The Lanchester Damper—A Design Procedure for Optimizing the Damping Ratio for a Cylindrical Slug Damper Fitted to a Machine Element

1979 ◽  
Vol 101 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Y. H. J. Au ◽  
K. W. Ng ◽  
R. W. New
Keyword(s):  
Kinetic Energy ◽  
Optimum Condition ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Design Procedure ◽  
Forced Vibrations ◽  
Parent Body ◽  
Standard Theory ◽  
Machine Element

The present work shows how the equations of motion for a Lanchester damper can be modified to include the effects of a damper slug rolling inside a cavity within the parent body, and of the kinetic energy of the damping fluid. The effect of the slug rolling is to reduce the performance of the damper below that predicted by the standard theory and to require a different value for damping at the optimum condition. These effects are significant when the build-up of self-excited type of vibrations are to be prevented, and when small forced vibrations are to be controlled. Fluid kinetic energy effects can be neglected when the damping fluid is gaseous, but not necessarily so when it is a liquid.

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

1976 ◽  
Vol 18 (6) ◽  
pp. 292-302 ◽  
Author(s):  
P. B. Davies
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Flow Equation ◽  
External Excitation ◽  
Signal Flow Graphs ◽  
Flow Compensation ◽  
Circular Functions ◽  
Flow Graphs

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy

2018 ◽  
Vol 233 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Duy-Chinh Nguyen
Keyword(s):  
Kinetic Energy ◽  
Torsional Vibration ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Tuned Mass Damper ◽  
Optimal Parameters ◽  
Lagrangian Equations ◽  
Tuning Ratio ◽  
Mass Damper

In this paper, an analytical method is presented to determine the optimal parameters of the symmetric tuned mass damper, such as the ratio between natural frequency of tuned mass damper and shaft (tuning ratio) and the ratio of the viscous coefficient of tuned mass damper (damping ratio). The optimal parameters of tuned mass damper are applied to reduce the torsional vibration of the shaft based on consideration of the vibration duration and stability criterion. The dynamic equations of the shaft are provided via Lagrangian equations, and the optimal parameters of tuned mass damper are derived by using the principle of minimum kinetic energy. Analytical and numerical examples are implemented to verify the reliability of the proposed method. The analytical and numerical results indicate that the optimal parameters of tuned mass damper have significant effects in the torsional vibration reduction of the shaft.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

scholarly journals Dynamics of nanodust particles emitted from elongated initial orbits

2018 ◽  
Vol 617 ◽  
pp. A43 ◽  
Author(s):  
A. Czechowski ◽  
I. Mann
Keyword(s):  
Solar Wind ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Dust Cloud ◽  
Theoretical Models ◽  
Ecliptic Plane ◽  
Parent Body ◽  
The Sun ◽  
Trapping Region ◽  
Eccentric Orbits

Context. Because of high charge-to-mass ratio, the nanodust dynamics near the Sun is determined by interplay between the gravity and the electromagnetic forces. Depending on the point where it was created, a nanodust particle can either be trapped in a non-Keplerian orbit, or escape away from the Sun, reaching large velocity. The main source of nanodust is collisional fragmentation of larger dust grains, moving in approximately circular orbits inside the circumsolar dust cloud. Nanodust can also be released from cometary bodies, with highly elongated orbits. Aims. We use numerical simulations and theoretical models to study the dynamics of nanodust particles released from the parent bodies moving in elongated orbits around the Sun. We attempt to find out whether these particles can contribute to the trapped nanodust population. Methods. We use two methods: the motion of nanodust is described either by numerical solutions of full equations of motion, or by a two-dimensional (heliocentric distance vs. radial velocity) model based on the guiding-center approximation. Three models of the solar wind are employed, with different velocity profiles. Poynting–Robertson and the ion drag are included. Results. We find that the nanodust emitted from highly eccentric orbits with large aphelium distance, like those of sungrazing comets, is unlikely to be trapped. Some nanodust particles emitted from the inbound branch of such orbits can approach the Sun to within much shorter distances than the perihelium of the parent body. Unless destroyed by sublimation or other processes, these particles ultimately escape away from the Sun. Nanodust from highly eccentric orbits can be trapped if the orbits are contained within the boundary of the trapping region (for orbits close to ecliptic plane, within ~0.16 AU from the Sun). Particles that avoid trapping escape to large distances, gaining velocities comparable to that of the solar wind.

scholarly journals Seismic Assessment of 10-Story Building Using Tuned Mass Damper

2020 ◽  
Author(s):  
Mohammad Aghajani Delavar
Keyword(s):  
Frequency Tuning ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Tuned Mass Dampers ◽  
Earthquake Excitation ◽  
Optimum Parameters ◽  
Seismic Records ◽  
Structural Responses ◽  
Lateral Displacements ◽  
Shear Building

In this paper, optimum parameters of Tuned Mass Dampers (TMD) are considered to control the responses of 10-story shear building under harmonic loading and 22 set of seismic records of FEMA-P695. The criterion used to obtain the optimum parameters is to select mass ratio, the frequency (tuning) and damping ratio that would result in smallest lateral displacements. State-space equations of motion are presented to compute the structural responses by developing a MATLAB file. A 10-story shear building is presented as a case study to assess the effects of TMDs on the multi-story structures. The results indicate that using TMD can reduce structural responses up to the average 20% under earthquake excitation and up to 90% under harmonic loadings. TMDs are not always effective under any type of ground motion; therefore, being aware of the given location is significant to design TMDs properly.

A Large Displacement Formulation Using Euler’s Angles

1999 ◽  
Author(s):  
G. Biakeu ◽  
F. Thouverez ◽  
J. P. Laine ◽  
L. Jezequel
Keyword(s):  
Kinetic Energy ◽  
Equations Of Motion ◽  
Static Solution ◽  
Element Formulation ◽  
First Order ◽  
Nonlinear Relation ◽  
Newton Raphson ◽  
Body Formulation ◽  
Multi Body ◽  
Euler’S Angles

Abstract The goal of this paper is to present a flexible multi-body formulation involving large displacements. This method is based on a separate discretisation of the kinetic and the internal energies. To introduce flexibility, we discretize the structure in elements (of two nodes): on each element of the beam discretisation, the local frame is defined using Euler’s angles. A finite element formulation is then applied to describe the evolution of these angles along the beam neutral fibre. For the kinetic energy, each element is cut into two rigid bars whose characteristics are given by a first order Taylor factorisation on the general kinetic energy expression. These bars are linked by a nonlinear relation. We obtain the equations of motion by applying the Lagrange’s equations to the system. These equations are solved using the Newmark method in dynamic and a Newton-Raphson technique while looking for a static solution. The method is then applied to very classic problems such as the curved beam problem proposed by authors such as Simo [6, 9], Lee [4] or the rotational rod presented by Avello [1] and Simo [7, 8] etc...

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

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