Intensity Structure Research Articles

Mid-frequency propagation path analysis on vehicle body using structural intensity

With the penetration of electric vehicles, reduction of structure-borne road noise gets important issue to realize comfortable vehicles for customers.Sound generation mechanism of structure-borne road noise on vehicle body is analyzed basically by modal analysis in low-frequency range. On the other hand, as frequency increases, modal analysis cannot clarify vibration mechanism because vibration wavelength gets shorter, mode density gets high and mode shape gets complicated. Therefore, it is difficult to identify efficient countermeasure parts and inefficient damping materials are added to response panels in mid-frequency range. So alternative analytical methods in mid-frequency range are under research to understand vibration mechanism. In this paper, Structural intensity (SI) analysis is introduced to clarify sound propagation mechanism. This analysis method makes it possible to clarify the main energy propagation path from input point to vibrating panels on vehicle body. The results show that SI analysis unveils the main energy propagation path and gives the opportunity to reduce the panel vibration efficiently by controlling the energy propagation path in body frame structure without damping materials.

A hybrid finite element and extended transfer matrix method for the dynamic modeling of fluid-conveying pipeline with breathing cracks

In this study, a hybrid finite element and extended transfer matrix method (FEM-ETMM) is formulated to simulate the breathing effect and fluid disturbances of a fluid-conveying cracked pipeline (FCCP). Furthermore, the frequency spectra of structural intensity (SI) responses and the normalized displacement-structural intensity (D-SI) curves are used to detect cracks. In this FEM-ETMM, the finite element method (FEM) is adopted to determine the contact state and establish the equivalent contact model, and the extended transfer matrix method (ETMM) is obtained by constructing the state transfer matrix in the crack region. Based on ETMM, the time-varying fluid disturbances are obtained. Furthermore, the model modal reduction and parametric modeling methods are used to improve solution efficiency. Finally, the effects of the crack parameters on vibration responses with and without considering fluid disturbances are analyzed. The results show that SI responses can amplify the odd-mode harmonics, thereby accurately detecting cracks at different depths and locations. In addition, the fluid disturbances change the contact states and enhance the damping effect. The proposed modeling and analysis method will provide valuable insights for crack detection of pipelines.

Damper arrangement to reduce structure born sound based on structural intensity

Vibration measures can be taken at three main locations: the vibration source, the propagating part, and the radiating part. However, implementing measures at the vibration source is often challenging, and countermeasures at the radiating part are inefficient. Therefore, measures taken at the propagation part are typically preferred. To achieve this, the technique of structural intensity (SI) is commonly used, which is effective in understanding the propagation path. In this paper, we propose reducing vibration using a viscous damper layout based on the SI distribution at the propagation part. We present the most effective layout for vibration reduction in a 3 degree of freedom (DOF) system. Our results show that adding a damper on the response side is effective. Additionally, we discuss the relationship between the ratio of change of SI and velocity for a flat plate. Based on these findings, we propose a new method for identifying the damper location by SI. The method involves determining the location where the spatial rate of change of SI is highest in the path from the excitation and response points. We verify the effectiveness of our proposed method on a flat plate and demonstrate its effectiveness on an automobile body for vibration reduction.

Dynamic modeling of vibration behavior and power flow of a plate structure embedded with an ABH indentation

A two-dimensional (2D) semi-analytical model is established for the analyses of vibration behavior and energy transmission of the plate structure with a power-law-profiled thickness variation, referred to as an Acoustic Black Hole (ABH) plate. Under the general Rayleigh-Ritz framework, a modified version of 2D Fourier series is employed as the admissible function of the transverse displacement of the ABH plate featuring a thickness variation. Thanks to such modified Fourier series, a high-order spatial derivative continuity over the entire solution domain is available to express the internal forces and bending moments, further calculating the corresponding structural intensity and power flow within the ABH plate. The proposed model allows an accurate prediction of the modal characteristics and dynamic response, which is verified by the FEM and experiment, respectively. Several numerical analyses are proceeded and the typical dynamic phenomena, including the wave compression and efficient vibrational suppression of the 2D ABH plate are observed. The structural intensity (SI) vector arrows of the ABH plate are given, which represent the magnitude of the vibrational energy and the flowing direction in a visual pattern. The energy transmission behaviors and the manipulation of power flow by the ABH are revealed in an energy perspective. The typical energy focalization and dissipation phenomena of the ABH plate are analyzed in the frequency domain. Finally, the enhancement of the energy transmission by the ABH feature on the plate is explored by the normalized power flow. It is noted that the proposed model offers a visual energy transfer analysis tool for the 2D ABH structures, which may provide a novel perspective in various studies of ABH structures.

A Power-Based Framework for Quantifying Parameter Uncertainties in Finite Vibroacoustic Metamaterial Plates.

Vibroacoustic metamaterials (VAMMs) are artificial materials that are specifically designed to control, direct, and manipulate sound waves by creating a frequency gap, known as the stop band, which blocks free wave propagation. In this paper, a new power-based approach that relies on the active structural intensity (STI) for predicting the stop band behavior of finite VAMM structures is presented. The proposed method quantifies the power loss in a locally resonant finite VAMM plate in terms of percentage, such as STI99% and STI90%, for stop band prediction. This allows for the quantitative analysis of the vibration attenuation capabilities of a VAMM structure. This study is presented in the context of a two-dimensional VAMM plate with 25 resonators mounted in the middle section of the plate. It has been demonstrated that this method can predict the stop band limits of a finite VAMM plate more accurately than using negative effective mass, unit cell dispersion analysis, or the frequency response function methods. The proposed approach is then implemented to establish a framework for investigating the influence of parameter uncertainties on the stop band behavior of the VAMM plate. Based on the STI99% method, which aims for significant vibration reduction, stricter tolerances in the mass fabrication process are required to ensure the robustness of VAMM. Conversely, the STI90% method suggests that larger fabrication tolerances can be leveraged to achieve a broader stop band range while still meeting the desired performance level, leading to cost savings in manufacturing.

Identifying dominant components of vibrational energy flow in U-rib plates of bridge based on structural intensity

Stiffened U-rib plates are the elementary components of steel box girders in bridges that directly bear the input external energy before transferring it to other components. Research on the dynamic characteristics of stiffened U-rib plates is the basis for examining vibration and noise in steel box girders. Most relevant studies have focused on the vibrational modes and single-frequency responses in this context, and few researchers have sought to optimize the design of stiffened U-rib plates to reduce responses due to vibrations and noise. This study identifies the global and local laws of vibrational transmission in stiffened U-rib plates subjected to harmonic loads through structural intensity (SI) analysis that is carried out by jointly using standard finite element software and a post-processing code created by the authors. The contributions of each component of vibrational waves are represented to reflect the dominant roles of the bending wave in the baseplate and the in-plane wave in the U-ribs, respectively. The effects of parameters of the U-rib plates on SI are also quantitatively investigated. SI analysis can be used as a new criterion for designing and optimizing bridges as well as formulating measures for vibration reduction.

A Basic Study of Damping Layout Based on Structural Intensity Distribution

Vibration measures can be taken at three main locations: the vibration source, the propagating part, and the radiating part. However, measures at the vibration source are often difficult to implement, and countermeasures at the radiating part are inefficient. Therefore, measures at the propagation part are expected. For measures at the propagation part, the technique of structural intensity (SI) is used, which is effective in understanding the propagation path. Then, we attempt to reduce the vibration by a viscous damper layout based on the SI distribution. In this paper, the most effective layout for vibration reduction is presented for 2 and 3 DOF systems. As a result, it was found that adding a damper on the response side is effective. For beam system, the relationship between the ratio of change of SI and the velocity was also discussed. Based on these findings, a method for identifying the damper location by SI is newly proposed, and its effectiveness is verified.

Measured and simulated examination of the propagation paths of structure‐borne sound using the structural intensity for fibre reinforced injection moulded thermoplastic parts

AbstractIn product development e.g. electromobility, engineers need to place special emphasis on acoustics. A large number of automotive interior components consist of injection‐moulded thermoplastic parts. If required these lightweight components are reinforced with fibres or fillings. This reinforcement leads to a higher vibration sensitivity and higher natural frequencies. Due to the fact that the auditory threshold decreases with a rising excitation frequency, a conflict of objective between acoustics and lightweight components exists. In order to influence the acoustic behaviour in early development stages, the structure‐borne sound including its source and propagation paths have to be analysed. An appropriate parameter by which to visualise these pieces is the structural intensity (STI) which is calculated by the product of velocity and stress. Previous investigations have mainly focused on the behaviour of isotropic materials e.g. steel calculated using FEM. An experimental determination of the STI is a challenge since the stress of a vibrating structure cannot be directly measured. Furthermore the experimental determination is limited to the surface of the structure. First investigations using FEM were carried out to examine composite materials with a unidirectional fibre orientation and revealed a high potential to influence the structural behaviour in acoustic matters, i.e. the transmission of structure‐borne sound. Therefore a current research project deals with the opportunities to influence the vibro‐acoustic behaviour of injection moulded parts using the structural intensity. In this paper a method is presented to examine the influence of fibres, fillings and geometric modifications on the STI for injection moulded parts using FEM. A method to measure the STI for orthotropic parts is also presented. In addition to a comparison between the measured and the simulated results, a look‐ahead at planned future investigations in the research project is given.

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.

Modeling of fiber composite structures for the calculation of the structural intensity

In structures, high vibration levels can destroy components; therefore, the reduction of the vibration levels represents a fundamental target in the industrial field. The structural intensity (STI) field provides information about the energy flow that propagates within a structure. It shows the position of dampers in structures, thus, it can be used for solving structure-borne noise problems. The analysis of the energy distribution on a structure allows to understand where to implement locally concentrated modifications introducing damping patches in order to reduce structure-borne noise. The aim of this paper is to investigate the structural intensity in composite structures and to evaluate the influence of some modeling parameters, such as mesh density, structural damping, etc., on the accuracy of the results. In this paper, numerical investigations on the STI in a fiber composite plate are carried out. Two different numerical models are considered: the first one with solid elements, the second one with shell elements. The two-dimensional model does not allow to analyze and study the composite plate on micro level. The first law of thermodynamics allows to define the accuracy of the STI evaluations. The investigation on two-dimensional and three-dimensional composite structure modeling presents the limits and the advantages of the two different types of approach. The different characteristics of the STI fields provided by these models are analyzed in order to understand the difference between local and global approach.

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.

Optimization of structure‐borne sound popagation using structural intensity

AbstractReducing noise in mobile applications such as cars, aircrafts and trains is a major challenge for today's engineers. In most cases, sound sources and sound radiating structures are locally separated. The airborne sound field is a result of the excitation and the transfer through the mechanical system. The resulting structure‐borne sound is propagated on transfer paths and finally radiated through plate‐like structures. Therefore, the structure‐borne sound energy should already be efficiently insulated and damped on the way of propagation.The structural intensity (STI) is a complex vectorial quantity that represents the flow of sound energy in the structure. The real part of STI, can identify areas with a high absorption of structure‐borne sound. These areas should correlate with high damping in the structure, e.g. areas with additionally applied damping measures. If the damping is homogeneously distributed, a uniform distribution of structure‐borne sound energy should be the objective in order to make optimal use of the material damping. The energy flow can be influenced by introducing structural changes. With the help of the direction information and the quantitative value of the STI, the position of such structural changes can be optimized.In this paper, an optimization procedure is investigated, with which a homogenization of the structure‐borne sound flow is aimed. Numerical studies on generic structures are carried out. The STI for a homogeneously and an inhomogeneously damped plate is calculated and specifically influenced by various measures (e.g. point masses, beads). The aim is the targeted guidance of sound in areas of high damping or the uniform distribution in the structure as well as a shift of eigenfrequencies in order to reduce the mean surface velocity in a defined frequency range.

Removal of ECG artifacts from EMG signals with different artifact magnitudes by template subtraction

AbstractThis work investigates the performance of eventsynchronous noise cancelling algorithms to separate ECG artifacts from thoracic EMG recordings. In focus are the precise detection of heart beats, the exact time alignment of the QRS segments and the construction of a template QRS signal. Among the utilized methods is a modified structural intensity (SI) approach based on the observation of extrema in low pass filtered versions of the second derivative as a detector. An adoption of this approach is also used to obtain the exact time alignment of QRS segments. Artificial test signals are constructed based on addition of ECG and sEMG with different magnitudes. We show that approaches based on the observation of extrema in different scales yield superior results.

Structural Intensity Analysis on Irregular Shells

A method is presented to assess the transmission path of vibration energy and to localize sources or sinks on shells with arbitrary shape, constant thickness, and isotropic material properties. The derived equations of the structural intensity (SI) are based on the Kirchhoff–Love postulates and are formulated in terms of displacements, Lamé parameters, principal curvatures, and their partial derivatives with respect to the principal curvilinear coordinates (PCC). To test the accuracy of the method, two numerical models of thin shells with nonuniform curvatures were developed. The coordinates, displacements, and principal curvature directions (PCDs) at the shell's outer surface were used to estimate the SI vector fields and the energy density at the shell's middle surface. The power estimated from the surface integral of the divergence of the SI over the source was compared to the actual power injected in the shell. The absolute error in both models did not exceed 1%, showing that, in theory, the method is able to handle the high-order spatial derivatives of the displacement and geometry data. The qualitative effect of varying the internal damping in the models on the energy transmission was also investigated.

Vibration control for slotted plate using structural intensity method

In this paper, we study the vibration performance of simply supported slotted plate using structural intensity (SI) method. First, the SI distribution of the slotted plate under given excitation for different slot depths is obtained using finite element methods. The SI streamline of each case shows that the SI distribution can be significantly affected by adjusting the slot depth. The optimal position of dampers which can effectively implement vibration control of slotted plate for the fixed value of exciting frequency can be obtained from the SI streamline distribution. In case of changing vibrating frequencies, a new strategy of vibration control by adding soft material (hydrogel) layers is proposed. The main advantage of this strategy is that the properties of hydrogel can be easily adjusted by changing the chemical potential, thereby achieving the desired vibration control for different excitation conditions. The effectiveness of the proposed vibration control using hydrogel layers is investigated using SI method. The SI distribution and SI streamlines of the slotted plate with the new vibration control show that the proposed strategy is convenient. Our proposed method conceptualizes a new approach toward vibration control using constrained hydrogel layer.

Dominant components of vibrational energy flow in stiffened panels analysed by the structural intensity technique

Stiffened panels are widely used in naval architecture and ocean engineering, and knowledge about their dynamic behaviour represents important issue in the design procedure. Ordinary vibration analysis consists of natural frequencies and mode shapes determination and can be extended to forced response assessment, while the Structural Intensity (SI) analysis, assessing magnitude and direction of vibrational energy flow provides information on dominant transmission paths and energy distribution including sink positions. In this paper, vibrational energy flow in stiffened panels under harmonic loading is analyzed by the SI technique employing the finite element method. Structural intensity formulation for plate and beam element is outlined, and developed system combining in-house code and general finite element tool is described. As confirmed within numerical examples, the developed tool enables separation of SI components, enabling generation of novel SI patterns and providing deeper insight in the vibrational energy flow in stiffened panels, comparing to existing works.

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.

Reduction of transmitted power on a plane by using mode pair cancellation

Reduction of structure-borne sound is an important issue for industry mechanical products. This paper presents a new idea for controlling structural intensity (SI) on panel structure derived from a cancellation of SI due to mode pairs of multiple roots. At first the modal formulation of SI on a flat plate is summarized. Next we discuss the change of SI on a flat plate by attaching a reinforcement beam cross the plate in one direction. It is shown that this attachment give multiple natural frequencies, and their mode pairs and the pairs of modal components of SI are in same phase in the area of half of the plate and in anti-phase in that of the other half. Then the modes and modal components of SI can be said to be canceled by each modal pairs in the area of half on the plate. Based on this cancellation due to modal pairs, a new method for reducing transmitted power to a given area on the plate has been derived and proposed by attaching a beam on the plate for providing partial symmetry on the plate. It is demonstrated that the partial attachment of a beam on the plate based on the proposed method can reduce the transmitted power to the given area by the cancellation due to the pairs of SI modal components.

Relation Between Structural Intensity-Based Scalars and Sound Radiation Using the Example of Plate-Rib Models

The ability of the structural intensity (STI) to predict changes in the sound radiation of structures due to geometric modifications is investigated using the academic example of plate-rib models. All models consist of the same plate and are modified by attaching a rib, whose position, orientation, and length are varied. Various scalar quantities are derived from the STI and quantitatively compared to the equivalent radiated sound power (ERP) for each model. Based on this comparison the relation between the STI-based scalars and the ERP is studied to determine an STI-based scalar that can serve as the objective function for numerical structural optimizations. The influence of the rib parameters on the most promising STI-based scalar is analyzed by means of a variance-based sensitivity analysis. The STI pattern of those models with very high and very low ERP values are additionally analyzed to describe the characteristics of STI. The results of this study indicate that the STI pattern of models with low ERP has paths and vortices that can be more clearly identified compared to those in models with high ERP. The angular orientation of the rib has by far the highest influence on changes in STI and ERP. The results reveal a correlation between the energy flow into a specific region of a structure, an STI-based scalar, and the ERP. Therefore, the vibrational energy flow can indeed serve as an objective function for numerical structural optimizations aiming at reducing the sound radiation.

Probabilistic Analysis of Random Structural Intensity for Structural Members under Stochastic Loadings

The concept of structural intensity (SI) is extended to the random domain by introducing a physical quantity denominated random structural intensity (RSI). This quantity is formulated for mechanical systems whose dynamical responses are stochastic due to random excitations. In order to fully characterize the stochastic behavior of a system under random loadings, it is imperative to obtain the probability density function (PDF) of RSI. Based on the elastic theory and the definition of SI, RSI is expressed as functions of system responses. In general, the PDF of system responses is governed by Fokker–Planck–Kolmogorov (FPK) equation under the assumption that random dynamic loadings are idealized as white noise excitations. Therefore, the PDF of RSI is derived with the joint PDF of system responses. In the present study, four demonstrating cases of beams and plates under separately concentrated and uniform random loadings are studied to investigate the properties of RSI. Stationary and non-stationary PDFs of RSI at arbitrary section of beam and plate are obtained. Numerical results show that the PDF of RSI is transient at early stage of stationary loading and then converges to the exact stationary ones as time increases. With the obtained PDFs of RSI, energy transmission path over the beam and plate can be determined, which is guided from the locations with lower probabilities of RSI to the ones with higher probabilities of RSI. Furthermore, virtual energy flow sinks on the plate and beam can be found, which are identified by the locations with the maximum probabilities of RSI.