Search results for "Stiffness matrix"
showing 10 items of 20 documents
Vibration reduction on city buses: Determination of optimal position of engine mounts
2010
International audience; This study is composed of three essential parts. The first part describes an indirect semi-experimental method which is used to reconstruct the excitation force of an operating diesel engine from the acceleration data measured at the mounting points. These internal forces can not be directly measured with force sensors; they have to be derived from the dynamic deformation of the engine support, so a theoretical analysis is carried out to derive the equations for the force re-construction.The second part deals with prevention of low frequency vibration of the powertrain from spreading to the rest of the vehicle. Three uncoupling techniques are used to minimize these v…
Preventing the oil film instability in rotor-dynamics
2016
Horizontal rotor systems on lubricated journal bearings may incur instability risks depending on the load and the angular speed. The instability is associated with the asymmetry of the stiffness matrix of the bearings around the equilibrium position, in like manner as the internal hysteretic instability somehow, where some beneficial effect is indeed obtainable by an anisotropic configuration of the support stiffness. Hence, the idea of the present analysis is to check if similar advantages are also obtainable towards the oil film instability. The instability thresholds are calculated by usual methods, such as the Routh criterion or the direct search for the system eigenvalues. The results …
Optical and Acoustic Vibrations Confined in Anatase TiO2 Nanoparticles under High-Pressure
2014
International audience; The effect of an applied high pressure on the optical and acoustic vibrations of small anatase TiO2 nanoparticles is studied using Raman scattering. All the Raman peaks show a significant variation of their frequency with pressure, except for the low-frequency peak which is due to acoustic vibrations confined in the nanoparticles. These variations (or lack thereof) are compared to first-principles calculations of the stiffness tensor and phonons of bulk anatase TiO2 as a function of pressure. In particular, the variation of the shape of the low-frequency peak is explained by the increase of the elastic anisotropy of anatase TiO2 as pressure is increased.
Nonlocal elasticity and related variational principles
2001
Abstract The Eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied. The model is refined by assuming an attenuation function depending on the `geodetical distance' between material particles, such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented. A suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model. The nonlocal elasticity boundary-value problem for infinitesimal displacements and quasi-static loads is addressed and the conditions for the solution uniqueness are established. Three variational principles, nonlocal…
A nonhomogeneous nonlocal elasticity model
2006
Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the int…
A symmetric nonlocal damage theory
2003
The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present app…
Integration of finite displacement interface element in reference and current configurations
2017
In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two i…
A regular variational boundary model for free vibrations of magneto-electro-elastic structures
2011
In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffne…
A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work
2013
Abstract In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios be…
Meshless meso-modeling of masonry in the computational homogenization framework
2017
In the present study a multi-scale computational strategy for the analysis of structures made-up of masonry material is presented. The structural macroscopic behavior is obtained making use of the Computational Homogenization (CH) technique based on the solution of the Boundary Value Problem (BVP) of a detailed Unit Cell (UC) chosen at the mesoscale and representative of the heterogeneous material. The attention is focused on those materials that can be regarded as an assembly of units interfaced by adhesive/cohesive joints. Therefore, the smallest UC is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter show an elastoplastic soft…