a clear differentiation from case by considering stresses at point of continuum as an integral defined in treated body. On other hand, strain is characterized non-classical because considers both potentia...

For classical elasticity, the constitutive equations (Hooke’s law) have the same functional form for both homogeneous and nonhomogeneous materials. However, for straingradient elasticity, such is not the case. This paper shows that for strain-gradient elasticity with volumetric and surface energy (Casal’s continuum), extra terms appear in the constitutive equations which are associated with the...

Fabrication, characterization and application of micro-/nano-rods/wires are among the hottest topics in materials science and applied physics. Micro-/nano-rod-based structures and devices are developed for a wide-ranging use in various fields of micro-/nanoscience (e.g. biology, electronics, medicine, optics, optoelectronics, photonics and sensors). It is well known that the structure and prope...

Nonlinear plate bending within Mindlin's strain gradient elasticity theory (SGT) is investigated by employing somewhat non-standard finite element methods. The main goal to compare the results provided geometrically nonlinear three-dimensional (3D) and Reissner–Mindlin theory, i.e., first-order shear deformation (FSDT), SGT. For 3D Green–Lagrange relations are adopted, while von Kármán strains ...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...