The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

We derive exact dispersion relations for axial and flexural elastic wave motion in a rod and a beam under finite deformation. For axial motion we consider a simple rod model, and for flexural motion we employ the EulerBernoulli kinematic hypothesis and consider both a conventional transverse motion model and an inextensional planar motion model. The underlying formulation uses the Cauchy stress...

This work deals with the LQG control problem of a flexible beam clamped at one end and with a point mass at the free end, where a boundary control force can be applied. A class of finite-dimensional control laws is proposed here, derived on the basis of the EulerBernoulli infinite-dimensional beam model. By means of this approach it is possible to take into account also the higher order modes t...

In order to extract as much energy as possible from ambient vibrations, many vibration-based energy harvesters (VEHs) are designed to resonate at a specific base excitation frequency. Unfortunately, many vibration energy sources are low frequency (0.5 Hz-100 Hz), intermittent, and broadband. Thus, resonant VEHs would not be excited continuously and would require a large mass or size to tune to ...

This work presents a comprehensive methodology for dimensional reduction of anisotropic slender structures with embedded anisotropic piezocomposite materials. The analysis is based on a variational-asymptotic formulation, and provides cross-sectional stiffness, inertia and actuation forces for a beam modeling of the structure. It can retain higher-order information corresponding to non-classica...