Assessing the Effects of Impedance Modifications Using the Moebius Transformation

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Y. Zhang ◽  
D. W. Herrin
Keyword(s):  
Insertion Loss ◽  
Transmission Loss ◽  
Mechanical Systems ◽  
Mechanical Impedance ◽  
Harmonic Excitation ◽  
Complex Domain ◽  
Moebius Transformation ◽  
Straight Lines

The Moebius transformation maps straight lines or circles in one complex domain into straight lines or circles in another. It has been observed that the equations relating acoustic or mechanical impedance modifications to responses under harmonic excitation are in the form of the Moebius transformation. Using the properties of the Moebius transformation, the impedance modification that will minimize the response at a particular frequency can be predicted provided that the modification is between two positions. To prove the utility of this method for acoustic and mechanical systems, it is demonstrated that the equations for calculation of transmission and insertion loss of mufflers, insertion loss of enclosures, and insertion loss of mounts are in the form of the Moebius transformation for impedance modifications. The method is demonstrated for enclosure insertion loss by adding a short duct in a partition introduced to an enclosure. In a similar manner, it is shown that the length or area of a bypass duct in a muffler can be tuned to maximize the transmission loss. In the final example, the insertion loss of an isolator system is improved at a particular frequency by adding mass to one side of the isolator.

Exploiting the Complex Plane: The Moebius Transformation and Vibro-Acoustic Optimization

2012 ◽  
Author(s):  
D. W. Herrin ◽  
Y. Zhang ◽  
J. Liu
Keyword(s):  
Linear System ◽  
Complex Plane ◽  
Insertion Loss ◽  
Transmission Loss ◽  
Complex Domain ◽  
System Property ◽  
Moebius Transformation ◽  
Design Changes ◽  
Straight Line ◽  
Straight Lines

If a mechanical or acoustical impedance modification is introduced between two positions, the effect of that modification can be plotted in the complex plane at a given frequency. It has been shown that the mechanical or acoustical response will trace a circle in the complex plane for straight-line modifications to impedance in the complex plane. In that case, the equations relating the response to an impedance modification are in a form consistent with the Moebius transformation, which maps straight lines or circles in one complex domain into straight lines or circles in another complex plane. It is demonstrated that the equations for muffler transmission loss and mount insertion loss are in a form consistent with the Moebius transformation for certain design changes. Accordingly, the usefulness of this linear system property will be illustrated for both muffler and mount design.

scholarly journals A New Design of Vibration Absorber for Periodic Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Kao-An Lin
Keyword(s):  
Mechanical Systems ◽  
Harmonic Excitation ◽  
Design Parameters ◽  
Vibration Absorber ◽  
Periodic Excitation ◽  
Dynamic Vibration Absorber ◽  
Dual Beam ◽  
Design Variables ◽  
Resonance Frequencies ◽  
Engineering Significance

The authors designed a novel type of dynamic vibration absorber, called periodic vibration absorber (PVA), for mechanical systems subjected to periodic excitation. Since the periodic rather than single harmonic excitation is themost occurring case in mechanical systems, the design of PVA is hence of engineering significance. The PVA designed in this paper is composed of a dual-beam interconnected with a discrete spring in between. By appropriately choosing the design parameters, the PVA can be of resonance frequencies in integer multiples of the base frequency such that the PVA can absorb significant amount of higher harmonics in addition to the base harmonic. The designed PVA was first experimentally verified for its resonance frequencies. The PVA implemented onto a mechanical system was then tested for its absorption ability. From both tests, satisfying agreement between experiments and numerical calculations has been obtained. The sensitivities of the design variables, such as the discrete spring’s stiffness and location, were discussed as well. The parameters’ sensitivities provided us with the PVA’s adjustable room for excitation frequency’s mismatch. Numerical results showed that within 3% of frequency mismatch, the PVA still performed better than a single DVA via adjusting the spring’s constant and location. All the results proved that the novel type of PVA could be a very effective device for vibration reduction of mechanical systems subjected to periodic excitation.

scholarly journals Cracking Diagnosis in Fiber-Reinforced Concrete with Synthetic Fibers Using Piezoelectric Transducers

Fibers ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 5
Author(s):  
Maristella E. Voutetaki ◽  
Maria C. Naoum ◽  
Nikos A. Papadopoulos ◽  
Constantin E. Chalioris
Keyword(s):  
Reinforced Concrete ◽  
Damage Detection ◽  
Mechanical Impedance ◽  
Harmonic Excitation ◽  
Fiber Reinforced Concrete ◽  
Repeated Loading ◽  
Fiber Reinforced ◽  
Damage Diagnosis ◽  
Promising Alternative ◽  
Synthetic Fibers

The addition of short fibers in concrete mass offers a composite material with advanced properties, and fiber-reinforced concrete (FRC) is a promising alternative in civil engineering applications. Recently, structural health monitoring (SHM) and damage diagnosis of FRC has received increasing attention. In this work, the effectiveness of a wireless SHM system to detect damage due to cracking is addressed in FRC with synthetic fibers under compressive repeated load. In FRC structural members, cracking propagates in small and thin cracks due to the presence of the dispersed fibers and, therefore, the challenge of damage detection is increasing. An experimental investigation on standard 150 mm cubes made of FRC is applied at specific and loading levels where the cracks probably developed in the inner part of the specimens, whereas no visible cracks appeared on their surface. A network of small PZT patches, mounted to the surface of the FRC specimen, provides dual-sensing function. The remotely controlled monitoring system vibrates the PZT patches, acting as actuators by an amplified harmonic excitation voltage. Simultaneously, it monitors the signal of the same PZTs acting as sensors and, after processing the voltage frequency response of the PZTs, it transmits them wirelessly and in real time. FRC cracking due to repeated loading ad various compressive stress levels induces change in the mechanical impedance, causing a corresponding change on the signal of each PZT. The influence of the added synthetic fibers on the compressive behavior and the damage-detection procedure is examined and discussed. In addition, the effectiveness of the proposed damage-diagnosis approach for the prognosis of final cracking performance and failure is investigated. The objectives of the study also include the development of a reliable quantitative assessment of damage using the statistical index values at various points of PZT measurements.

scholarly journals Virtual Vibration Measurement Using KLT Motion Tracking Algorithm

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Joseph Morlier ◽  
Guilhem Michon
Keyword(s):  
Computer Vision ◽  
Video Processing ◽  
High Speed ◽  
Motion Tracking ◽  
Mechanical Systems ◽  
Harmonic Excitation ◽  
Vibration Measurement ◽  
Mode Shapes ◽  
Output Analysis ◽  
Virtual Sensors

This paper presents a practical framework and its applications of motion tracking algorithms applied to structural dynamics. Tracking points (“features”) across multiple images are a fundamental operation in many computer vision applications. The aim of this work is to show the capability of computer vision (CV) for estimating the dynamic characteristics of two mechanical systems using a noncontact, markerless, and simultaneous single input multiple output analysis. Kanade–Lucas–Tomasi trackers are used as virtual sensors on mechanical systems’ video from a high speed camera. First we introduce the paradigm of virtual sensors in the field of modal analysis using video processing. To validate our method, a simple experiment is proposed: an Oberst beam test with harmonic excitation (mode 1). Then with the example of a helicopter blade, frequency response functions’ (FRFs) reconstruction is carried out by introducing several signal processing enhancements (filtering and smoothing). The CV experimental results (frequencies and mode shapes) are compared with the classical modal approach and the finite element model (FEM) showing high correlation. The main interest of this method is that displacements are simply measured using only video at fps respecting the Nyquist frequency.

A Practical Method for Trace Exposure and Roughness Measurements and Implementation in High Speed Package Design

2012 ◽  
Author(s):  
Valentina Korchnoy ◽  
Jacov Brener
Keyword(s):  
Transmission Lines ◽  
Insertion Loss ◽  
High Frequency ◽  
High Speed ◽  
Transmission Loss ◽  
Signal Propagation ◽  
Practical Method ◽  
High Frequency Signal ◽  
Advantages And Disadvantages ◽  
Conductor Surface

Abstract High frequency signal propagation through transmission lines has been an important discipline for RF engineers. With advancements in digital technologies, especially when data rates reached multiple Gb/s, package designers have to consider parameters such as transmission loss and trace impedance in order to maintain signal integrity. For high frequency signals, the surface roughness of the copper trace becomes increasingly significant in determining conduction loss, due to current confinement to the conductor surface by the skin effect. Accurate 3D conductor surface maps are required for correct trace insertion loss simulation. Practical methods for package trace exposure and 3D surface height map acquisition are discussed in this paper. Advantages and disadvantages of these methods, and their implementation to real packages are shown. Using electrical parameters resulting from a 3D trace surface map, the error between electrical simulations and actual measurements of insertion loss in an FCBGA package have been reduced from 6% to nearly zero, enabling tighter margins in 10GB/s high speed serial design.

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