Although acoustics is one of the disciplines of mechanics, its ”geometrization” is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research a...

A recently developed Finite-Element (FE) model for the precise computation of electrostatic driven MEMS (Micro-ElectroMechanical-Systems) is presented. Thereby, we fully take geometric nonlinearity, contact in the snap-in mode, nonlinear electrostatic coupling forces as well as the moving of charged thin membrane-plate structures (electrodes) in an electric field into account. Furthermore, sinc...

Abstract The response of slender bridge piers to horizontal actions may be significantly influenced by geometric nonlinearities. In such conditions, the use sophisticated models implemented in complex structural analysis software can economically disadvantageous, especially preliminary design phases. This paper proposes a simple numerical procedure compute nonlinear pushover cantilever subject ...

A rectangular plate with a wedge profile creating an Acoustic Black Hole (ABH) termination is studied numerically. particular emphasis put on combining two different types of nonlinearity in order to improve the passive damping capacity ABH by transferring energy high-frequency range where it more efficient. First, addition contact points create vibro-impact black hole (VI-ABH) taken into accou...

1. Background/Problem In real-time surgery simulation and planning, the Finite Element Method (FEM) is often used to simulate small and large deformation of human tissue for applications such as laparoscopy training [4], needle insertion planning [1], and image registration [2]. In using FEM, assumptions must be made about material properties and the scale of deformation of human tissues in and...

Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton’s second law. The method of multiple scales...

Realistic soft tissue models running in real-time are required for the development of computer-based surgical training systems. To construct a realistic soft tissue model, finite element (FE) modeling techniques are preferred over the particle-based techniques since the material properties can be integrated directly into the FE model to provide more accurate visual and haptic feedback to a user...

A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a C2 function H to be the mean curvature of some conformal flat metric is that H is positive somewhere. We show that, when the boundary is umbilic and the function ...

The numerical assessment of T-tail flutter requires a nonlinear description the structural deformations when unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, deformation vertical tail plane (VTP) out-of-plane bending results in spurious stiffening proportional to steady lift forces, which is corrected by incorporating second-order equations While ...