Effect of End Rubber Gasket on the Performance of Parabolic Leaf Spring

Leaf springs play an important role in the handling stability and ride comfort of vehicle. End rubber gaskets are widely used to reduce the friction between leaves, but they also have considerable effect on the stiffness of the suspension assembly. The ride comfort may deteriorate with the stiffness of leaf spring changes. In this paper the influence of the end rubber gasket on the static stiffness performance of a parabolic leaf spring is studied. A finite element model of the leaf spring is developed and verified against the static stiffness test. Effects of the end rubber gasket parameters on the static stiffness of the leaf spring are analyzed based on an orthogonal experiment. The sensitivities of the five parameters are identified including the width, the length, the end thickness, the tail thickness and the distance to the end of the middle leaf. It is found that the contributions can be ranked in descending order as the tail thickness, the end thickness, the distance from end rubber gasket to the end of Leaf 2, and the width and length. The first two factors are considered of significant effects on the leaf spring stiffness. According to single-factor analysis, it is found that under the same load, as the tail thickness and the end thickness increase, the maximum deformation of the rubber gasket decreases, the stiffness of the rubber gasket increases, and the stiffness of the leaf spring increases, which provides a reference for the forward design of the end rubber gasket and the stiffness matching of leaf springs.

A Linear Acoustic Phased Array for Nonreciprocal Transmission and Reception

Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.

Effect of Geometric Shape of Periodic Cavities in Attenuating Baseframe Vibration

Vibration attenuation is an important factor while designing rotating machinery since frequency lying in the range corresponding to natural modes of structures can result in resonance and ultimately failure. Damping dissipates energy in the system, which reduces the vibration level. The mitigation of vibrations can be achieved by designing the base frame with periodic air holes. The periodicity in air holes result in vibration attenuation by providing a stop band. A finite element-based approach is developed to predict the modal and frequency response. The analysis is carried out with different shapes of periodic cavities in order to study the effectiveness of periodic stop bands in attenuating vibrations. The amount of mass removed due to the periodic cavities is kept constant. It is seen that better attenuation is obtained in case of periodic cavities compared to a uniform base frame. Among the different geometries tested, rectangular cavities showed better results than circular and square cavities. As a result, it is seen that waves propagate along periodic cells only within specific frequency bands called the “Pass bands”, while these waves are completely blocked within other frequency bands called the “Stopbands”. The air cavities filter structural vibrations in certain frequency bands resulting in effective attenuation.

Development and Characterization of Fly Ash Nanoparticles Reinforced Epoxy Resin Composite for Acoustic Applications

Noise is an unwanted sound; requires reduction and control through the use of absorptive materials. This is imperative due to the adverse effect noise poses to human health, knowledge dissemination, and tranquility which is increasing daily due to industrialization and heightened allied activities. The use of natural and synthetic reinforced composites in noise pollution control is an emerging area of research. This study aims to develop and characterize fly ash nanoparticles reinforced epoxy resin composite for acoustic applications. Samples were prepared with fly ash nanoparticles reinforcement at 5%, 10%, 15%, 20%, and 25% and investigation of noise reduction coefficient (NRC), porosity and mechanical properties (hardness, impact, flexural strength) of samples were done. Cenospheres were obtained when fly ash particles were characterized separately with the aid of sieve analysis and x-ray fluorescence analysis. The cenospheres are hollow spherical and lightweight, inertfiller material. Correlation between porosity of the samples and their sound absorption properties was observed and showed that as porosity increased, the NRC values increased and as the porosity decreased the NRC values decreased. It was also observed that heat of polymerization, fly ash nanoparticles structure and air bubbles during sample preparation (mixing) influenced the porosity values which in turn influenced the NRC values of the composite. There was also a steady decrease in mechanical properties, as reinforcements were added (5%, 10%, 15%, 20%, and 25%), this was attributed to the high surface areas and shape of reinforcement added.

Quantifying Non-Linearity in Early Decay Curves of Measured and Computer-Modeled Room Impulse Responses of a Highly Non-Diffuse Room Exhibiting Flutter Echo

This paper investigates the use of two room acoustics metrics designed to evaluate the degree to which the linearity assumptions of the energy density curves are valid. The study focuses on measured and computer-modeled energy density curves derived from the room impulse response of a space exhibiting a highly non-diffuse sound field due to flutter echo. In conjunction with acoustical remediation, room impulse response measurements were taken before and after the installation of the acoustical panels. A very dramatic decrease in the reverberation time was experienced due to the addition of the acoustical panels. The two non-linearity metrics used in this study are the non-linearity parameter and the curvature. These metrics are calculated from the energy decay curves computed per octave band, based on the definitions presented in ISO 3382-2. The non-linearity parameter quantifies the deviation of the EDC from a straight line fit used to generated T20 and T30 reverberation times. Where the reverberation times are calculated based on a linear regression of the data relating to either −5 to −25 dB for T20 or −5 to −35 dB for T30 reverberation time calculations. This deviation is quantified using the correlation coefficient between the energy decay curve and the linear regression for the specified data. In order to graphically demonstrate these non-linearity metrics, the energy decay curves are plotted along with the linear regression curves for the T20 and T30 reverberation time for both the measured data and two different room acoustics computer-modeling techniques, geometric acoustics modeling and finite-difference wave-based modeling. The intent of plotting these curves together is to demonstrate the relationship between these metrics and the energy decay curve, and to evaluate their use for quantifying degree of non-linearity in non-diffuse sound fields. Observations of these graphical representations are used to evaluate the accuracy of reverberation time estimations in non-diffuse environments, and to evaluate the use of these non-linearity parameters for comparison of different computer-modeling techniques or room configurations. Using these techniques, the non-linearity parameter based on both T20 and T30 linear regression curves and the curvature parameter were calculated over 250–4000 Hz octave bands for the measured and computer-modeled room impulse response curves at two different locations and two different room configurations. Observations of these calculated results are used to evaluate the consistency of these metrics, and the application of these metrics to quantifying the degree of non-linearity of the energy decay curve derived from a non-diffuse sound field. These calculated values are also used to evaluate the differences in the degree of diffusivity between the measured and computer-modeled room impulse response. Acoustical computer modeling is often based on geometrical acoustics using ray-tracing and image-source algorithms, however, in non-diffuse sound fields, wave based methods are often able to better model the characteristic sound wave patterns that are developed. It is of interest to study whether these improvements in the wave based computer-modeling are also reflected in the non-linearity parameter calculations. The results showed that these metrics provide an effective criteria for identifying non-linearity in the energy decay curve, however for highly non-diffuse sound fields, the resulting values were found to be very sensitive to fluctuations in the energy decay curves and therefore, contain inconsistencies due to these differences.

An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction

An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and nonpolynomial nonlinearities, and it has considerable advantages over the other methods.

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Steerable Unidirectional Wave Emission From a Single Piezoelectric Transducer Using a Shape Memory Alloy Composite Metasurface

Structural Health Monitoring (SHM) and Nondestructive Evaluation (NDE) systems generally adopt piezoelectric transducers which emit omnidirectional wave fields. The achievement of directionality of guided wave generation will benefit the structural sensing purpose, which allows better detection and localization of the damage sites. In this study, a type of metamaterial ultrasonic radar is proposed for the steerable unidirectional wave manipulation. It contains a circular array of unit cells stuck in an aluminum plate which are delicately arranged in a circular fashion. Each unit cell is composed of a shape memory alloy substrate and a lead stub. The controllable bandgap of such metamaterial system can be achieved due to the stiffness change of nitinol between its martensite phase and austenite phase under a thermal load. This research starts with a Finite Element Model (FEM) of the unit cell to compute its frequency-wavenumber domain dispersion characteristics, demonstrating the adjustable bandgap feature. Then, numerical modeling of the metamaterial radar is performed by shifting the bandgap of one sector of the metasurface away from the excitation frequency. The modeling results demonstrate that the martensite phase metasurface area forms a bandgap region where guided wave energy cannot penetrate, while the bandgap of the austenite sector shifts away from the excitation frequency, opening up a transmission path for the ultrasonic waves. By rotating the austenite sector, the metamaterial structure can work like a wave emission radar, realizing of the steerable unidirectional wave radiation with a single transducer. Such an active metasurface possesses great application potential in future SHM and NDE systems.

Acoustic Amplification of Flow Ripple and Cavitation Damage in an Aerospace Fuel System Component

In a recent investigation of external fuel leaks from an aerospace pressure control valve, cavitation damages were discovered in a small deadheaded cavity, which was created by the axial clearance between the mating subcomponents. Experiments using high bandwidth pressure sensors showed that there were severe pressure fluctuations in the cavity and that the pressure repeatedly fell below the local vapor pressure of the fuel, which would cause cavitation. Spectral analyses showed resonance-like amplification of flow ripple in the valve surrounding inside the valve cavity. The apparent resonance frequency matched the computed fundamental Helmholtz resonance frequency of the cavity. These findings led to a venting solution of the deadheaded cavity by placing an appropriately sized through hole. Back-to-back testing with unvented valves showed stark improvements of the vented solution. This paper presents test and analytical data on the formation of a Helmholtz resonator in the small deadhead cavity of a gas turbine fuel delivery system component. This paper also demonstrates the validity of simple engineering formulas widely available in acoustics literature for predicting the Helmholtz resonance frequencies as a function of neck geometry, neck arrangement, and fuel properties.

Development of a Low Cost High-Speed Video Motion Capture System for Planar Motion

This project focuses on the development and characterization of a high speed video motion capture system for the measurement of planar, rigid body motions. The ability to collect information related to the accelerations, velocities and positions of points on a rigid body as it moves in planar space is very important in the fields of science and engineering. Traditional techniques, including the use of accelerometers, extensors and lasers, either rely on contact between the rigid body and the sensor or only measure out of plane motion. In this project, an inexpensive monochromatic high speed camera was used in conjunction with markers adhered to the objects under investigation to measure the planar displacement of a point on a moving object. The high speed camera is able to capture video at a rate of up to 20,000 frames per second, however, at this speed the field of view is very small. For a larger field of view, the frames per second is diminished to close to 3,000 frames per second. The goal of this project was to develop the hardware parameters and software necessary to collect and process 2D motion data at different frequencies and then evaluate the efficacy of video motion capture through comparison with simultaneously captured acceleration data. The efficacy was evaluated over a range of accelerations using variable frequency oscillations. The video footage was processed, frame by frame in order to extract x and y position for the center of the marker. Extraction of the position data was completed using the MATLAB computer vision toolbox, which provides tools for identifying the x and y locations of corners, circle centers and other defining features. The project began by identifying size, shape, color and material of markers for effective data collection using the motion capture system. Additionally, camera settings, field of view, capture rate, lighting and mounting conditions were evaluated to determine what conditions would result in the most accurate position sensing. In order to validate the measurements from the motion capture system, position data were correlated with accelerations measured from a traditional accelerometer located on the object under test. In order for the position data collected through the high speed video capture to be compared with the acceleration data collected using measurement from accelerometers, numerical differentiation of the position signals gathered from the high speed footage was performed. The efficacy of different shape and size markers, along with other camera settings, will be demonstrated for specific oscillatory test profiles.