PROPAGATION AND RESONANCE OF COMPOSITE WAVES IN PRISMATIC RODS

1936 ◽  
Vol 14a (3) ◽  
pp. 66-70
Author(s):  
R. Ruedy
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Experimental Results ◽  
Cubic Equation ◽  
Resonance Frequencies ◽  
Good Agreement

By taking into account the three main terms of the equation of motion of the prismatic rod, there is obtained for the frequency a cubic equation which is in good agreement with the experimental results when the thickness of the rod is not negligible compared with its length but does not exceed about one-fifth of the length. It corresponds to the equation obtained for a system with three degrees of freedom.For a composite vibration consisting of a wave of dilatation and a wave of distortion in the direction of the smallest dimension of the rod, and waves of dilatation in the two other directions, the equations of motion combined with some of the boundary conditions yield another cubic equation for the resonance frequencies.

PROPAGATION AND RESONANCE OF LONGITUDINAL WAVES IN PRISMATIC RODS

1936 ◽  
Vol 14a (2) ◽  
pp. 48-55
Author(s):  
R. Ruedy
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Equations Of Motion ◽  
Poisson's Ratio ◽  
Longitudinal Waves ◽  
Fundamental Frequencies ◽  
Cubic Equation ◽  
Resonance Frequencies ◽  
Fourth Series ◽  
Shearing Motion

For vibrations involving shearing and rotation, and for those involving both distortion and dilatation, the equations of motion combined with the boundary conditions yield in the simplest case a cubic equation for the resonance frequencies; its solution depends on Poisson's ratio and on the resonance frequencies fx, fy, fz, which the rod possesses when in pure shearing motion in the direction of its three axes. Three series of resonance frequencies are obtained when fy and fz are constant and the frequencies of the overtones are inserted for fx. A fourth series of resonance frequencies begins above the highest of the fundamental frequencies fx, fy, fz.

Dynamic Characteristics of a Six-Bar Hinge Mechanism as Used in Cabinets

2004 ◽  
Author(s):  
Fu-Chen Chen
Keyword(s):  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Simulation Results ◽  
Good Agreement

The dynamic characteristics of a six bar hinge mechanism as used in home cabinets were investigated using the method of equation of motion. The derived equations of motion were numerically solved and the motion of the hinge mechanism was simulated. The influence of mass and width of the cabinet door on the dynamic characteristics of the hinge mechanism as well as the effect of the hinge number on the force applied on the handle were also investigated. The experimental and simulation results showed good agreement with an error of under 2%, which validated the simulation results. The proposed approach can be used by hinge manufacturers for the design and analysis of similar hinge mechanisms.

Vibration Analysis of Drug Delivery CNTs Using Transfer Matrix Method

2011 ◽  
Author(s):  
Anooshiravan Farshidianfar ◽  
Ali A. Ghassabi ◽  
Mohammad H. Farshidianfar ◽  
Mohammad Hoseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Equation Of Motion ◽  
Beam Model ◽  
Multi Wall Carbon Nanotubes ◽  
Resonance Frequencies ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

The free vibration and instability of fluid-conveying multi-wall carbon nanotubes (MWCNTs) are studied based on an Euler-Bernoulli beam model. A theory based on the transfer matrix method (TMM) is presented. The validity of the theory was confirmed for MWCNTs with different boundary conditions. The effects of the fluid flow velocity were studied on MWCNTs with simply-supported and clamped boundary conditions. Furthermore, the effects of the CNTs’ thickness, radius and length were investigated on resonance frequencies. The CNT was found to posses certain frequency behaviors at different geometries. The effect of the damping corriolis term was studied in the equation of motion. Finally, a useful simplification is introduced in the equation of motion.

The Influence of Oil Lubricated Journal Bearings on the Dynamics of Rotating Systems

1976 ◽  
Vol 190 (1) ◽  
pp. 627-633 ◽  
Author(s):  
H. McCallion ◽  
D. R. Wales
Keyword(s):  
Boundary Conditions ◽  
Computer Program ◽  
Translational Motion ◽  
Journal Bearings ◽  
Experimental Results ◽  
Oil Film ◽  
Rotating Systems ◽  
Film Boundary ◽  
Good Agreement

SYNOPSIS A computer program representing a shaft and rotor whirling in bearings which allows for realistic oil film boundary conditions and non-circular bearing profiles has been developed. It gave good agreement with experimental results published by Brown and France. With the aim of increasing understanding of the influence of bearing profile on system instability, the program calculates the timewise variation of the energy in translational motion supplied to the rotor by oil film forces. One case is illustrated.

The Effects of Shear Deformation and Rotary Inertia on the Lateral Frequencies of Cantilever Beams in Bending

1972 ◽  
Vol 94 (1) ◽  
pp. 267-278 ◽  
Author(s):  
W. Carnegie ◽  
J. Thomas
Keyword(s):  
Finite Difference ◽  
Shear Deformation ◽  
Matrix Equation ◽  
Equations Of Motion ◽  
Flexural Vibration ◽  
Experimental Results ◽  
Rotary Inertia ◽  
Cantilever Beams ◽  
Algebraic Equations ◽  
Good Agreement

This paper deals with the effect of shear deformation and rotary inertia on the frequencies of flexural vibration of pre-twisted and non-pre-twisted uniform and tapered cantilever beams. The equations of motion are derived and transformed into a set of linear simultaneous algebraic equations by using finite-difference solutions for the derivatives. The resulting eigenvalue matrix equation is solved for the frequency parameters by a QR transformation. The effects of various tapers, depth-to-length ratios and pre-twist angles on the frequencies of vibration are investigated for the first five modes. Results obtained are compared with those presented by other investigators where available and show good agreement. The experimental results presented also show good agreement with the corresponding theoretical values.

A Generalized Formulation of the Vectorial Equations of Motion for Nonprismatic Thin Space Beams

1971 ◽  
Vol 38 (4) ◽  
pp. 955-960 ◽  
Author(s):  
M. F. Massoud
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Displacement Vector ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Linear Displacement ◽  
Characteristic Dimension ◽  
Center Line ◽  
Thin Beam ◽  
Arbitrary Space

The formulation of a generalized vectorial equation of motion for small vibrations of any nonprismatic thin beam, which center line is an arbitrary space curve, is presented. The thin beam is such that any characteristic dimension of any cross section is assumed to be small compared to the local radii of curvature and geometric torsion. The equations of motion are given in terms of two independent vectors; a linear displacement vector of the centroid of the cross section and a rotation displacement vector about the centroid. A brief discussion of the boundary conditions in terms of these two vectors is given. The effects of rotary inertia and the shear deformation upon the general derived expressions are discussed.

scholarly journals Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Nikola Vladimir ◽  
Dae Seung Cho
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Thick Plate ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Mixed Boundary Conditions ◽  
Free Vibrations ◽  
Force Displacement ◽  
Good Agreement

In the present thick plate vibration theory, governing equations of force-displacement relations and equilibrium of forces are reduced to the system of three partial differential equations of motion with total deflection, which consists of bending and shear contribution, and angles of rotation as the basic unknown functions. The system is starting one for the application of any analytical or numerical method. Most of the analytical methods deal with those three equations, some of them with two (total and bending deflection), and recently a solution based on one equation related to total deflection has been proposed. In this paper, a system of three equations is reduced to one equation with bending deflection acting as a potential function. Method of separation of variables is applied and analytical solution of differential equation is obtained in closed form. Any combination of boundary conditions can be considered. However, the exact solution of boundary value problem is achieved for a plate with two opposite simply supported edges, while for mixed boundary conditions, an approximate solution is derived. Numerical results of illustrative examples are compared with those known in the literature, and very good agreement is achieved.

Modelling Flame-Generated Noise in a Partially Premixed, Bluff Body Stabilized Model Combustor

2012 ◽  
Author(s):  
Saverio Tufano ◽  
Phil Stopford ◽  
J. C. Roman Casado ◽  
J. B. W. Kok
Keyword(s):  
Gas Turbine ◽  
Bluff Body ◽  
Cfd Simulation ◽  
Experimental Results ◽  
Combustion Model ◽  
Acoustic Oscillations ◽  
Gas Turbine Combustors ◽  
Resonance Frequencies ◽  
Partially Premixed ◽  
Good Agreement

Numerical simulation using Computational Fluid Dynamics (CFD) has become increasingly important as a tool to predict the potential occurrence of combustion instabilities in gas turbine combustors operating in lean premixed mode. Within the EU-funded Marie Curie project, LIMOUSINE (Limit cycles of thermo-acoustic oscillations in gas turbine combustors), a model test burner has been built in order to have reproducible experimental results for model validation. The burner consists of a Rijke tube of rectangular section having a flame-stabilizing wedge at about 1/4 of its length. Fuel and air supplies were carefully designed to give closed end acoustic inlet boundary conditions while the atmospheric outlet representing an acoustically open end. A transient CFD simulation of the turbulent, partially premixed, bluff body stabilized combusting flow has been carried out for the LIMOUSINE burner using ANSYS CFX commercial software. A 2-D section has been modelled by means of the scale resolving turbulence model, Scale-Adaptive Simulation (SAS), and a two-step Eddy Dissipation combustion model. Experiments were performed on the LIMOUSINE model burner to measure the dynamic variation of pressure and temperature. Results were obtained for several cases with power input ranging from 40 to 60 kW and air factors between 1.2 and 1.8. The CFD results are found to be in good agreement with experiments: the flame is predicted to stabilise on the bluff body in the fluid recirculation zone; resonance frequencies are found to change depending on power and air excess ratio and have a good agreement with experimental results and analytical values; pressure oscillations are consistent with pipe acoustic modes.

Longitudinal Vibration and Damping Analysis of Adhesively Bonded Double-Strap Joints

1992 ◽  
Vol 114 (3) ◽  
pp. 330-337 ◽  
Author(s):  
S. He ◽  
M. D. Rao
Keyword(s):  
Boundary Conditions ◽  
Complex Modulus ◽  
Longitudinal Vibration ◽  
Structural Parameters ◽  
Equations Of Motion ◽  
Adhesive Layer ◽  
Adhesively Bonded ◽  
Searching Strategy ◽  
Resonance Frequencies ◽  
Loss Factors

A mathematical model to study the longitudinal vibration of an adhesively bonded double-strap joint is presented in this paper. Energy method and Hamilton’s principle are used to derive the governing equations of motion and natural boundary conditions of the joint system. The adhesive is modeled as a viscoelastic material using complex modulus approach. Both the shear and longitudinal deformation in the adhesive layer are included in the analysis. The equations to predict the system resonance frequencies and loss factors are derived from the system natural and forced boundary conditions for the case of simply supported boundary conditions. A special searching strategy for finding the zeros of a complex determinant has been utilized to obtain the numerical results. The effects of the adhesive shear modulus and structural parameters such as lap ratio, adhesive and strap thickness on the system resonance frequencies and loss factors are also studied.

Equations of Motion for an Inextensible Beam Undergoing Large Deflections

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Earl Dowell ◽  
Kevin McHugh
Keyword(s):  
Boundary Conditions ◽  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Large Deflections ◽  
Lagrange Equations ◽  
Cantilevered Beam ◽  
Alternative Approaches ◽  
Transverse Deflection ◽  
Free Beam

The Euler–Lagrange equations and the associated boundary conditions have been derived for an inextensible beam undergoing large deflections. The inextensibility constraint between axial and transverse deflection is considered via two alternative approaches based upon Hamilton's principle, which have been proved to yield equivalent results. In one approach, the constraint has been appended to the system Lagrangian via a Lagrange multiplier, while in the other approach the axial deflection has been expressed in terms of the transverse deflection, and the equation of motion for the transverse deflection has been determined directly. Boundary conditions for a cantilevered beam and a free–free beam have been considered and allow for explicit results for each system's equations of motion. Finally, the Lagrange multiplier approach has been extended to equations of motion of cantilevered and free–free plates.

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