A Phase Resonance Approach for Modal Testing of Structures with Nonlinear Dissipation
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Frequency Response = K − Ml
Frequency Response 1. Introduction We will examine the response of a second order linear constant coefficient system to a sinusoidal input. We will pay special attention to the way the output changes as the frequency of the input changes. This is what we mean by the frequency response of the system. In particular, we will look at the amplitude response and the phase response; that is, the amplitude and phase lag of the system’s output considered as functions of the input frequency. In O.4 the Exponential Input Theorem was used to find a particular solution in the case of exponential or sinusoidal input. Here we will work out in detail the formulas for a second order system. We will then interpret these formulas as the frequency response of a mechanical system. In particular, we will look at damped-spring-mass systems. We will study carefully two cases: first, when the mass is driven by pushing on the spring and second, when the mass is driven by pushing on the dashpot. Both these systems have the same form p(D)x = q(t), but their amplitude responses are very different. This is because, as we will see, it can make physical sense to designate something other than q(t) as the input. For example, in the system mx0 + bx0 + kx = by0 we will consider y to be the input. (Of course, y is related to the expression on the right- hand-side of the equation, but it is not exactly the same.) 2. Sinusoidally Driven Systems: Second Order Constant Coefficient DE’s We start with the second order linear constant coefficient (CC) DE, which as we’ve seen can be interpreted as modeling a damped forced harmonic oscillator. -
Modal Analysis of Dynamic Behavior of Buildings Allowed to Uplift at Mid-Story
Modal Analysis of Dynamic Behavior of Buildings Allowed to Uplift at Mid-story T. Ishihara Building Research Institute, Japan T. Azuhata National Institute for Land and Infrastructure Management, MLIT,Japan M. Midorikawa Hokkaido University, Japan SUMMARY: In this paper, dynamic behavior of buildings allowed to uplift at mid-story is investigated. The system considered is a two dimensional uniform shear-beam model allowed to uplift at mid-story. On account of piece-wise linear characteristics, classical modal analysis is applied to evaluate dynamic behavior during uplift. At first, the equations of motion are derived and eigenproblem is solved. Their free-vibrational responses under gravity are analyzed during the first excursion of uplift following to the first mode vibration in contact phase. Parameters are height/width ratio of whole buildings, height ratio of mid-story uplift system and intensity of vibration. The results show reduction effect due to uplift at mid-story with modal contributions to responses. Keywords: Uplift at mid-story, Uniform shear beam, Story shear coefficient 1. INTRODUCTION It has been pointed out that buildings during strong earthquakes have been subjected to foundation uplift (Rutenberg et al. 1982, Hayashi et al. 1999). Some studies dealing with foundation uplift in flexible systems have already been conducted (e.g. Muto et al. 1960, Meek 1975, 1978, Psycharis 1983, Yim et al. 1985). The authors also studied experimentally and analytically from the point of view of utilizing transient uplift motion for reduction of seismic-force response (e.g. Ishihara et al. 2006a, 2006b, 2007, 2008, 2010, Azuhata et al. 2008, 2009, Midorikawa et al. -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
To Learn the Basic Properties of Traveling Waves. Slide 20-2 Chapter 20 Preview
Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide 20-2 Chapter 20 Preview Slide 20-3 Chapter 20 Preview Slide 20-5 • result from periodic disturbance • same period (frequency) as source 1 f • Longitudinal or Transverse Waves • Characterized by – amplitude (how far do the “bits” move from their equilibrium positions? Amplitude of MEDIUM) – period or frequency (how long does it take for each “bit” to go through one cycle?) – wavelength (over what distance does the cycle repeat in a freeze frame?) – wave speed (how fast is the energy transferred?) vf v Wavelength and Frequency are Inversely related: f The shorter the wavelength, the higher the frequency. The longer the wavelength, the lower the frequency. 3Hz 5Hz Spherical Waves Wave speed: Depends on Properties of the Medium: Temperature, Density, Elasticity, Tension, Relative Motion vf Transverse Wave • A traveling wave or pulse that causes the elements of the disturbed medium to move perpendicular to the direction of propagation is called a transverse wave Longitudinal Wave A traveling wave or pulse that causes the elements of the disturbed medium to move parallel to the direction of propagation is called a longitudinal wave: Pulse Tuning Fork Guitar String Types of Waves Sound String Wave PULSE: • traveling disturbance • transfers energy and momentum • no bulk motion of the medium • comes in two flavors • LONGitudinal • TRANSverse Traveling Pulse • For a pulse traveling to the right – y (x, t) = f (x – vt) • For a pulse traveling to -
Modal Analysis1
© 1994 by Eric Marsh & Alexander Slocum Precision Machine Design Topic 10 Vibration control step 1: Modal analysis1 Purpose: The manner in which a machine behaves dynamically has a direct effect on the quality of the process. It is vital to be able to measure machine performance. Outline: • Introduction • Measurement process outline • Practical issues • Vibration fundamentals • Experimental results • Data collection: Instrumentation summary • Case study: A wafer cassette handling robot • Case study: A precision surface grinder "There is nothing so powerful as truth" Daniel Webster 1 This section was written by Prof. Eric Marsh, Dept. of Mechanical Engineering, Penn State University, 322 Reber Bldg., University Park, State College, 16802; [email protected] 10-1 © 1994 by Eric Marsh & Alexander Slocum Introduction • Experimental Modal Analysis allows the study of vibration modes in a machine tool structure. • An understanding of data acquisition, signal processing, and vibration theory is necessary to obtain meaningful results. • The results of a modal analysis are: • Modal natural frequencies • Modal damping factors • Vibration mode shapes • This information may be used to: • Locate sources of compliance in a structure • Characterize machine performance • Optimize design parameters • Identify the weak links in a structure for design optimization •Identify modes which are being excited by the process (e.g., an end mill) so the structure can be modified accordingly. • Identify modes (parts of the structure) which limit the speed of operation (e.g., in a Coordinate Measuring Machine). •Use modal analysis to measure an older machine that achieves high surface finish, but is to be replaced with a more accurate machine. • The new machine can be specified to have a dynamic stiffness at least as high as the old machine. -
Resonance Beyond Frequency-Matching
Resonance Beyond Frequency-Matching Zhenyu Wang (王振宇)1, Mingzhe Li (李明哲)1,2, & Ruifang Wang (王瑞方)1,2* 1 Department of Physics, Xiamen University, Xiamen 361005, China. 2 Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China. *Corresponding author. [email protected] Resonance, defined as the oscillation of a system when the temporal frequency of an external stimulus matches a natural frequency of the system, is important in both fundamental physics and applied disciplines. However, the spatial character of oscillation is not considered in the definition of resonance. In this work, we reveal the creation of spatial resonance when the stimulus matches the space pattern of a normal mode in an oscillating system. The complete resonance, which we call multidimensional resonance, is a combination of both the spatial and the conventionally defined (temporal) resonance and can be several orders of magnitude stronger than the temporal resonance alone. We further elucidate that the spin wave produced by multidimensional resonance drives considerably faster reversal of the vortex core in a magnetic nanodisk. Our findings provide insight into the nature of wave dynamics and open the door to novel applications. I. INTRODUCTION Resonance is a universal property of oscillation in both classical and quantum physics[1,2]. Resonance occurs at a wide range of scales, from subatomic particles[2,3] to astronomical objects[4]. A thorough understanding of resonance is therefore crucial for both fundamental research[4-8] and numerous related applications[9-12]. The simplest resonance system is composed of one oscillating element, for instance, a pendulum. Such a simple system features a single inherent resonance frequency. -
Understanding What Really Happens at Resonance
feature article Resonance Revealed: Understanding What Really Happens at Resonance Chris White Wood RESONANCE focus on some underlying principles and use these to construct The word has various meanings in acoustics, chemistry, vector diagrams to explain the resonance phenomenon. It thus electronics, mechanics, even astronomy. But for vibration aspires to provide a more intuitive understanding. professionals, it is the definition from the field of mechanics that is of interest, and it is usually stated thus: SYSTEM BEHAVIOR Before we move on to the why and how, let us review the what— “The condition where a system or body is subjected to an that is, what happens when a cyclic force, gradually increasing oscillating force close to its natural frequency.” from zero frequency, is applied to a vibrating system. Let us consider the shaft of some rotating machine. Rotor Yet this definition seems incomplete. It really only states the balancing is always performed to within a tolerance; there condition necessary for resonance to occur—telling us nothing will always be some degree of residual unbalance, which will of the condition itself. How does a system behave at resonance, give rise to a rotating centrifugal force. Although the residual and why? Why does the behavior change as it passes through unbalance is due to a nonsymmetrical distribution of mass resonance? Why does a system even have a natural frequency? around the center of rotation, we can think of it as an equivalent Of course, we can diagnose machinery vibration resonance “heavy spot” at some point on the rotor. problems without complete answers to these questions. -
PHASOR DIAGRAMS II Fault Analysis Ron Alexander – Bonneville Power Administration
PHASOR DIAGRAMS II Fault Analysis Ron Alexander – Bonneville Power Administration For any technician or engineer to understand the characteristics of a power system, the use of phasors and polarity are essential. They aid in the understanding and analysis of how the power system is connected and operates both during normal (balanced) conditions, as well as fault (unbalanced) conditions. Thus, as J. Lewis Blackburn of Westinghouse stated, “a sound theoretical and practical knowledge of phasors and polarity is a fundamental and valuable resource.” C C A A B B Balanced System Unbalanced System With the proper identification of circuits and assumed direction established in a circuit diagram (with the use of polarity), the corresponding phasor diagram can be drawn from either calculated or test data. Fortunately, most relays today along with digital fault recorders supply us with recorded quantities as seen during fault conditions. This in turn allows us to create a phasor diagram in which we can visualize how the power system was affected during a fault condition. FAULTS Faults are unavoidable in the operation of a power system. Faults are caused by: • Lightning • Insulator failure • Equipment failure • Trees • Accidents • Vandalism such as gunshots • Fires • Foreign material Faults are essentially short circuits on the power system and can occur between phases and ground in virtually any combination: • One phase to ground • Two phases to ground • Three phase to ground • Phase to phase As previously instructed by Cliff Harris of Idaho Power Company: Faults come uninvited and seldom leave voluntarily. Faults cause voltage to collapse and current to increase. Fault voltage and current magnitude depend on several factors, including source strength, location of fault, type of fault, system conditions, etc. -
Sinusoidal Signals Sinusoidal Signals
SINUSOIDAL SIGNALS SINUSOIDAL SIGNALS x(t) = cos(2¼ft + ') = cos(!t + ') (continuous time) x[n] = cos(2¼fn + ') = cos(!n + ') (discrete time) f : frequency (s¡1 (Hz)) ! : angular frequency (radians/s) ' : phase (radians) 2 Sinusoidal signals A cos(ω t) A sin(ω t) A 0 −A 0 T/2 T 3T/2 2T xc(t) = A cos(2¼ft) xs(t) = A sin(2¼ft) = A cos(2¼ft ¡ ¼=2) - amplitude A -amplitude A - period T = 1=f -period T = 1=f - phase: 0 -phase: ¡¼=2 3 WHY SINUSOIDAL SIGNALS? ² Physical reasons: - harmonic oscillators generate sinusoids, e.g., vibrating structures - waves consist of sinusoidals, e.g., acoustic waves or electromagnetic waves used in wireless transmission ² Psychophysical reason: - speech consists of superposition of sinusoids - human ear detects frequencies - human eye senses light of various frequencies ² Mathematical (and physical) reason: - Linear systems, both physical systems and man-made ¯lters, a®ect a signal frequency by frequency (hence low- pass, high-pass etc ¯lters) 4 EXAMPLE: TRANSMISSION OF A LOW-FREQUENCY SIGNAL USING HIGH-FREQUENCY ELECTROMAGNETIC (RADIO) SIGNAL - A POSSIBLE (CONVENTIONAL) METHOD: AMPLITUDE MODULATION (AM) Example: low-frequency signal v(t) = 5 + 2 cos(2¼f¢t); f¢ = 20 Hz High-frequency carrier wave vc(t) = cos(2¼fct); fc = 200 Hz Amplitude modulation (AM) of carrier (electromagnetic) wave: x(t) = v(t) cos(2¼fct) 5 8 6 4 2 v 0 −2 −4 −6 −8 8 6 4 2 x 0 −2 −4 −6 −8 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 t Top: v(t) (dashed) and vc(t) = cos(2¼fct). -
Characteristics of Sine Wave Ac Power
CHARACTERISTICS OF BY: VIJAY SHARMA SINE WAVE AC POWER: ENGINEER DEFINITIONS OF ELECTRICAL CONCEPTS, specifications & operations Excerpt from Inverter Charger Series Manual CHARACTERISTICS OF SINE WAVE AC POWER 1.0 DEFINITIONS OF ELECTRICAL CONCEPTS, SPECIFICATIONS & OPERATIONS Polar Coordinate System: It is a two-dimensional coordinate system for graphical representation in which each point on a plane is determined by the radial coordinate and the angular coordinate. The radial coordinate denotes the point’s distance from a central point known as the pole. The angular coordinate (usually denoted by Ø or O t) denotes the positive or anti-clockwise (counter-clockwise) angle required to reach the point from the polar axis. Vector: It is a varying mathematical quantity that has a magnitude and direction. The voltage and current in a sinusoidal AC voltage can be represented by the voltage and current vectors in a Polar Coordinate System of graphical representation. Phase, Ø: It is denoted by"Ø" and is equal to the angular magnitude in a Polar Coordinate System of graphical representation of vectorial quantities. It is used to denote the angular distance between the voltage and the current vectors in a sinusoidal voltage. Power Factor, (PF): It is denoted by “PF” and is equal to the Cosine function of the Phase "Ø" (denoted CosØ) between the voltage and current vectors in a sinusoidal voltage. It is also equal to the ratio of the Active Power (P) in Watts to the Apparent Power (S) in VA. The maximum value is 1. Normally it ranges from 0.6 to 0.8. Voltage (V), Volts: It is denoted by “V” and the unit is “Volts” – denoted as “V”. -
Modal Analysis for Free Vibration of Four Beam Theories
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/315549591 MODAL ANALYSIS FOR FREE VIBRATION OF FOUR BEAM THEORIES Conference Paper · January 2015 DOI: 10.20906/CPS/COB-2015-0991 CITATIONS READS 10 615 2 authors: Anderson Soares Da Costa Azevêdo Simone dos Santos Universidade Federal do Piauí 8 PUBLICATIONS 17 CITATIONS 22 PUBLICATIONS 24 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Dynamic Analysis of Beam View project Natural Frequency Optimization using Genetic Algorithm View project All content following this page was uploaded by Simone dos Santos on 27 July 2017. The user has requested enhancement of the downloaded file. MODAL ANALYSIS FOR FREE VIBRATION OF FOUR BEAM THEORIES Anderson Soares da Costa Azevêdo Universidade Federal do Piauí [email protected] Simone dos Santos Hoefel Universidade Federal do Piauí [email protected] Abstract. Beams are structural elements frequently used for support buildings, part of airplanes, ships, rotor blades and most engineering structures. In many projects it is assumed that these elements are subjected only to static loads, how- ever dynamic loads induce vibrations, which changes the values of stresses and strains. Furthermore, these mechanical phenomenon cause noise, instabilities and may also develop resonance, which improves deflections and failure. Therefore study these structural behavior is fundamental in order to prevent the effects of vibration. The mechanical behavior of these structural elements may be described by differential equations, four widely used beam theories are Euler-Bernouli, Rayleigh, Shear and Timoshenko. This paper presents a comparison between these four beam theories for the free trans- verse vibration of uniform beam.