Asymptotic Modal Analysis of Structure Borne Noise in Cross Beams

1989 ◽  
Vol 111 (4) ◽  
pp. 472-479
Author(s):  
R. M. Chi
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Intersection Point ◽  
Point Load ◽  
Upper And Lower Bounds ◽  
Analysis Technique ◽  
Coupling Constraint ◽  
Coupled Beams ◽  
Arbitrary Location ◽  
Limiting Case

The dynamic response (structure borne noise) of two cross beams intersecting perpendicularly to each other is studied for a point load applied vertically at an arbitrary location on one beam. The modal analysis technique is used to analyze the bending and torsional responses of the system of coupled beams. The modal equations of motion are derived from Lagrange’s equations with the coupling constraint at the beam intersection point included via Lagrange multipliers. For the limiting case of a large number of participating modes, an asymptotic modal analysis is performed resulting in simple estimates of the upper and lower bounds of the beam responses. These bound estimates are compared with the corresponding SEA results.

Investigation of Impact Profile and Isolation Effect in Automated Impact Device Design and Control for Operational Modal Analysis

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Z. C. Ong ◽  
C. C. Lee
Keyword(s):  
Modal Analysis ◽  
Isolation Effect ◽  
Time Averaging ◽  
Impact Device ◽  
Lack Of Information ◽  
Analysis Technique ◽  
And Control ◽  
Phase Angles ◽  
Synchronous Time

A novel modal analysis technique called impact-synchronous modal analysis (ISMA) was introduced in previous research. With the utilization of impact-synchronous time averaging (ISTA), this modal analysis can be performed in presence of ambient forces whereas the conventional analysis method requires machines to be totally shut down. However, lack of information of phase angles with respect to impact in ISMA has caused it to be labor-intensive and time-consuming. An automated impact device (AID) is introduced in this study in the effort to replace the manually operated impact hammer and prepare it to be used in the current practice of ISMA on the purpose of enhancing its effectiveness and practicability. Impact profile and isolation effect are noted to be the contributing parameters in this study. This paper devoted on calibrating and controlling of the AID which gives the desired impact profiles as compared to the manual impact hammer. The AID is found effective in the determination of dynamic characteristics when the device is isolated from the boundary condition of the test structure.

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Towards a Technique for Nonlinear Modal Analysis

2012 ◽  
Author(s):  
Simon A. Neild ◽  
Andrea Cammarano ◽  
David J. Wagg
Keyword(s):  
Normal Form ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Transformation Process ◽  
Second Order ◽  
Identity Transformation ◽  
Modal Testing ◽  
System Response ◽  
Weakly Nonlinear ◽  
Nonlinear Modal Analysis

In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.

Modeling, Simulation, and Modal Analysis Hydraulic Valve Lifter With Oil Compressibility Effects

1989 ◽  
Author(s):  
T. Hatch ◽  
A. P. Pisano
Keyword(s):  
Differential Equations ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Check Valve ◽  
Linear Differential Equations ◽  
Third Order ◽  
Mode Behavior ◽  
Special Cases ◽  
Linear Differential ◽  
Hydraulic Valve

Abstract A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multi-mode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid In the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, non-linear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.

Modal Analysis of Multi Layer Viscoelastic Rotors Considering Higher Order Model

2013 ◽  
Author(s):  
S. Chandraker ◽  
H. Roy ◽  
G. Maurya
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Stability Limit ◽  
Higher Order ◽  
Constitutive Relationship ◽  
Order System ◽  
Order Model ◽  
Rotor Shaft ◽  
Number Of Layers ◽  
Modal Damping

This paper involves the development of mathematical model of multilayered viscoelastic rotor using beam finite element and at the same time studying their modal analysis. The operator based constitutive relationship is used to obtain the equations of motion. The FE formulation contents higher order system where the number of order increases with the number of layers exists in the rotor shaft. Under these conditions, the complex modal behaviour of the rotor-shaft is studied to get an insight of the dynamic characteristics of the system, in terms of Modal Damping Factors, Stability Limit of Spin-speed (SLS), the directional Frequency Response Function (dFRF) as well as the direction of whirl of the shaft in different modes. Many researchers adopted this methodology for obtaining the dynamic behaviour of a second order system. This work is started by motivation of the absentia of work for higher order system.

Study on the Fluidelastic Vibration of Tube Arrays Using Modal Analysis Technique

1984 ◽  
Vol 106 (1) ◽  
pp. 17-24 ◽  
Author(s):  
K. Ohta ◽  
K. Kagawa ◽  
H. Tanaka ◽  
S. Takahara
Keyword(s):  
Modal Analysis ◽  
Heat Exchangers ◽  
Vibration Mode ◽  
Fluid Dynamic ◽  
Cross Flow ◽  
Dynamic Force ◽  
Reversed Flow ◽  
Critical Flow Velocity ◽  
Analysis Technique ◽  
Tube Arrays

This paper presents a method to calculate the critical flow velocity of fluidelastic vibration of tube arrays in heat exchangers. The method is based upon the modal analysis technique, which combines the fluid dynamic force caused by cross flow and the vibration characteristics of the complicated tube array to obtain its response. The analytical method enables us not only to take into account the vibration mode of tube array and nonuniformity of velocity and density distribution of cross flow, but also to estimate the effect of antivibration devices, such as spacer, connecting band, and so on. Numerical examples of constrained single-tube array, multi-tube array in reversed flow, and group of panels with spacers are described.

Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space

1962 ◽  
Vol 29 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Julius Miklowitz
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Integral Transform ◽  
Formal Solution ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Frequency Equation ◽  
Point Load ◽  
Phase Method ◽  
Stationary Phase Method

The problem treated is that of an infinite free plate excited symmetrically by two equal and normally opposed step point-loads on its faces. The problem is equivalent to that of the surface normal point-load excitation of an infinite elastic layer, half the thickness of the plate, overlying a rigid half-space with lubricated contact. The formal solution is obtained from the equations of motion in linear elasticity with the aid of a double integral transform technique and residue theory. The stationary phase method, and known characteristics of the governing Rayleigh-Lamb frequency equation, are used to analyze and evaluate numerically the far field displacements. It is shown that the head of the disturbance is composed predominantly of the low-frequency long waves from the lowest mode of wave transmission.

scholarly journals Dynamic Modal Analysis of Vertical Machining Centre Components

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Anayet U. Patwari ◽  
Waleed F. Faris ◽  
A. K. M. Nurul Amin ◽  
S. K. Loh
Keyword(s):  
Modal Analysis ◽  
Mode Shape ◽  
Modal Testing ◽  
Machine Component ◽  
Vibration Modes ◽  
Structural Dynamic ◽  
Element Simulation ◽  
Analysis Technique ◽  
Design Software

The paper presents a systematic procedure and details of the use of experimental and analytical modal analysis technique for structural dynamic evaluation processes of a vertical machining centre. The main results deal with assessment of the mode shape of the different components of the vertical machining centre. The simplified experimental modal analysis of different components of milling machine was carried out. This model of the different machine tool's structure is made by design software and analyzed by finite element simulation using ABAQUS software to extract the different theoretical mode shape of the components. The model is evaluated and corrected with experimental results by modal testing of the machine components in which the natural frequencies and the shape of vibration modes are analyzed. The analysis resulted in determination of the direction of the maximal compliance of a particular machine component.

Extensional Vibrations of Elastic Orthotropic Spherical Shells

1961 ◽  
Vol 28 (2) ◽  
pp. 229-237 ◽  
Author(s):  
W. H. Hoppmann ◽  
W. E. Baker
Keyword(s):  
Orthotropic Material ◽  
Orthotropic Shell ◽  
Equations Of Motion ◽  
Special Consideration ◽  
Uniform Thickness ◽  
Spherical Shells ◽  
Isotropic Shell ◽  
Principal Directions ◽  
Limiting Case ◽  
Orthotropic Shells

The extensional vibrations (momentless) of spherical shells of elastic orthotropic material have been studied theoretically. Equations of motion have been derived and solved. The principal directions of the elastic compliances are assumed to be along parallels of latitude and along meridians. In addition to the case of orthotropic shells of uniform thickness, the analysis may be applied in the case of shells with stiffeners attached. Special consideration is given to the isotropic shell as a limiting case of the orthotropic shell.

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