Search results for "Equations Of Motion"
showing 10 items of 143 documents
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…
Seismic response of braced frames with and without friction dampers
1995
Abstract The dynamic response of friction damped bracing systems and ordinary cross-bracing systems inserted into surrounding frames without lateral stiffness is analysed in order to compare the typical behaviour of the two different bracing systems. The cyclic force-displacement relationship in the two cases is accurately modelled on the basis of experimental and related numerical models which are available in the literature, and the structural dimensionless parameters defining the shapes of the cycles are stressed. Systems having the same average period of vibration in the elastic phase of the response are assumed to be comparable with one another, which leads to a relationship linking th…
A Simple Multibody Dynamic Model of Cross-Country Ski-Skating
2013
The purpose of this paper is to present the development of a simple multibody dynamic model matching the observed movements of the center of mass of a skier performing the skating technique in cross-country skiing. The formulation of the equation of motion was made using the Euler–Lagrange equations applied to a multibody tree-type system in three dimensions. The description of the lower limb of the skier and the ski was completed by employing three bodies, one representing the ski, and two representing the natural movements of the leg of the skier. This simple model is able to show an approximation of the movement of the center of mass of the skier and its velocity behavior allowing to stu…
3D simulations and experiments of guided wave propagation in adhesively bonded multi-layered structures
2010
Understanding guided wave propagation in multi-layered plates and interaction with discontinuities can be difficult, as well as the interpretation of the ultrasonic signals. Propagation of guided waves can be studied analytically solving the equations of motion with the proper boundary conditions; nevertheless analytical models can be difficult to solve for complex multi-layered structures or having inner discontinuities. The problem can be efficiently studied using numerical techniques. Simulation of guided wave propagation in multi-layered structures, for ultrasonic waves in the MHz range, is solved here with the finite element analysis based on an explicit integration rule to solve the e…
Application of viscoelastic hybrid models to vehicle crash simulation
2011
This paper presents an application of physical models composed of springs, dampers and masses in various arrangements to simulate a real car collision with a rigid pole. Equations of motion of these systems are being established and subsequently solutions to obtain differential equations are formulated. We begin with a general model consisting of two masses, two springs and two dampers and illustrate its application to modelling fore-frame and aft-frame of a vehicle. Hybrid models, as being particular cases of two-mass–spring–damper model, are elaborated afterwards and their application to predict results of real collision is shown. Models’ parameters are obtained by fitting their response …
Combining TMD and TLCD: analytical and experimental studies
2017
Abstract In these years several research efforts have been focused on developing efficient and reliable control devices for mitigating the structural response of tall and lightly damped buildings in case of strong dynamic excitations, such as wind and earthquake ones. In this context, Tuned Mass Dampers (TMDs) represent probably the most common control device due to their high control performances. On the other hand, Tuned Liquid Column Dampers (TLCDs) are increasingly becoming more popular because of some of their attractive features, cost-effectiveness among the others, even though they yield slightly less control performance compared to the classical TMDs. Aiming at combining the benefic…
A pedagogical flight simulator for longitudinal airplane flight
2009
This article presents a bi-dimensional model of flight and describes the implementation of a flight simulator able to describe the different phases of longitudinal flight of a real airplane. After identifying the relevant physical variables, the equations of motion are written and solved using a numerical integration method. Using computer simulations, flight paths and time evolution of the kinematics variables are analyzed for a complete flight of a light commercial airplane. The simulations take into account and reproduce the basic actions of a pilot to control the flight. The main maneuvers involved in pilotage are also predicted and explained in terms of model parameter variations induc…
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
2003
This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of…
Theoretical investigations of different excitation modes for Penning trap mass spectrometry
2013
Abstract In Penning trap mass spectrometry the motion of trapped ions is manipulated by external radio-frequency fields. This paper describes a general theoretical framework to classify the various types of excitation of the ion's motional modes, to identify the resonance frequencies, and to find the effective interaction Hamiltonians which are valid in the vicinity of the resonances. Instead of Cartesian or cylindrical coordinates and momenta our theoretical approach uses the complex oscillator amplitudes of the cyclotron, magnetron, and axial oscillators as its basic dynamical variables. Equations of motion are set up, which can be simplified in the vicinity of resonances by the resonatin…
Control of hysteretic instability in rotating machinery by elastic suspension systems subject to dry and viscous friction
2010
Abstract Most of the undesired whirling motions of rotating machines can be efficiently reduced by supporting journal boxes elastically and controlling their movement by viscous dampers or by dry friction surfaces normal to the shaft axis, which rub against the frame. In the case of dry dampers, resonance ranges of the floating support configuration can be easily cut off by planning a motionless adhesive state of the friction surfaces. On the contrary, the dry friction contact must change automatically into sliding conditions when the fixed support resonances are to be feared. Moreover, the whirl amplitude can be restrained throughout the speed range by a proper choice of the suspension-to-…