Related papers: Addressing geometric non-linearities with cantilev…
Group-VI transition metal dichalcogenides (TMDs), MoS$_2$ and MoSe$_2$, have emerged as prototypical low-dimensional systems with distinctive phononic and electronic properties, making them attractive for applications in nanoelectronics,…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena…
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navier-Stokes problem and in the von K\'{a}rm\'{a}n equations.…
The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the 'classical' approach…
It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that…
In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical-systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic…
Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than…
A linear decomposition of states underpins many classical systems. This is the case of the Helmholtz decomposition, used to split vector fields into divergence-free and potential components, and of the dry Boussinesq system in atmospheric…
Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a…
Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast…
This work investigates and compares the response of piezoelectrically actuated nonlinear microelectromechanical devices (MEMS) to direct and to degenerate parametric drives. We describe the regime of degenerate parametric amplification in…
We report on experiments performed on a cantilever-based tri-port nano-electro-mechanical (NEMS) device. Two ports are used for actuation and detection through the magnetomotive scheme, while the third port is a capacitively coupled gate…
This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively nonlinear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilizes the moment chain approach, where the…
Statistical physics in equilibrium grants us one of its most powerful tools: the equipartition principle. It states that the degrees of freedom of a mechanical system act as a thermometer: temperature is equal to the mean variance of their…
Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's…
State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly…
Nanoelectromechanical systems (NEMS) are devices integrating electrical and mechanical functionality on the nanoscale. Because of individual electron tunneling, such systems can show rich self-induced, highly non-linear dynamics. We show…