Line Moment Research Articles

ACTIVE CONTROL OF SOUND RADIATION FROM A RECTANGULAR PLATE EXCITED BY A LINE MOMENT

This paper analytically investigates the active control of sound radiation from a simply supported rectangular plate with line moment excitation. This model simulates ship hull vibration due to the flutter of the ship's deck or the vibration of a fuselage due to the flutter of an aircraft wing. Two control strategies, volume velocity cancellation and radiated sound power minimization, are applied to drive a long and narrow piezoelectric actuator to reduce the radiated power. The result shows that a reduction of radiated power by these two control strategies is made possible by the mechanisms of modal suppression and modal restructuring. A numerical analysis shows that the performance of the active control method is related to the location of the line moment and an actuator. For the case in which the line moment is excited at the midline of the plate, the strategy of volume velocity cancellation is unable to reduce the sound radiated power. However, in the case where the actuator is located at the midline of the plate, both control strategies lead to the same reduction in radiated power except the control of the radiation of modes (even, 1). On the other hand, there exists a large amount of sound power radiation near the low frequency resonate mode (even, 1) when the line moment and the actuator are located off the midline of a plate and volume velocity cancellation is applied to control the radiated power from the plate.

Active control of sound radiation from rectangular plates using multiple piezoelectric actuators

Active control of sound radiation from a vibrating plate excited by a harmonic line moment is analytically investigated. This model of simply supported rectangular plate with a line moment excitation is used to simulate the vibration of a ship hull or aircraft fuselage from the flutter of ship deck or aircraft wing, respectively. The control is achieved using various configurations of piezoelectric actuators, and the strategy of radiated power minimization is used to obtain the optimal control input voltage. The efficiency of the active control is dependent on the location of the line moment and the actuators, and the attenuation of radiated sound power is related to two physical mechanisms that are modal suppression and modal restructuring. The numerical result shows that significant attenuation of radiated sound power for volumetric modes (odd, 1) in the low frequency range can be achieved with one control actuator located at the center of plate. Irrespective of whether the excitation is on or off resonance, more actuators result in higher attenuation of radiated sound power.

Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω2〉 and the frequency of only one singularity ω2 of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.

Active Structural Acoustic Control for Rectangular Plate with a Line Moment Excitation

AbstractActive control of noise radiation from vibrating plate excited by a harmonic line moment is analytically investigated. This study model of simple supported rectangular plate with a line moment excitation is used to simulate the vibration of ship hull or fuselage from the flutter of ship deck or aircraft wing respectively. The control is achieved by various configurations of piezoelectric actuators. The strategy of radiated power minimization is used to obtain the optimal control input unit voltage. The numerical results show that the significant attenuation of noise radiated power for volumetric modes in the low frequency range can be achieved with one control actuator located at the center of plate, irrespective of whether the excitation is on or off resonance. The efficiency of the active control is dependent on the location of the line moment and the actuators. It is also shown that the modal suppression and modal restructuring are two physical mechanisms of radiated power attenuation.

Numerical Simulation of Baffle-Supported Tube Bundle Vibration by the Method of Finite Differences

Tube bundles in heat exchangers are often damaged due to flow-induced vibrations. To simulate the fluid-structure interaction between the tubes and the flow field, which seems to be the only reliable way to predict flow-induced vibration of tube bundles, a coupled numerical solver for the governing Navier-Stokes equations of the flow field as well as for the structural response has to be used. Since commercial codes still require a large computational effort to calculate the fluid-structure interaction, one has to develop special program codes for certain technical problems. This paper deals with a numerical method to calculate the structural response of baffle-supported heat exchanger tubes due to outer forces such as flow and contact forces. The equations of motion for a cylindrical tube including torsional movement are developed. They are discretized in space by the means of Finite Differences and in time by Newmark′s method of constant acceleration. Non-linear frictional impact forces due to the baffle supports are introduced as additional line loads and line moments. Flow forces at this stage of development are modeled by simplified assumptions concerning vortex shedding. Numerical examples show the consistency of the calculated solutions. The algorithm is stable and converges for parameters of practical importance. Only little mathematical effort is needed compared to the Finite Element technique or modal analysis. A Navier-Stokes flow solver already developed can now be integrated into the vibration simulation code.

A study on sound radiation from isotropic plates stiffened by unsymmetrical beams

The determination of sound pressure radiated from periodic plate structures is fundamental in the estimation of noise level in aircraft fuselages or ship hull structures. As a robust approach to this problem, here a very general and comprehensive analytical model is developed for predicting the sound radiated by a vibrating plate stiffened by periodically spaced orthogonal unsymmetrical beams subjected to a sinusoidally time varying point load. The plate is assumed to be infinite in extent, and the beams are considered to exert both line force and moment reactions on it. Using this theoretical model, the sound pressure levels on axis in a semi-infinited fluid (water) bounded by the plate were calculated using three numerical tools such as the Gauss-Jordan method, the LU decomposition method and the IMSL numberial package. Especially, the variation in the sound pressure levels and their modes were investigated according to the change in frequency, bay spacing and bay distance.

Active Control of Vibration

Introduction to Mechanical Vibrations: Terminology. Single-degree-of-freedom (SDOF) Systems. Free Motion of SDOF Systems. Damped Motion of SDOF Systems. Forced Response of SDOF Systems. Transient Response of SDOF Systems. Multi-degree-of-freedom (MDOF) Systems. Free Motion of MDOF Systems. Forced Response of MDOF Systems. Damped Motion of MDOF Systems. Finite Element Analysis of Vibrating Mechanical Systems. Introduction to Waves in Structures: Longitudinal Waves. Flexural Waves. Flexural Response of an Infinite Beam to an Oscillating Point Force. Flexural Wave Power Flow. Flexural Response of an Infinite Thin Beam to an Oscillating Line Moment. Free Flexural Motion of Finite Thin Beams. Response of a Finite Thin Beam to an Arbitrary Oscillating Force Distribution. Vibration of Thin Plates. Free Vibration of Thin Plates. Response of a Thin Rectangular Simply Supported Plate to an Arbitrary Oscillating Force Distribution. Vibration of Infinite Thin Cylinders. Free Vibration of Finite Thin Cylinders. Harmonic Forced Vibration of Infinite Thin Cylinders. Feedback Control: Single-channel Feedback Control. Stability of a Single-Channel System. Modification of the Response of an SDOF System. The Effect of Delays in the Feedback Loop. The State Variable Approach. Example of a Two-degree-of-freedom System. Output Feedback and State Feedback. State Estimation and Observers. Optimal Control. Modal Control. Feedforward Control: Single Channel Feedforward Control. The Effect of Measurement Noise. Adaptive Digital Controllers. Multichannel Feedforward Control. Adaptive Frequency Domain Controllers. Adaptive Time Domain Controllers. Equivalent Feedback Controller Interpretation. Distributed Transducers for Active Control of Vibration. Active Control of Vibration in Structures: Feedforward Control of Finite Structures. Feedback Control of Finite Structures. Feedforward Control of Wave Transmission. Actuator Arrays for Control of Flexural Waves. Sensor Arrays for Control of Flexural Waves. Feedforward Control of Flexural Waves. Feedback Control of Flexural Waves. Active Isolation of Vibrations: Isolation of Periodic Vibrations of an SDOF System. Vibration Isolation From a Flexible Receiver the Effects of Secondary Force Location. Active Isolation of Periodic Vibrations Using Multiple Secondary Force Inputs. Finite Element Analysis of an Active System for the Isolation of Periodic Vibrations. Practical Examples of Multi-Channel Feedforward Control for the Isolation of Periodic Vibrations. Isolation of Unpredictable Vibrations from a Receiving Structure. Isolation of Vibrating Systems from Random External Excitation the Possibilities for Feedforward Control. Isolation of Vibrating Systems from Random External Excitation Analysis of Feedback Control Strategies. Isolation of Vibrating Systems from Random External Excitation Formulation in Terms of Modern Control Theory. Active Isolation of Vehicle Vibrations from Road and Track Irregularities. Active Structural Acoustic Control, I. Plate Systems: Sound Radiation by Planar Vibrating Surfaces the Rayleigh Integral. The Calculation of Radiated Sound Fields by Using Wavenumber Fourier Transforms. Sound Power Radiation From Structures in Terms of Their Multi-Modal Response. General Analysis of Active Structural Acoustic Control (ASAC) for Plate Systems. Active Control of Sound Transmission Through a Rectangular Plate Using Point Force Actuators. Active Control of Structurally Radiated Sound Using Multiple Piezoelectric Actuator Interpretation of Behaviour in Terms of the Spatial Wavenumber Spectrum. The Use of Piezoelectric Distributed Structural Error Sensors in ASAC. An Example of the Implementation of Feedforward ASAC. Feeback Control of Sound Radiation From a Vibrating Baffled Piston. Feedback Control of Sound Radiation From Distributed Elastic Structures. Active Structural Acoustic Control, II. Cylinder Systems: Coupled Cylinder Acoustic Fields. Response of an Infinite Cylinder to a Harmonic Forcing Function. Active Control of Cylinder Interior Acoustic Fields Using Point Forces. Active Control of Vibration and Acoustic Transmission in Fluid-Filled Piping Systems. Active Control of Sound Radiation From Vibrating Cylinders. Active Control of Sound in Finite Cylinder Systems. Control of Interior Noise in a Full Scale Jet Aircraft Fuselage. Appendix. References. Index.

LINE ADMITTANCE AT THE JUNCTION OF TWO PLATES WITH AND WITHOUT FLUID LOADING

A time harmonic line force or moment is applied at the junction of two plates in welded contact, with or without unilateral fluid loading. The objective is the 2 x 2 matrix of admittances relating the applied force and moment to the deflection and rotation at the load. The structural asymmetry leads to coupling between force and rotation, and between moment and deflection, even in the absence of fluid loading. The impedance matrix is derived for sources with linear phase variation of the form e ik, y for real k y . The dry plate problem is addressed first, and displays the possibility of a resonance when the drive is in phase with a flexural Stoneley wave, which is defined here. The fluid-loaded problem is attacked by expressing the vibration of either plate and the acoustic response in the fluid as transforms, the integrands of which are derived using the Wiener-Hopf technique. It is found that the wet response shows the same general behaviour as for the dry plates, but without possibility of a structural resonance. Numerical examples are presented showing the frequency dependence of the admittance matrix for joined steel plates in water. The general theory for distinct plates under fluid loading also provides a new formula for the line admittance of a uniform plate in a fluid.

Impedance-Based Modeling of Actuators Bonded to Shell Structures

When discrete piezoelectric actuator patches bonded on structures are used for active shape, vibration, and acoustic control, the desired deformation field in the structure is obtained through the application of localized line forces and moments generated by expanding or contracting bonded piezoelectric actuators. An impedance-based model to predict the dynamic response of cylindrical shells subjected to excitation from surface-bonded induced strain actuators is presented. The essence of the impedance approach is to match the actuator impedance with the structural impedance at the ends of the actuators, which will retain the dynamic characteristics of the actuators. A detailed derivation of the actuator and structural impedance is included. It is found that the actuator's output dynamic force in the axial and tangential direction are not equal. Various case studies of a cylindrical thin shell are performed to illustrate the capabilities of the developed impedance model. Out-of-phase actuation is shown to be the most efficient in exciting the lower order bending modes of shell structures. The paper is concluded with a finite element analysis verification of the derived impedance model.

Equivalent forces and wavenumber spectra of shaped piezoelectric actuators

Uniformly polarized flat piezo-actuators of elementary shapes (e.g., rectangular, triangular, circular, elliptic, etc.) are analyzed in terms of their equivalent forces and wavenumber spectra to develop a basic understanding of the influence of actuator shape on the modal response characteristics of a flat plate. A general expression for the equivalent forces is derived and transformed into different co-ordinate systems depending on the actuator shape. Several general trends are noted. Piezoelectric actuators generate line moments along the boundaries of the actuator regardless of shape. The line moments are generally constant, with the exception of elliptic actuators. Transverse point forces exist at the corners of the actuators when the corner is not a right angle and the aspect ratio of the actuator is not unity. In addition to line moments, actuators with curved boundaries generate a transverse line force along the boundary. If the curvature of the boundary varies with angle (as for example in an elliptic actuator), the line moments and line forces will vary with angle. The wavenumber spectra of these shaped piezoelectric actuators surface-bonded to rectangular plates also show several general trends. Uniformly polarized piezo-actuators generally have a higher order mode coupling tendency irrespective of shape. This is primarily due to the line moment exerted along the boundaries and is more pronounced for smaller actuators. The wavenumber spectra of shaped piezo-actuators are generally dominated by line moments, except at low wavenumbers where the effect of the point and line forces become comparatively more pronounced.

Axisymmetrical buckling behavior of truncated shallow spherical shells subjected to line moment loads

This paper is concerned with the nonlinear stability of simply supported shallow spherical shells with a center hole under the action of a uniformly distributed line moment along a circle concentric with the shell boundary. A set of truncated monomials have been used in representing various discontinuous distributions in order to simplify formulations. We have computed the load-deflection curves, buckling loads, radial membrane forces and the critical geometrical parameter Kc for shells with various center-hole radii. Our numerical results show that (1) both the initial shell stiffness and the buckling load are decreased due to the presence of a center hole with a free boundary. If the hole edge is reinforced with a rigid ring, the truncation not only raises the initial shell stiffness and the buckling load of the shell but also its critical geometrical parameter Kc. The effects of the truncation increase upon increasing the radius of the center hole; (2) for shells with large geometrical parameter K, the radial membrane forces at critical buckling become partly tensional and the buckling load will be almost unaffected by the truncation if the center hole is situated inside the tensile region.

Investigation of the Alignment of Cholesterylmiristat Liquid Crystal Phases by Proton NMR

Abstract Order parameter and the orientation of the molecular “long axis” were determined from second and fourth NMR line moments of the “polycrystalline” samples of cholesterylmiristat in smectic phase. The effects of the molecular diffusion in cholesteric phase are discussed.

Comparison of Different Impedance-Based Models for Out-of-Phase Actuation of Actuators Bonded on Ring Structures

Two different impedance models representing out-of-phase actuation of induced strain actuators bonded to the surface of a circular ring are compared. The first impedance model derivation is based on the use of eigenfunctions to determine the structural impedance of the ring, while the second model is based on modal expansion. A discussion of the proper way to apply the equivalent loading due to the out-of-phase actuation is done. A finite element analysis using piezoelectric elements is performed. A comparison between the impedance modeling and the more conventional static modeling approach is also made. Based on the governing equations derivation, the equivalent actuator loading can be included either as an induced uniform moment over the footprint of the actuators or as an external line moment at the ends of the actuators. A dynamic finite element analysis is performed using ANSYS 5.0 piezoelectric elements. The structural responses predicted by both eigenfunctions and modal expansion impedance models show a good match with those obtained using finite element analysis.

NQR Method for Stress and Pressure Imaging

Pure nuclear quadrupole resonance parameters such as the linewidth, the line moments, and the resonance frequency are influenced by mechanical stress or pressure. A surface-coil method is described which permits the spatially resolved measurement of those quantities near surfaces of solid objects. The rotating-frame nuclear quadrupole resonance imaging (ρNQRI) technique makes depth resolution feasible with the aid of gradients of the radiofrequency amplitude. Test experiments for the determination of the spatial distribution of bending stress and pressure are reported. Diverse probe substances are suggested. It is demonstrated that the technique is suitable for contactless pressure or stress measurements.

Reflection of a subsonic flexural wave on a plate at an air–water interface and far-field observations of the transition radiation in water

An investigation of radiation by subsonic flexural plate waves due to a discontinuity in fluid loading is described. A tone burst of flexural waves propagates down a plate, the lower section of which is submerged in water. Measurements indicate that there occurs a branching of energy as the flexural wave passes through the air–water interface, with little reflected energy. A portion of the transmitted energy continues along the plate as a subsonic flexural wave with an associated evanescent wave. A second acoustic wave (which is referred to here as term transition radiation) originates at or near where the plate crosses the interface, and propagates in water to the far field. The near-field interference between the two acoustic waves in water results in a series of pressure nulls [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 94, 1877 (A) (1993); T. J. Matula, Ph.D. dissertation (1993)]. Far-field observations of the transition-radiation angular pattern resemble that of a line quadrupole (approximating the farfield radiation due to a line moment on an uniformly loaded thin plate). The agreement between measured and modeled patterns is improved, however, by displacing the quadrupole horizontally behind the surface of the plate. [Work supported by ONR.]

Recognition and inspection of manufactured parts using line moments of their boundaries

A model-based scene analysis is presented for the recognition of two-dimensional (2D) polygonal outlines of manufactured parts, which may be flawed and/or partially occluded. The method is based upon the use of moments of outline segments, which leads to some simplifications when compared to the use of area moments. An application of the Hough transform is used to arrive at the most probable identity of the unknown object from a model database. The process of identification employs only the elements of the outline that are determined to be correct. This leads to a reliable association between the contour elements making up the object to their counterpart in the model. Consequently it also leads to the determination of the errors in the remaining sides of the object. The affine transformations between the object and the matched model are extracted with procedure detailed here. Examples using simulated outlines of manufactured parts are included.

Piezoelectric Actuator Models for Active Sound and Vibration Control of Cylinders

Analytical models for piezoelectric actuators, adapted from flat plate concepts, are developed for noise and vibration control applications associated with vibrating circular cylinders. The loadings applied to the cylinder by the piezoelectric actuators for the bending and in-plane force models are approximated by line moment and line force distributions, respectively, acting on the pe rimeter of the actuator patch area. Coupling between the cylinder and interior acoustic cavity is ex amined by studying the modal spectra, particularly for the low-order cylinder modes that couple effi ciently with the cavity at low frequencies. Within the scope of this study, the in-plane force model produced a more favorable distribution of low-order modes, necessary for efficient interior noise control, than did the bending model.

Natural Frequencies And Modes Of A Circular Plate Welded To A Circular Cylindrical Shell At Arbitrary Axial Positions

The modal characteristics of a plate-shell coupled structure consisting of a simply supported thin circular cylindrical shell and a circular plate which may be joined to the shell at any arbitrary axial position were studied using the receptance method. Line receptances were formulated from the responses of the plate and the shell to line force and line moment loadings distributed harmonically along the interface of the plate and the shell, utilizing natural modes and frequencies of the plate and shell, respectively. The system frequency equation was generated and solved numerically to obtain the natural frequencies and mode shapes of the combined structure under different joining configurations. The effects of length, thicknesses and joining positions on the modal characteristics of the combined structure were investigated. Certain results obtained from the receptance method and a finite element program were compared for verification purposes and showed good agreement. The structural coupling behavior between the plate and the shell and the coupling relationship between the line force loading and the line moment loading were explored.

Steel frame design with flexible connections

Abstract A systematic procedure is developed for the consideration of flexible connections in steel frame design. An analytical model for the prediction of nonlinear M‐ϕ curves of semi‐rigid steel beam‐to‐column connections is developed using the nonlinear finite element method. Simplified design guidelines are suggested for the design of flexibly jointed frames with the concepts of beam line stiffness and moment transferring ratio. The applications of this versatile method are explained by several related examples.

Response of regularly ribbed fluid loaded panels

The paper largely presents computer estimations of the response of models of mechanically driven regularly ribbed fluid loaded panels. The estimates are presented in terms of the spectral distribution of the acceleration of the panel and the spectral distribution of the pressure in the fluid. The ribs are defined in terms of line and line moment impedances and these may be mass, resistance, and/or stiffness controlled, and of various values and combinations thereof. Typical estimations of the spectral distribution of the magnitudes of the acceleration are displayed as functions of the normalized wavenumber that lies in the plane of the panel and normal to the ribs, and the normalized frequency. It is found that the magnitudes of the acceleration vanish at the sonic loci when fluid loading is included. A sonic gorge, with a nadir at the sonic loci, characterizes the acceleration of the fluid loaded panel, whether it is unribbed or ribbed. If the magnitudes of the line impedances (and, when appropriate, also the line moment impedances) of the ribs are not unusually high, the magnitudes of the acceleration and their patterns elsewhere in the spectral domain remain substantially similar to those obtained in the absence of fluid loading. The dissimilarities are readily accounted for by straightforward arguments relating to the increase in the surface mass and the radiation damping that manifest fluid loading on panels. The corresponding magnitudes of the pressure on the surface of the panel do not vanish at the sonic loci as do the magnitudes of the acceleration. Rather, a moderate sonic peak appears at the sonic loci and a sonic ridge replaces the sonic gorge. The loss of subsonic components in the pressure on a plane as the plane is removed from the surface of the panel, is clearly and dramatically displayed.