scholarly journals Dynamics of Stress-Driven Two-Phase Elastic Beams

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1138
Author(s):  
Marzia Sara Vaccaro ◽  
Francesco Paolo Pinnola ◽  
Francesco Marotti de Sciarra ◽  
Raffaele Barretta
Keyword(s):  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Nonlocal Continuum ◽  
Two Phase ◽  
Structural Problems ◽  
Nonlocal Equations ◽  
Convenient Approach ◽  
Slender Beams ◽  
Strain Gradient Model ◽  
Well Posed

The dynamic behaviour of micro- and nano-beams is investigated by the nonlocal continuum mechanics, a computationally convenient approach with respect to atomistic strategies. Specifically, size effects are modelled by expressing elastic curvatures in terms of the integral mixture of stress-driven local and nonlocal phases, which leads to well-posed structural problems. Relevant nonlocal equations of the motion of slender beams are formulated and integrated by an analytical approach. The presented strategy is applied to simple case-problems of nanotechnological interest. Validation of the proposed nonlocal methodology is provided by comparing natural frequencies with the ones obtained by the classical strain gradient model of elasticity. The obtained outcomes can be useful for the design and optimisation of micro- and nano-electro-mechanical systems (M/NEMS).

scholarly journals Numerical study on the influence of acoustic natural frequencies on the dynamic behaviour of submerged and confined disk-like structures

2017 ◽  
Vol 73 ◽  
pp. 53-69 ◽  
Author(s):  
Matias Bossio ◽  
David Valentín ◽  
Alexandre Presas ◽  
David Ramos Martin ◽  
Eduard Egusquiza ◽  
...  
Keyword(s):  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Numerical Study

Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Distribution Patterns ◽  
Continuous Systems ◽  
Cantilever Beams ◽  
Transverse Vibrations ◽  
Discretization Technique

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

An Original Setup Test Rig for Analysing Lubricated Contact Under Dynamic Normal Excitation Forces

2003 ◽  
Author(s):  
Toufiq El Kilali ◽  
Joe¨l Perret-Liaudet ◽  
Denis Mazuyer
Keyword(s):  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Normal Load ◽  
Point Of View ◽  
Test Rig ◽  
Dynamic Excitation ◽  
Lubricated Contacts ◽  
Lubricated Contact ◽  
Set Up ◽  
New Machine

This paper concerns a new experimental set-up based on an optical EHL machine fitted with a dynamic excitation system. The test rig has been built and presented in this paper. Apparatus design derives from two previously defined experimental test rig. With this new machine, we can study the dynamic behaviour of lubricated contacts under sliding conditions on the both tribological and dynamical point of view. It allows to measure the oil film thickness and to visualise the lubricated dynamically loaded contact under sliding condition. It allows also to measure the dynamic response (acceleration) of the loaded contact under harmonic or random external normal load excitation superimposed on a static one. Capabilities of the apparatus are given in this paper. In particular, theoretical and experimental results concerning the system natural frequencies.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

Shock Waves ◽  
2017 ◽  
Vol 28 (2) ◽  
pp. 253-266 ◽  
Author(s):  
R. R. Tukhvatullina ◽  
S. M. Frolov
Keyword(s):  
Two Phase Flow ◽  
Bubbly Liquid ◽  
Phase Flow ◽  
Two Phase ◽  
Euler Model ◽  
Well Posed

The effect of annular two-phase flow upon the natural frequencies of a pipe

1998 ◽  
Vol 20 (8) ◽  
pp. 726-731 ◽  
Author(s):  
D.G. Gorman ◽  
Man Liu ◽  
J. Horacek
Keyword(s):  
Natural Frequencies ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase

Vibration Modelling of String-Harnessed Beam Structures Using Homogenization Techniques

2014 ◽  
Author(s):  
Blake Martin ◽  
Armaghan Salehian
Keyword(s):  
Continuum Model ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Strain Tensor ◽  
Space Structures ◽  
Power Cables ◽  
Structural Elements ◽  
Equivalent Continuum Model ◽  
Lagrange Strain ◽  
Equivalent Continuum

Harnessing structural elements with strings, power cables, and signal cables increases the complexity in modelling the dynamic behaviour of such structures. Developing models capable of accurately predicting the dynamic behaviour of these systems is of great importance for space structures that cannot be tested prior to launch. The focus of this work is obtaining an equivalent continuum model for string-harnessed beam-like structures with periodic wrapping patterns. The tension in the string is assumed to vary as the beam deflects. The displacement field with second-order terms is determined and from which the Green-Lagrange strain tensor is obtained. After finding kinetic and potential energy expressions Hamilton’s principle is used to obtain the partial differential equation and boundary conditions. Numerical results for the shift in the natural frequencies are presented for various string properties to investigate their effects on the structure.

scholarly journals Vibration frequency of prestress slender beams resting on Winkler elastic foundation

2006 ◽  
Vol 28 (4) ◽  
pp. 241-251
Author(s):  
Nguyen Dinh Kien
Keyword(s):  
Axial Force ◽  
Vibration Frequency ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Winkler Foundation ◽  
The Finite Element Method ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Mass Matrices ◽  
Slender Beams

The present paper investigates the vibration frequency of slender beams prestressing by axial force and resting on an elastic Winkler foundation by the finite element method. A beam element taking the effects of both the prestress and foundation support into account is formulated using the expression of strain energy. Using the developed element, the natural frequencies of beams having various boundary conditions are computed for different values of the axial force and foundation stiffness. The influence of the axial force and the foundation stiffness on the frequency of the beams is investigated. The effect of partial support by the foundation and the type of mass matrices on the vibration frequency of the beam is also studied and highlighted.

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