Applications of force vibration. Rotating unbalance Base excitation Vibration measurement devices

Similar documents
FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf

Harmonic excitation (damped)

Capítulo. of Particles: Energy and Momentum Methods

Transistor configurations: There are three main ways to place a FET/BJT in an architecture:

Fundamental Vehicle Loads & Their Estimation

Introduction to Mechanical Vibrations

INF 5460 Electronic noise Estimates and countermeasures. Lecture 13 (Mot 10) Amplifier Architectures

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

Chapter 2: Introduction to Damping in Free and Forced Vibrations

Viscous Damping Summary Sheet No Damping Case: Damped behaviour depends on the relative size of ω o and b/2m 3 Cases: 1.

SHM SHM. T is the period or time it takes to complete 1 cycle. T = = 2π. f is the frequency or the number of cycles completed per unit time.

Supplementary Information

PHYS PRACTICE EXAM 2

Introduction to Numerical Analysis. In this lesson you will be taken through a pair of techniques that will be used to solve the equations of.

Niraj Sir. circular motion;; SOLUTIONS TO CONCEPTS CHAPTER 7

[ m] x = 0.25cos 20 t sin 20 t m

EN40: Dynamics and Vibrations. Midterm Examination Tuesday March

Chapter 1: Basics of Vibrations for Simple Mechanical Systems

Optical flow equation

Physics 232 Exam I Feb. 14, 2005

Homework 6: Forced Vibrations Due Friday April 6, 2018

Lecture 23 Damped Motion

Ideal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory

ES 330 Electronics II Homework 03 (Fall 2017 Due Wednesday, September 20, 2017)

Cameras and World Geometry

MOSFET device models and conventions

Problems and Solutions for Section 3.2 (3.15 through 3.25)

Circular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.

Outline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem

Thus the force is proportional but opposite to the displacement away from equilibrium.

ECE-314 Fall 2012 Review Questions

M x t = K x F t x t = A x M 1 F t. M x t = K x cos t G 0. x t = A x cos t F 0

Solutions Manual 4.1. nonlinear. 4.2 The Fourier Series is: and the fundamental frequency is ω 2π

Electrical Engineering Department Network Lab.

Parameter Optimization of Multi-element Synthetic Aperture Imaging Systems

Practice Problems - Week #4 Higher-Order DEs, Applications Solutions

Sharif University of Technology - CEDRA By: Professor Ali Meghdari

LINEAR MOMENTUM Physical quantities that we have been using to characterize the motion of a particle

Lecture 23: Central Force Motion

Mechanical Vibrations

SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9

Computer Propagation Analysis Tools

Response of MDOF systems

Monitoring and system identification of suspension bridges: An alternative approach

On Acoustic Radiation by Rotating Dipole Sources in Frequency Domain

Reading. Lecture 28: Single Stage Frequency response. Lecture Outline. Context

The Production of Polarization

(a) Calculate the apparent weight of the student in the first part of the journey while accelerating downwards at 2.35 m s 2.

RESPONSE OF A RECTANGULAR PLATE TO BASE EXCITATION Revision E W( )

which proves the motion is simple harmonic. Now A = a 2 + b 2 = =

CHAPTER 5: Circular Motion; Gravitation

Pseudosteady-State Flow Relations for a Radial System from Department of Petroleum Engineering Course Notes (1997)

F = 0. x o F = -k x o v = 0 F = 0. F = k x o v = 0 F = 0. x = 0 F = 0. F = -k x 1. PHYSICS 151 Notes for Online Lecture 2.4.

Physics 232 Exam I Feb. 13, 2006

IMPACT VIBRATION ABSORBER OF PENDULUM TYPE

Walter D. Pilkey. Dmitry V. Balandin. Nikolai N. Bolotnik. Sergey V. Purtsezov. Introduction. Nomenclature

Physics 207 Lecture 13

School of Mechanical Engineering Purdue University. ME375 Transfer Functions - 1

Electromagnetic Wave Absorber with Isotropic and Anisotropic Metamaterials

Mechanical System. Seoul National Univ. School of Mechanical and Aerospace Engineering. Spring 2008

Announcements: The Rydberg formula describes. A Hydrogen-like ion is an ion that

= 4 3 π( m) 3 (5480 kg m 3 ) = kg.

Lecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light

Lecture 28: Single Stage Frequency response. Context

Neutron Slowing Down Distances and Times in Hydrogenous Materials. Erin Boyd May 10, 2005

ECE 145B / 218B, notes set 5: Two-port Noise Parameters

i sw + v sw + v o 100V Ideal switch characteristics

ME203 Section 4.1 Forced Vibration Response of Linear System Nov 4, 2002 (1) kx c x& m mg

physicsandmathstutor.com

Physics 2001 Problem Set 5 Solutions

Dynamic Response of Linear Systems

Circular motion. Objectives. Physics terms. Assessment. Equations 5/22/14. Describe the accelerated motion of objects moving in circles.

Dynamic Model and Analysis of Nonlinear Vibration Characteristic of a Curve-Face Gear Drive Cai, Z. Lin, C. Zhiqin Cai Chao Lin*

Physics 41 HW Set 1 Chapter 15 Serway 7 th Edition


t = s D Overview of Tests Two-Sample t-test: Independent Samples Independent Samples t-test Difference between Means in a Two-sample Experiment

DETERMINATION OF NATURAL FREQUENCY AND DAMPING RATIO

Physics 235 Chapter 5. Chapter 5 Gravitation

Chapter 31 Faraday s Law

Transfer Function Analysis

Ch23. Introduction to Analytical Separations

F.Y. Diploma : Sem. II [AE/CH/FG/ME/PT/PG] Applied Mathematics

C(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12

In this section we will study periodic signals in terms of their frequency f t is said to be periodic if (4.1)

ME 375 EXAM #1 Friday, March 13, 2015 SOLUTION

Tidal forces. m r. m 1 m 2. x r 2. r 1

The Recovery of Rockets.

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)

Chapter 9 Sinusoidal Steady State Analysis

Physics 211: Newton s Second Law

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Mechanical Vibrations. Seventh Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.

By the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences

6.4 Period and Frequency for Uniform Circular Motion

PI3B V, 16-Bit to 32-Bit FET Mux/DeMux NanoSwitch. Features. Description. Pin Configuration. Block Diagram.

Describing Circular motion

Chapter 7-8 Rotational Motion

LECTURE 15. Phase-amplitude variables. Non-linear transverse motion

KINEMATICS OF RIGID BODIES

5/09/06 PHYSICS 213 Exam #1 NAME FEYNMAN Please write down your name also on the back side of the last page

Sta$s$cal physics (microcanonical ensemble) Introduc$on. Introduc$on 18/09/2014. W.J. Briels. How do we tell one molecule from another?

Transcription:

Applicaios of foce viaio Roaig ualace Base exciaio Viaio easuee devices

Roaig ualace 1 Roaig ualace: Viaio caused y iegulaiies i he disiuio of he ass i he oaig copoe.

Roaig ualace 0 FBD 1 FBD x x 0 e 0 F x F kx c x FBD 1 FBD x x F 0 0 x F cx kx x 0 x cx kx 0 x x esi e si x cx kx e si 0

Roaig ualace 3 x cx kx e si 0 0e x x x si z, Ze x I[ z ] z z z 0e e Z 0e 0e 1 H 0e x H si θ ; θ a 1 1

Roaig ualace 4 0e x H si θ X si θ H X e 0

Exaple: washig achie A odel of a washig achie is illusaed i he figue. A udle of we clohes fo a ass of 10 kg 0 ad causes a oaig ualace. The oaig ass id 0 kg icludig 0 ad he diaee of he washe aske e is 50 c. Assue ha he spi cycle oaes a 300 p. Le k e 1000 N/ ad 0.01. a Calculae he foce asied o he sides of he washig achie. The quaiies, 0 e ad ae all fixed y he pevious desig. Desig he isolaio syse so ha he foce asied o he side of he washig achie is less ha 100 N.

Exaple: Ualace oo A elecic oo has a ecceic ass of 1 kg 10% of he oal ass ad is se o wo ideical spigs k 3. N/. The oo us a 1750 p, ad he ass ecceiciy is 100 fo he cee. The spigs ae oued 50 apa wih he oo shaf i he cee. Neglec dapig ad deeie he apliude of veical viaio.

Base exciaio io Exaples Sesiive equipe placed o viaig foudaio A auooive suspesio syse Buildigs sueced o eahquakes

Base exciaio 1 EOM x c x y k x y 0 Assupio: y he ase oves haoically cos FBD 1s ehod: supeposiio x cx kx c si k cos 1s haoic ipu d haoic ipu x p x p 1 x p

Base exciaio d ehod: Fequecy espose ehod x cx kx cy ky x x x y y y cos z, Ze Re[ e ] x Re[ z ] Su. io EOM o chage o coplex fo Coplex EOM z z z e e Ze e Z 1 1 ;

Base exciaio 3 ] Re[ z x Ze z H Z 1 1 e H Z θ θ θ e H e e H z H 1 1 cos θ H x cos θ X x H X ;

Displacee asissiiliy 1 Disp. asissiiliy Oupu disp. Ipu disp. X H 1 1 Disp. Tasissiiy specifies how oio is asied fo he ase o he ass a vaious divig fequecy.

Displacee asissiiliy Icease Icease 1. 0 D.T. 1. 1 D.T. lage 3. < D.T. > 1 Lage, sall D.T. D.T. 1 > D.T. < 1 Lage, lage D.T. X H 1 1

Foce asissiiliy 1 The foce asied o he ass is doe hough he spig ad dape. 0 y x k y x c x y x c y x k F Fo EOM x y x k y x c F cos θ H x Fo cos θ H x cos cos θ θ F H F T

Foce asissiiliy cos cos θ θ F H F T H F T 1 1 k F T F T 1 1 1 1 k F T F.T. ells how uch foce is asied fo he ase o he ass a vaious divig fequecies

Foce asissiiliy 3 F T k 1 1

Exaple Base exciaio y 0.01si 0. 909v v k/h ad/s Deeie he effec of speed o he apliude of displacee of he auooile as well as he effec of he value of he ca s ass. Assue ha he suspesio syse povides a equivale siffess of 4 10 5 N/ ad dapig of 0 10 3 N.s/.

Exaple Base exciaio Deeie he apliude of veical viaio of he spig-oued aile as i avels a a velociy of 5 k/h ove he oad whose coou ay e expessed y a siusoid. The ass of he aile is 500 kg ad ha of he wheels aloe ay e egleced. Duig loadig, each 75 kg added o he load caused he aile o sag 3 o is spigs. Assue ha he wheels ae i coac wih he oad a all ies ad eglec dapig. A wha ciical speed v c is he viaio of he aile geaes? [J. L. Meia & L. G. Kaige 8/71]

Measuee devices 1 y : Acual viaio of he ieesed oec x : Viaio of he ass iside a easuee device Measued value : w x y FBD EOM x c x y k x y 0 w cw kw y Assupio: he ase oves haoically y cos

Measuee devices w cw kw y w w w y y cos z Ze, Re[ e ] w Re[ z ] Su. io EOM o chage o coplex fo Coplex EOM z z z e Ze e Z 1 Fequecy espose H o T

Measuee devices 3 θ θ e T e e T Ze z cos cos ] Re[ θ θ W T z w 1 T W e T T Z θ 1 Acual viaio Measued viaio Displacee Tasissiiliy Diffe fo Displacee asissiiliy of ase exciaio

Seisoee Is used o easue displacee of viaio The value of T appoaches uiy whe is lage Seisoee egio > 3 Low aual fequecy lage ass o sall k Ca easue i a age fo 10 o 500 Hz wih is aual fequecy of 1 o 5 Hz T W Iceasig Rage fo seisoee

Acceleoee 1 Is used o easue acceleaio of viaio Use piezoelecic effec: Foce acceleaio Volage Quaz o ceaic cysals 1 T W 1 1 A W y 1 A W y

Acceleoee T appoaches uiy whe is sall acceleoee egio Acceleoee age is wides whe dapig aio 0.65-7 0 < < 0.6 High aual fequecy sall ass ad lage k Ca easue i a age fo 0 o ove 10 khz wih is aual fequecy of 30 o 50 khz ad weigh less ha 0 g. Iceasig W A 1 y

Exaple : Acceleoee A acceleoee has a suspeded ass of 0.01 kg wih a daped aual fequecy of viaio of 150 Hz. Whe oued o a egie udegoig a acceleaio of 1 g a a opeaig speed of 6000 p, he acceleaio is ecoded as 9.5 /s y he isue. Fid he dapig cosa ad he spig siffess of he acceleoee. [Sigiesu S. Rao, Ex 10.3]

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback