Structural Intensity Fields Research Articles

A method to investigate mid and high-frequency vibration energy transfer paths using the irrotational intensity

Structural intensity fields provide a clear understanding of the noise, vibration and harshness (NVH) behavior of complex structures by showing the vibration energy flow between zones of excitation and dissipation. The use of models with fine meshes for automotive structures has allowed structural intensity calculations to be performed at high frequencies. However, fields are difficult to understand at medium and high frequencies: the intensity field has a vortical character that hides the vibration energy flow in these frequency ranges. In this work, a methodology is presented to filter out vortices in the structural intensity field. The approach uses the Hodge–Helmholtz decomposition: the structural intensity field is decomposed into rotational, irrotational, and harmonic components. Among them, only the irrotational component is needed to describe the path of energy flow from sources to sinks. The proposed methodology involves calculating the dynamic response and solving a diffusion equation similar to the thermal conduction equation to obtain the irrotational field of interest. Plate examples are used to illustrate the efficiency of the method, which provides a better understanding of the mid- and high-frequency energy transmission paths.

Damping vibration of platform structure using modified acoustic black holes

We propose waveguide absorbers (WGAs) to dampen structural vibrations of platforms supporting vibrating systems. The waveguide absorber is designed by modifing a spiral acoustic black hole (ABH) to improve its damping performance while saving installation space and weight. The proposed WGA absorbs the flexural wave propagating in a platform to its end, resulting in vibration damping in the platform. To maximize the damping capability of WGA, we analyze the structural intensity field of the platform and attach the WGA based on the intensity field. Numerical and experimental results show that large reductions of peaks in mobility are achieved using the WGAs, showing the possibility to utilize the WGA in practice.

Vibrational energy flow cancelling by loading a reverse excitation: Visualization and analysis

Vibration control is a permanent and significant issue in all forms of structural dynamic analysis with the consistent objective being to minimize vibration levels. Considering that the propagation of vibration waves is essentially the transmission of vibrational energy flow (VEF), the fundamental requirement, therefore, is to minimize the VEF transmitted from sources to sinks and then to control and block the flow of vibration energy. Structural intensity (SI) method, combining forces with velocities to assess the magnitude and directions of VEF, is alternative to classical dynamic assessment methods offering insight into the transmission of VEF and studying additional phenomena which cannot be obtained by conventional dynamic analysis. In the field of noise, active noise control has been widely used in vehicles and headphones, which has achieved remarkable results by introducing a cancelling ‘anti-noise’ wave through an appropriate array of secondary sources. Analogically, it is considered whether the vibration of the structure can be attenuated by introducing a secondary reverse excitation (SRE) to offset the VEF transmitted in the structure. Therefore, this article combines the SI method and SRE to carry out related research on this issue. The rectangular plate with the circular hole subjected to the transient sinusoidal force, being widely used and found in various engineering branches, is taken as the research object. The developed simulation system consisting of the finite element tool and the in-house program is used to assess and visualize the instantaneous SI fields. The effects of the SRE acting on this structure on the transmission behaviours of VEF and the vibration suppression have been investigated in detail. Moreover, the transmission, conversion and balance relationships of the VEF have been derived from the general equation of motion and analysed as well. This study sheds new light on the vibration attenuation by introducing the secondary source from the perspective of VEF.

Analysis of Instantaneous Vibrational Energy Flow for an Aero-Engine Dual-Rotor–Support–Casing Coupling System

Abstract The aero-engine casing is a key component for carrying loads. With the purpose of improving the thrust-weight ratio of the aero-engine, the casing is required to be designed to be as thin as possible. Therefore, the vibration of aero-engine's rotor, support, and casing will be easily coupled causing the whole engine's vibration to be more serious. Considering the structural vibration propagation is essentially the vibration energy transmission, the structural intensity (SI) method is popular and widely used to investigate the transmission phenomena of vibration energy in vibrating structures. This method combines forces with velocities to quantify the vibrational energy flow (VEF) transmitted in the structures by its directions and magnitude. Therefore, the SI fields are quantified by the developed computation system which combines the finite element design language and the in-house code. And a model of dual-rotor–support–casing coupling system subjected to the unbalanced forces of the rotors is established in this paper. The scalar and vector diagrams of instantaneous SI fields are visualized to show the main vibration energy transmission paths among these three parts. Moreover, the relationship between the SI and the mechanical energy is derived from the kinetic equation. According to this relationship, the phenomenon that the vibration energy and the strain energy are always converted to each other in the middle part of the rotor shaft with the first-order bending mode is discussed, which reveals the cause of the first-order bending mode of the rotor from a microscopic point of view.

Effects of mount positions on vibrational energy flow transmission characteristics in aero-engine casing structures

The main goal of the study is to apply the structural intensity method to analyze the effects of positions of the main-mount and the sub-mount on the vibrational energy flow transmission characteristics in aero-engine casing structures, so as to attenuate the vibration of the casing and the whole aero-engine. Structural intensity method, indicating magnitude and direction of the vibrational energy flow, is a powerful tool to study vibration problems from the perspective of energy. In this paper, a casing-support-rotor coupling model subjected to the rotor unbalanced forces is established by the finite element method. Formulations of the structural intensity of a shell element and the structural intensity streamline are given. A simulation system consisting of the finite element tool and the in-house program is developed to carry out forced vibration analysis and structural intensity calculation. The structural intensity field of the casing is visualized in the forms of vector diagram and streamline representation. The vibrational energy flow behaviors of the casing at the rotor design rotating speed are analyzed, and the vibrational energy flow transmission characteristics of the casing with different axial positions of the main-mount and the sub-mount are investigated. Moreover, some measures to attenuate the vibration of the casing are obtained from the numerical results, and their effectiveness is verified in the frequency domain and the time domain. The results shed new light on the effects of the mount positions on the vibration energy transmission behaviors of the casing structure. The structural intensity method is a more advanced tool for solving vibration problems in engineering. Furthermore, it may provide some guidance for the vibration attenuation of the casing and the whole aero-engine.

Damage detection through structural intensity and vibration based techniques

The development systems for the Structural Health Monitoring has attracted considerable interest from several engineering fields during the last decades and more specifically in the aerospace one. In fact, the introduction of those systems could allow the transition of the maintenance strategy from a scheduled basis to a condition-based approach providing cost benefits for the companies. The research presented in this paper consists of a definition and next comparison of four methods applied to numerical measurements for the extraction of damage features. The first method is based on the determination of the Structural Intensity field at the on-resonance condition in order to acquire information about the dissipation of vibrational energy throughout the structure. The Damage Quantification Indicator and the Average Integrated Global Amplitude Criterion methods need the evaluation of the Frequency Response Function for a healthy plate and a damaged one. The main difference between these two parameters is their mathematical definition and therefore the accuracy of the scalar values provided as output. The fourth and last method is based on the Mode-shape Curvature, a FRF-based technique which requires the application of particular finite-difference schemes for the derivation of the curvature of the plate. All the methods have been assessed for several damage conditions (the shape, the extension and the intensity of the damage) on two test plates: an isotropic (steel) plate and a 4-plies composite plate.

The Relationship between Structural Intensity and Sound Field Characteristics of Cylindrical Shells

It is an important subject in many engineering areas to recognize the vibro-acoustic behaviors of vibrational structures. Many researches have been done to study this characteristics of plane structure with structural intensity (SI) analysis. This paper extends the subject to study this subject by structural intensity approach in cylindrical shell structure and present a method of controlling the sound energy transmission. Structural intensity, a powerful method, can not only quantitatively reflect power flow strength, but also can provide the energy flow directions and distributions. The structural intensity patterns vary under different load and damping conditions, and thus affects the energy level of radiation sound field in cylindrical shell. In this paper, Numerical simulation system was built to represent the simply supported thin cylindrical shell coupled vibration and acoustical radiation structure which excited by harmonic normal point force. We get the corresponding results of structural intensity distribution, sound pressure and acoustic intensity of internal radiation sound field by adjusting damper positions, and calculating the sound field energy. The characteristics of SI of thin cylindrical shell are investigated, and the relationships between SI and sound field are established. We hope that our works could provide researchers new ideas for noise reduction of similar shell structures in potential applications.

Reconstruction and separation of vibratory field using structural holography

A method for reconstructing and separating vibratory field on a plate-like structure is presented. The method, called “Structural Holography” is derived from classical Near-field Acoustic Holography (NAH) but in the vibratory domain. In this case, the plate displacement is measured on one-dimensional lines (the holograms) and used to reconstruct the entire two-dimensional displacement field. As a consequence, remote measurements on non directly accessible zones are possible with Structural Holography. Moreover, as it is based on the decomposition of the field into forth and back waves, Structural Holography permits to separate forces in the case of multi-sources excitation. The theoretical background of the Structural Holography method is described first. Then, to illustrate the process and the possibilities of Structural Holography, the academic test case of an infinite plate excited by few point forces is presented. With the principle of vibratory field separation, the displacement fields produced by each point force separately is reconstructed. However, the displacement field is not always meaningful and some additional treatments are mandatory to localize the position of point forces for example. From the simple example of an infinite plate, a post-processing based on the reconstruction of the structural intensity field is thus proposed. Finally, Structural Holography is generalized to finite plates and applied to real experimental measurements

Numerical and experimental investigations on structural intensity in plates

The need of reducing the vibration levels is one of the most important points in many engineering fields. Therefore, the knowledge of the vibrational field can be a useful and efficient tool in problems regarding acoustic and mechanical insulation. This paper is focused on the experimental measurements and numerical predictions of the structural intensity fields in rectangular plates. The method is applied by simulating finite plates and the effects of constraints, load conditions, damping, thickness and fibres orientation are investigated. Experimental measurements are carried out on both aluminium sandwich and composite (orthotropic) panels; the results are compared through a mixed numerical/experimental approach with purely numerical predictions. The mixed approach based on both experimental and numerical information is proposed since it can give good indications of the structural intensity fields, can offer information about the energy transmission paths and can fruitfully use the numerical generated information.

Structural intensity analysis of a large container carrier under harmonic excitations of propulsion system

The structural intensity analysis, which calculates the magnitude and direction of vibrational energy flow from vibratory velocity and internal force at any point of a structure, can give information on dominant transmission paths, positions of sources and sinks of vibration energy. This paper presents a numerical simulation system for structural intensity analysis and visualization to apply for ship structures based on the finite element method. The system consists of a general purpose finite element analysis program MSC/Nastran, its pre- and post-processors and an in-house program module to calculate structural intensity using the model data and its forced vibration analysis results. Using the system, the structural intensity analysis for a 4,100 TEU container carrier is carried out to visualize structural intensity fields on the global ship structure and to investigate dominant energy flow paths from harmonic excitation sources to superstructure at resonant hull girder and superstructure modes.

Numerical study of structural intensity for a model airframe structure in healthy and damaged states.

Structural damage due to fatigue or material flaws presents a major challenge for many engineering applications. To address this challenge, structural health monitoring techniques have been developed in an effort to determine the type, severity, and location of the damage. Many of these techniques are based on the nonlinear contact phenomenon. In this paper, structural intensity methods are used as a damage-detection metric on a simplified airframe structure. A finite-element model was created and the structural intensity field was mapped over the surface using individual element power flow estimates. Damage was then introduced into the model by removing connectivity between elements and including nonlinear stress-strain relationships and contact at the damage location. Structural intensity maps were then compared to the healthy case to correlate the changes with the damage state. More specifically, the increase in structural intensity at the sub- and super-harmonics was found to be indicative of the damage state. The results of this numerical study show the potential of surface structural intensity in autonomous damage detection for flight vehicles. The implications of this type of damage detection metric with respect to damage size and location will also be discussed.

A Method to Simulate Structural Intensity Fields in Plates and General Structures Induced by Spatially and Temporally Random Excitation Fields

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. Most studies to date, however, have considered only the structural intensity induced by deterministic localized drives. Many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations. Additionally, such studies typically employ finite differencing techniques to estimate the shear, bending, and twisting components of intensity, and are therefore only applicable to simple homogenous uniform structures such as thin plates and beams. Often, however, finite differencing techniques are not applicable to practical structures of interest. The present study introduces a new analytic method to compute the structural intensity induced by spatially random pressure fields in general structures, which does not require the use of finite differencing techniques. This method uses multiple-input multiple-output random analysis techniques, combining frequency response function matrices generated from analytic or finite element (FE) models with cross-spectral density matrices of spatially random pressure fields to compute intensities in structures. The results of this method are validated using those obtained using finite-difference-based techniques in a flat plate. Both methods show intensity patterns different from those caused by deterministic point drives. The new general method, combined with FE analysis techniques, may be applied in the future to complex nonhomogenous structures, which include discontinuities, curvature, anisotropic materials, and general three-dimensional features.

A three-dimensional human head finite element model and power flow in a human head subject to impact loading

A three-dimensional finite element model of the human head is presented. The model has been validated against two sets of experimental results. To assess injury likelihood of the head subjected to impact loading, the structural intensity (SI) methodology is introduced in accordance with the prevailing practice in experimental biomechanics. SI is a vector quantity indicating the direction and magnitude of power flow inside a dynamically loaded structure. In this paper, the SI field inside the head model is computed for three cases, namely frontal, rear and side impacts. The results for the three cases have revealed that there exist power flow paths. The skull is, in general, a good energy flow channel. The study has also revealed the high possibility of spinal cord injury due to wave motion inside the head.

Simulating and Measuring Structural Intensity Fields in Plates Induced by Spatially and Temporally Random Excitation

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in flat plates excited by such fields are presented here. The structural intensity at various frequencies in a simply supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives. Specifically, no clear source regions are apparent in the randomly driven intensity fields, although the energy flow patterns do clearly converge toward a point damper attached to the plate.

Streamline representation for structural intensity fields

Streamline representation for structural intensity fields

Computation of structural intensity for plates with multiple cutouts

The structural intensity fields of rectangular plates with single cutout and multiple cutouts are studied. The main objective is to examine the effect of the presence of cutouts on the flow pattern of vibrational energy from the source to the sink on a rectangular plate. The computation of the structural intensity is carried out using the finite element method. The magnitude of energy flow is significantly larger at the edges on the plate near the cutout boundary parallel to the energy flow. The effects of cutouts with different shape and size at different positions on structural intensity of a rectangular plate are presented and discussed. A case study on a plate with two cutouts is also presented.

Computation of structural intensity for plates with multiple cutouts

The structural intensity fields of rectangular plates with single cutout and multiple cutouts are studied. The main objective is to examine the effect of the presence of cutouts on the flow pattern of vibrational energy from the source to the sink on a rectangular plate. The computation of the structural intensity is carried out using the finite element method. The magnitude of energy flow is significantly larger at the edges on the plate near the cutout boundary parallel to the energy flow. The effects of cutouts with different shape and size at different positions on structural intensity of a rectangular plate are presented and discussed. A case study on a plate with two cutouts is also presented.

Summary of energy flow measurements and calculations made on the INCE standard test structures

In 1996 a series of standard test structures was conceived and manufactured by members of the Institute of Noise Control Engineering (INCE) [Cuschieri, Burroughs, and Carroll, Evaluation of Structure-Borne Noise Prediction Techniques Review, Proceedings of Noise-Con 98, April 1998, pp. 315–320]. The structures include a Lexan T-shaped beam and two ribbed panels of identical geometries but different materials: aluminum and lexan. In subsequent years, a wide variety of investigators from the U.S. and around the world have conducted experimental and numerical studies on the test structures, particularly on energy flow parameters, such as power input, power dissipation, and power flow. Most of the studies have been performed at low frequencies, and have shown phenomena such as the conversion of flexural wave power to longitudinal wave power at the T-beam joint and the nature of the structural intensity fields in the ribbed panels. Measurements and computations compare well. At high frequencies, Statistical Energy Analysis (SEA) techniques have shown that energy tends to become trapped in the drive leg of the T-beam. SEA studies on the ribbed panels show that the Lexan panel transmits less energy across the ribs than the aluminum panel does due primarily to differences in material loss factor.

Pulsed TV-holography recording for vibration analysis applications

TV-holography is a well-known tool for vibration analysis. Using the so-called time-average method, this technique allows to record interferograms showing the mode shapes of a structure submitted to vibration excitation and is currently used for modal identification. Within the frames of a BRITE-EURAM program called vibration intensity processing using full-field multi-pulse laser technique (VIP), a TV-holography equipment has been developed, working with a 25 Hz pulsed laser and allowing easy on-site measurements. A measurement procedure has been defined and a specific data processing has been developed for the determination of structural intensity fields, which give transfer path of the vibration energy within a structure. The measurement of these quantities is possible the using classical means (accelerometers, stress gauges, etc.) but the data processing is complex and require a lot of accurate sensors because it is based on spatial derivatives of high order. The optical techniques (laser vibrometry, holography, etc.) are more suited for that purpose because of the high density of measuring points and because of the well-known advantages of these methods: reduced measurement time and no modification of the mass parameters of the structure as it is the case when using contact sensors. Different kinds of output data are then given: operational deflection shape, amplitude and phase, structural intensity field and its divergence through a further step of data processing. The complete procedure with the associated data processing has been tested (for various configurations of excitation and damping) first on a clamped plate, then on a cylinder and at the end on several industrial components. This paper describes the general measurement procedure and the equipment used. The data processing is also presented and various measurement results are shown. The conclusion gives the main advantages and limitations of the method and evaluates the application possibilities.

Structural intensity in a line-excited infinite elastic plate in the high-frequency range

An infinite elastic plate is excited by a mechanical line force, which generates an active structural intensity field in the plate. In an earlier paper [Hayek et al., J. Acoust. Soc. Am. 105, 1299 (1999)], the structural intensity was evaluated analytically for a plate using the Bernoulli–Euler theory, which is valid in the low-frequency range. The paper then employed the same theory for the active control of total structural intensity by use of colocated point forces and moments. In this paper, the evaluation of the structural intensity field due to line forces and moments is modeled by use of the more exact Mindlin plate theory, which is valid in a much higher frequency range. The main objective is to achieve active control of the total structural intensity in infinite elastic plates using the Mindlin plate theory through a colocated line force and a line moment actuators at an arbitrary location on the plate.