Dynamic analysis of second strain gradient elasticity through a wave finite element approach

In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-local” Lattice Spring Models (LSM) expounded, giving unified description SSG torsion. These LSM can be regarded as discrete micro-structural resulting transformed Fourier series. Weak both established based on theory. Subsequently, WFEM to formulate spectral problem compute wave dispersion characteristics from unit-cell structures. Finally, relations forced responses in micro-sized structures calculated Classical Theory (CT), some useful conclusions discussed.