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Frame NVH (Part - 1) | Skill-Lync | Workshop — Transcript

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  1. 0:00[Music]
  2. 0:07everyone
  3. 0:07and welcome to the webinar on the topic
  4. 0:09introduction to frame nvh
  5. 0:11i would like to go through the following
  6. 0:13contents in the webinar
  7. 0:15uh which would be a quick revision of
  8. 0:18what we have studied in vibrations in
  9. 0:20our engineering days
  10. 0:21then we look into what is nvh uh what
  11. 0:24are the different areas of nvh and how
  12. 0:26is in which applied to
  13. 0:28a frame then what do we do with respect
  14. 0:31to a frame
  15. 0:31analysis from in which point of view and
  16. 0:34we break it up into different steps
  17. 0:36that is modal analysis frequency
  18. 0:37response functions stiffness and control
  19. 0:40etc and once we are done with that part
  20. 0:43we'll focus on what is the fear approach
  21. 0:45which is used in the industry
  22. 0:47and also we look into certain set of
  23. 0:49tools which are
  24. 0:50which are in demand and which are used
  25. 0:52in the industry for carrying out nvh
  26. 0:54analysis
  27. 0:55and on concluding remarks i would like
  28. 0:58to discuss
  29. 0:59regarding the industry open
  30. 1:00opportunities for students who are fresh
  31. 1:02passouts
  32. 1:03and what roles they would be playing and
  33. 1:05also
  34. 1:06what all industries they can target for
  35. 1:08nvh related roles
  36. 1:10and then that will be followed up by a q
  37. 1:12a session where
  38. 1:13i would like to clear most of your
  39. 1:15doubts related to the image area
  40. 1:18yeah let's start with vibrations
  41. 1:21so all of us have
  42. 1:25have studied vibrations i believe in our
  43. 1:27engineering courses
  44. 1:29and i also understand that it was
  45. 1:30probably one of the most difficult
  46. 1:32subjects to understand
  47. 1:34so let me try to give a small revision
  48. 1:37of vibrations before we go into nvh
  49. 1:39because
  50. 1:40these concepts are very very essential
  51. 1:43in going forward to carry out nvh
  52. 1:45analysis
  53. 1:46so vibration in in the simplest terms
  54. 1:50is nothing but a motion that repeats
  55. 1:52itself
  56. 1:54from time to time or within an interval
  57. 1:56of time
  58. 1:57and its most simplest representation
  59. 2:00would be a sine wave
  60. 2:02and a sine wave when you plot it on the
  61. 2:03x and y axis
  62. 2:05you can you can read it as alternate
  63. 2:08crests and drops
  64. 2:10and that is how a usual vibration system
  65. 2:13is
  66. 2:14visualized in a mechanical engineering
  67. 2:17world
  68. 2:18coming to the layman terms if you see
  69. 2:21around us or if you
  70. 2:22take the human body itself you will be
  71. 2:24surprised to know that
  72. 2:26vibration plays a very vital role in
  73. 2:28most of the
  74. 2:29our day-to-day activities but to name a
  75. 2:32few
  76. 2:33we are able to hear only because of
  77. 2:35vibrations and how is that
  78. 2:37that is because our eardrums vibrate
  79. 2:39whenever there is
  80. 2:40there are sound waves which are going to
  81. 2:41come and impinge on the eardrums
  82. 2:44and the eardrum is going to resonate and
  83. 2:46that is going to send signals to the
  84. 2:47brain
  85. 2:48and that is how our brain perceives
  86. 2:50sound which is going to be
  87. 2:52which is going to affect us then
  88. 2:57even breathing for example if you take
  89. 3:00so it is nothing but
  90. 3:01a compression and relaxation of the
  91. 3:02lungs of the human body
  92. 3:04that will also constitute a type of
  93. 3:06vibration
  94. 3:07and even speaking for that matter is
  95. 3:10also a kind of
  96. 3:12is also an output from the vibration of
  97. 3:14the larynx in the throat
  98. 3:15of the human body so human body itself
  99. 3:19has so many areas where vibrations are
  100. 3:22involved and coming out of the human
  101. 3:25body and if you want to look at the
  102. 3:26surroundings
  103. 3:27you can find vibrations in almost every
  104. 3:29every part or every region of it
  105. 3:32for example there are numerous machines
  106. 3:34which exhibit vibrations
  107. 3:36there are engineering there are
  108. 3:38buildings and structures which undergo
  109. 3:39vibrations
  110. 3:40there are if you take automotive sector
  111. 3:42almost all of the automotive sector
  112. 3:45engines and bodies go undergo vibrations
  113. 3:47so hence vibration
  114. 3:49is a very interesting branch of study
  115. 3:51and it becomes all the more interesting
  116. 3:53when you want to
  117. 3:54analyze a system for a given vibration
  118. 3:57and how is it going to behave
  119. 3:58for a given set of forces what will be
  120. 4:01the response of the system
  121. 4:03so that's that's a very interesting uh
  122. 4:06part of study
  123. 4:07and in order to understand vibrations in
  124. 4:09a better way
  125. 4:10what we had studied in engineering was
  126. 4:12that
  127. 4:13it will get we can divide the vibration
  128. 4:15systems into
  129. 4:16a single degree of freedom system uh 2
  130. 4:18degree of freedom system
  131. 4:19and multiple degree of freedom systems
  132. 4:21and the respective examples for them
  133. 4:23would be spring mass systems
  134. 4:25a double pendulum and a railway bracket
  135. 4:28in other terms if you want to define
  136. 4:30vibration you can actually bring in the
  137. 4:32spring damper analogy spring mass damper
  138. 4:35analogy
  139. 4:36that is each and every system or each
  140. 4:38and every body
  141. 4:40can be subdivided into a spring mass and
  142. 4:42damper
  143. 4:44and by spring mass and damper to speak
  144. 4:46in very simplistic terms
  145. 4:48they are nothing but forms of energies
  146. 4:50where spring will represent the
  147. 4:51potential energy
  148. 4:52mass will represent the kinetic energy
  149. 4:54and damper will represent the
  150. 4:56dissipation energy
  151. 4:57so what happens usually whenever there
  152. 5:00is vibration happening is
  153. 5:02the potential energy and the kinetic
  154. 5:04energy are interchanging themselves
  155. 5:06and the dissipation energy or the damper
  156. 5:08is going to act as
  157. 5:10the as the force of the source which is
  158. 5:12going to reduce the potential in the
  159. 5:14kinetic energy in every cycle
  160. 5:16so if you can take a look at the image
  161. 5:17which is on the right you can see that a
  162. 5:19pendulum is
  163. 5:20continuously clocking across the
  164. 5:22midpoint so if you see here when it is
  165. 5:25at the midpoint
  166. 5:26its potential energy is going to be at
  167. 5:28the highest and the kinetic energy is
  168. 5:29going to be
  169. 5:30zero and let us say if you just strike
  170. 5:33the pendulum once
  171. 5:34then the pendulum is going to start
  172. 5:36clocking itself
  173. 5:37and at the extreme end of it we can say
  174. 5:40that the potential energy is going to be
  175. 5:42zero
  176. 5:42but it is going to have maximum kinetic
  177. 5:44energy and
  178. 5:46that is how the potential and the
  179. 5:47kinetic energies are going to
  180. 5:48interchange themselves
  181. 5:50and help the pendulum to keep on rocking
  182. 5:53and where does damping come here
  183. 5:54so now if this pendulum is allowed to
  184. 5:57freely
  185. 5:59rock on itself rock by itself then it's
  186. 6:02going to come to rest after certain
  187. 6:03point of time
  188. 6:04and that is because of the internal
  189. 6:06friction forces and also because of the
  190. 6:08air which is going to offer resistance
  191. 6:09to the movement of the pendulum
  192. 6:11and that is how damping is perceived in
  193. 6:14nature
  194. 6:16then some terminologies which we learned
  195. 6:19with respect to vibrations where
  196. 6:21natural frequencies then damping
  197. 6:23different equations of motion
  198. 6:25what are the different types of free and
  199. 6:27forced responses so
  200. 6:28all of them are nothing but means to
  201. 6:31characterize the vibration
  202. 6:33vibratory system natural frequencies
  203. 6:36define the characteristic
  204. 6:38moments of the system then damping will
  205. 6:40define
  206. 6:41how good the system is with respect to
  207. 6:43dissipating the vibration energy
  208. 6:45equations of motions were derived to
  209. 6:48simplify the actual vibration vibratory
  210. 6:50system into mathematical models
  211. 6:52and mathematical terminologies and the
  212. 6:54solution of
  213. 6:55those equations of motion will actually
  214. 6:58give you the vibration parameters which
  215. 6:59are needed to solve
  216. 7:01or which are needed to characterize the
  217. 7:04system
  218. 7:05and we have different types of
  219. 7:07vibrations that is
  220. 7:09what are free vibrations what are forced
  221. 7:11vibrations how is the system going to
  222. 7:13behave with a free and a forced
  223. 7:15vibration under a free enforced
  224. 7:17vibrations etc
  225. 7:19and then we also spoke about
  226. 7:21transmissibility
  227. 7:22so whenever there is a vibration set up
  228. 7:26into a system
  229. 7:26there is definitely going to be a force
  230. 7:28involved
  231. 7:30and when the four and when the force
  232. 7:31excites the system
  233. 7:33the system is going to vibrate with some
  234. 7:35energy
  235. 7:36and this energy is going to get
  236. 7:38transmitted to all the connected members
  237. 7:40of the body
  238. 7:41and that is the area of interest which
  239. 7:44engineer would be looking into
  240. 7:46what how much amount of force is getting
  241. 7:48transmitted to another body
  242. 7:50is that force under limits is is however
  243. 7:53how am i going to control that force is
  244. 7:55that force necessary or is it unwanted
  245. 7:58so those were the areas which we have
  246. 8:00studied
  247. 8:01previously in engineering and
  248. 8:04that was a quick brush up of the
  249. 8:07fundamentals of vibrations and also the
  250. 8:08terminologies which are used in
  251. 8:10vibrations
  252. 8:12now let's take a quick look at the
  253. 8:15nvh perspective of the entire whole
  254. 8:18thing of the
  255. 8:18whole thing so what do you mean by nvh
  256. 8:22nvh is an acronym for noise vibration
  257. 8:24and harshness
  258. 8:25and why are they used together let's
  259. 8:28come to that
  260. 8:29so in the previous slide when we spoke
  261. 8:31about a force which is going to induce
  262. 8:33certain
  263. 8:34vibration into a machine what are going
  264. 8:36to be the side effects or what are going
  265. 8:38to be the
  266. 8:39further effects of that forcing function
  267. 8:41which is going to induce vibrations
  268. 8:43in most of the cases that vibration
  269. 8:46which is
  270. 8:47induced into the system is going to
  271. 8:50interact with the surrounding medium and
  272. 8:52it is going to radiate
  273. 8:54energy into the surrounding medium and
  274. 8:56let us say if it is
  275. 8:57air that the energy which is radiated
  276. 9:01into the surrounding medium
  277. 9:02is going to go in forms of pressure
  278. 9:04waves and these pressure waves are
  279. 9:06nothing but what we call it as
  280. 9:08sound waves so vibration is going to
  281. 9:11give rise
  282. 9:12to sound and whatever sound is generated
  283. 9:16if it is going to go beyond a level or
  284. 9:19if it is going to go beyond the limit of
  285. 9:21human ear perception
  286. 9:23then we call it as noise so vibration
  287. 9:26unwanted vibration is going to lead to
  288. 9:28unwanted sound
  289. 9:29which we call it as noise and if the
  290. 9:32unwanted
  291. 9:33vibrations reaches a peak or what we
  292. 9:35call it
  293. 9:36at resonant frequencies then it is the
  294. 9:39sound which or the noise which is
  295. 9:40generated
  296. 9:41is going to be much more irritating and
  297. 9:44unpleasant to the human ears
  298. 9:45and that is what we call it as harshness
  299. 9:48so
  300. 9:49nvh that is noise vibration and rashness
  301. 9:51are all interrelated
  302. 9:53the source being the vibration which is
  303. 9:55in turn going to generate the noise
  304. 9:57and from noise whatever is the level of
  305. 10:00perception of the human ear we can
  306. 10:01classify it as
  307. 10:02harshness so what would our engineer
  308. 10:06typically do when we say nvh engineer
  309. 10:09nvh analyst etc the typical role of an
  310. 10:12engineer
  311. 10:12would be to reduce the vibrations at the
  312. 10:15source
  313. 10:16so that whatever noise is going to
  314. 10:19come into the system that is reduced to
  315. 10:22an extent
  316. 10:23and also in turn that is going to reduce
  317. 10:25the amount of unpleasant
  318. 10:27things which which the user is going to
  319. 10:29experience
  320. 10:30also it can be in the reverse way uh
  321. 10:33sound source can generate structural
  322. 10:34vibrations
  323. 10:36and that can also be very unpleasant and
  324. 10:38that is also another area of study
  325. 10:41wherein an acoustic source is going to
  326. 10:43generate
  327. 10:45a vibration in the structure but since
  328. 10:47we're talking about frame nvh let's
  329. 10:48focus on
  330. 10:50the frame frame itself acting as a
  331. 10:52source as a vibratory source
  332. 10:54and also as a path to transfer different
  333. 10:56forces from
  334. 10:57one part of the car body to another so
  335. 11:01an engineer's duty would be to
  336. 11:03understand how vibrations are generated
  337. 11:05from where the vibrations are going to
  338. 11:07come onto the frame
  339. 11:09and how much of a vibration is too much
  340. 11:13there are certain set of standards which
  341. 11:14the industry uses to
  342. 11:17identify what what level is good and
  343. 11:18what level is bad
  344. 11:20and also how much of sound or noise
  345. 11:23is required inside automotive cabin or
  346. 11:26how much is the desired level for a
  347. 11:28human
  348. 11:29being so if you can see the images here
  349. 11:33the one on the right side that's the
  350. 11:35image of a shaker
  351. 11:37which is uh which is having a forced
  352. 11:38induced vibration
  353. 11:40so if you can uh if you can
  354. 11:44make it analogous to something like a
  355. 11:47cup of water
  356. 11:48so that is how the vibrations are going
  357. 11:49to look if you can
  358. 11:52transfer those vibrations or if you keep
  359. 11:53a glass of water on the shaker and
  360. 11:56that's how the water would vibrate
  361. 11:57so that's the transmissibility which i
  362. 11:59was talking about in the previous slide
  363. 12:01and if you look at the left side here
  364. 12:03there's a small there's a graph which
  365. 12:05has two plots in it
  366. 12:06so the top one would be called as music
  367. 12:10uh because it's it's quite repetitive
  368. 12:12and it's quite smooth
  369. 12:13whereas the one below it would be called
  370. 12:15as noise and that would be our area of
  371. 12:17interest
  372. 12:18when we try to reduce this unwanted
  373. 12:21noise and harshness
  374. 12:22which are going to get generated because
  375. 12:23of the undue vibrations
  376. 12:25in the body yeah so
  377. 12:28uh i would i would like to stick to a
  378. 12:32car body a car model
  379. 12:34whenever we talk about frame in vh but
  380. 12:36you can also extend it to
  381. 12:37different other areas because the
  382. 12:39technical concepts and the
  383. 12:41workload almost remain the same so
  384. 12:45whenever let us say you are sitting in a
  385. 12:46car and whenever you start the car
  386. 12:49so you are going to experience certain
  387. 12:52vibrations for example say add the
  388. 12:55stirring wheel
  389. 12:56on the gear pedal on the clutch pedal on
  390. 12:58the floor of the car
  391. 13:00etc so and also when you start
  392. 13:03when you close off your windows of the
  393. 13:05car and let us say you're cruising at
  394. 13:06around 80 or 100 kilometers per hour
  395. 13:08you are also going to hear some noise
  396. 13:11inside the car cable
  397. 13:12so there can be different sources of
  398. 13:15uh of those vibrations as well as noise
  399. 13:18so
  400. 13:19what can they be they can be it can be a
  401. 13:22road noise which are going to get
  402. 13:23generated because of the
  403. 13:25rolling of the tires on the road and
  404. 13:26then those in turn will be affecting the
  405. 13:28suspension systems and the suspension
  406. 13:29systems will be transferring
  407. 13:31the energies to the frame and the frame
  408. 13:34on which the
  409. 13:36on which the seats of the car are fixed
  410. 13:39so
  411. 13:39there you will be the driver will be
  412. 13:41experiencing the vibrations on the seat
  413. 13:43of the car
  414. 13:44and also the steering system is
  415. 13:46connected to the main body
  416. 13:48so the driver will be experiencing
  417. 13:50certain set of vibrations on the
  418. 13:51steering wheel
  419. 13:52and also the gear similarly with the
  420. 13:54gear pedal and
  421. 13:55the floor of the car and also all of
  422. 13:58this
  423. 13:58in combination will also add to the
  424. 14:01sound which is going to be
  425. 14:02experienced inside the cabin of a car so
  426. 14:06all of this would constitute the
  427. 14:09understanding of noise and vibrations
  428. 14:11inside a car body
  429. 14:12inside a car caving as such and our area
  430. 14:15of interest
  431. 14:16in today's webinar would be to
  432. 14:17understand what we do to reduce the
  433. 14:19vibrations in a frame
  434. 14:21and how do we go about understanding the
  435. 14:24different aspects and parameters of
  436. 14:27analyzing a frame from nvh perspective
  437. 14:32so in the previous slide the image which
  438. 14:34i had shown was quite
  439. 14:36simple and it was for a very layman
  440. 14:38approach
  441. 14:39but for an nvh engineer whenever he we
  442. 14:42speak about nvh
  443. 14:44analysis we have to divide the system
  444. 14:47into different areas or different
  445. 14:48levels and then we need to analyze the
  446. 14:51system and understand the nvh behavior
  447. 14:53so usually an automotive component
  448. 14:57would be divided into different levels
  449. 15:00wherein you
  450. 15:00you can just work on only the dream body
  451. 15:03of the car
  452. 15:04which will have only the frame and the
  453. 15:06body of the car with some other
  454. 15:07components
  455. 15:08or you can start working especially only
  456. 15:10with sub components
  457. 15:12which we usually call it as a component
  458. 15:14level or system level
  459. 15:16wherein you analyze a a simple component
  460. 15:20along with its uh inbound accelerace and
  461. 15:23also system level
  462. 15:25where you define a complete system and
  463. 15:27then you try to figure out what are what
  464. 15:29is the
  465. 15:30for what are the causes of vibrations
  466. 15:32what are the forces which are going
  467. 15:33to come onto the machine and also you
  468. 15:35can have the full vehicle analysis and
  469. 15:37try to understand
  470. 15:38how much of vibrations are going to get
  471. 15:40transferred in a complete vehicle
  472. 15:42and what is the sound level which is
  473. 15:44going to get generated
  474. 15:46inside the cabin of the car so in our
  475. 15:48study now
  476. 15:49we are going to work talk more about the
  477. 15:51system level
  478. 15:52and here the system under consideration
  479. 15:54would be the frame of the car
  480. 15:56which i would say would like we usually
  481. 15:59work with
  482. 16:00three distinct areas whenever we do
  483. 16:03analysis of that
  484. 16:04and that would be divided broadly into a
  485. 16:07modal analysis
  486. 16:08then a forced response analysis which
  487. 16:10involves frequency response functions
  488. 16:12and then the vibration control wire
  489. 16:14stiffness
  490. 16:15different stiffness methods
  491. 16:19let's start looking at each of them in
  492. 16:21detail
  493. 16:23modal analysis so i am sure pretty sure
  494. 16:26that most of you all have heard this
  495. 16:28term moral analysis natural frequencies
  496. 16:31mood shapes
  497. 16:32and blah blah blah so let's quickly see
  498. 16:34what what model analysis
  499. 16:36is how important it is to understand
  500. 16:40the frame nvh and how is it going to
  501. 16:43help the engineer to
  502. 16:45make the frame nvh better so
  503. 16:48modal analysis is a broad area wherein
  504. 16:53we study that we study the component
  505. 16:55behavior or we study the
  506. 16:57behavior of the model under test for its
  507. 16:59modal characteristics
  508. 17:01and by modal characteristics i mean what
  509. 17:03are its natural frequencies
  510. 17:05in a free free state what are its
  511. 17:06natural frequencies in a constrained
  512. 17:08state
  513. 17:09what what what what frequency will it
  514. 17:12resonate
  515. 17:13uh what types of displacements it's
  516. 17:16going to have what types of moments it
  517. 17:17is going
  518. 17:18to have is it a
  519. 17:21lateral mode or is it a torsional mode
  520. 17:23etc so
  521. 17:26when i say natural frequency it's
  522. 17:28nothing but of
  523. 17:29the fundamental frequency of the body at
  524. 17:31which it will
  525. 17:33start vibrating when you when you excite
  526. 17:36it and you leave it
  527. 17:37so for example if you take a guitar a
  528. 17:40string of a guitar
  529. 17:42you pluck the string of the guitar and
  530. 17:44you leave it so the guitar is going to
  531. 17:46vibrate at
  532. 17:47a certain frequency and that frequency
  533. 17:50is known as the fundamental frequency of
  534. 17:52the guitar
  535. 17:53and that is going to remain constant so
  536. 17:56this is very important
  537. 17:57this the fundamental frequency is a
  538. 18:00characteristic
  539. 18:01of the system or characteristics of the
  540. 18:04body
  541. 18:05so it is like young's modulus or
  542. 18:08stiffness so it is not going to change
  543. 18:11unless and until you
  544. 18:12change certain boundary conditions or
  545. 18:15certain constraints
  546. 18:16the natural frequency is going to remain
  547. 18:18the same
  548. 18:19especially in a free free analysis so if
  549. 18:23you can see the image here
  550. 18:24there's a tuning fork which has uh
  551. 18:28for which an uh free free run has been
  552. 18:30uh given
  553. 18:32and it is go uh a customer has been
  554. 18:34given and it is go
  555. 18:35it is showing its small shape so you can
  556. 18:38see that the two prongs
  557. 18:41moving away from each other and that
  558. 18:43this is one of the fundamental
  559. 18:45frequency modes of the tuning fork
  560. 18:48coming to resonance so whenever any body
  561. 18:52is subjected to a forcing
  562. 18:54frequency and the body has a certain set
  563. 18:57of natural frequencies associated with
  564. 18:59it
  565. 18:59and the forcing frequency overlaps or
  566. 19:03matches the fundamental frequency of the
  567. 19:05body
  568. 19:06then the amplitude which is generated
  569. 19:09will be quite high
  570. 19:10and that phenomenon we call it as a
  571. 19:12resonance
  572. 19:13a resonance can be both advantageous and
  573. 19:15disadvantageous
  574. 19:17and with respect to frame and we're
  575. 19:20concepts or with respect to frame in
  576. 19:21which
  577. 19:23analysis i would say we are at a
  578. 19:24disadvantage whenever we talk about
  579. 19:26resonance
  580. 19:27so this is very important to
  581. 19:30understand and we also need to identify
  582. 19:33at what
  583. 19:34forcing functions and or what flow
  584. 19:35forcing frequencies the
  585. 19:37resonance is going to happen next coming
  586. 19:40to mode shape
  587. 19:41mode shape is nothing but the direction
  588. 19:44of displacement of the body
  589. 19:46and which is going to help us understand
  590. 19:48at a particular frequency
  591. 19:51in what direction the body is going to
  592. 19:53displace itself
  593. 19:54and that will really help the engineer
  594. 19:57to
  595. 19:58make corrections to the design and to
  596. 20:01also
  597. 20:03stiffen the body or make the body more
  598. 20:06durable
  599. 20:06so that the frequencies are not excited
  600. 20:09and the
  601. 20:10particular mode shape is not attained
  602. 20:13so the different types of mode shapes
  603. 20:16which are
  604. 20:17the different terminologies being rigid
  605. 20:19modes
  606. 20:20then you have the lateral modes you have
  607. 20:21the torsional modes
  608. 20:23you can have vertical mode there is
  609. 20:25something called as local and global
  610. 20:26modes
  611. 20:28which usually are applied to the whole
  612. 20:30body
  613. 20:31so global modes are the ones where you
  614. 20:34can say 85 to 90 percent of the body
  615. 20:36is having a displacement and local are
  616. 20:39usually where the only one one part of
  617. 20:41the body is going to have
  618. 20:42certain displacements that is which is
  619. 20:45usually observed at higher frequencies
  620. 20:46and
  621. 20:47global modes are of more interest at
  622. 20:49lower frequencies
  623. 20:51the formula for natural frequency
  624. 20:53mathematically would be given by
  625. 20:54omega n is equal to root k by m where
  626. 20:58k would be the stiffness of the body and
  627. 21:00m would be the mass of the body
  628. 21:02and omega n usually denotes the natural
  629. 21:04frequency
  630. 21:05and omega n would be the undamped
  631. 21:09natural frequency of the body so
  632. 21:12let us quickly try to understand uh what
  633. 21:16are these different mode shapes and how
  634. 21:17do they
  635. 21:18help us so if you can see here a plate
  636. 21:21has been subjected to
  637. 21:23a free free analysis model analysis and
  638. 21:26these are the different mode shapes
  639. 21:27which the plate will undergo at
  640. 21:29different
  641. 21:31natural frequencies and each of them if
  642. 21:34you plot each of them those are called
  643. 21:35as modes
  644. 21:36and the more shapes will help the
  645. 21:38engineer to understand the behavior of
  646. 21:40the system
  647. 21:40better so in a practical application let
  648. 21:44us say
  649. 21:44you can consider that if this is the
  650. 21:47frame of the car
  651. 21:48okay and this is the excitation of the
  652. 21:51first mode and let us say it has
  653. 21:53a certain frequency or single digit
  654. 21:55frequency of say
  655. 21:57four or five hertz and
  656. 22:00at this point above it you have you have
  657. 22:03located the
  658. 22:04seat of the driver so
  659. 22:07what does this mean is if the road
  660. 22:10frequency or say even the excitation
  661. 22:12frequency from the
  662. 22:13engines is going to match the frequency
  663. 22:17which is going to
  664. 22:18get transmitted to the frame and it is
  665. 22:21going to be off 5 hertz
  666. 22:23this is the amplitude the amplitude
  667. 22:25would be magnified to a greater extent
  668. 22:28and the person and the model or the body
  669. 22:32which is attached to it that is the seat
  670. 22:33would experience very heavy vibrations
  671. 22:36and that would cause great discomfort to
  672. 22:38the driver
  673. 22:39and this would be then the area of
  674. 22:41interest
  675. 22:42for the engineer to arrest the
  676. 22:44vibrations of this mode
  677. 22:45either move the vibrate either move the
  678. 22:47fundamental frequency to a lower grade
  679. 22:49or a higher
  680. 22:50band and then try to again rerun the
  681. 22:53analysis and see if
  682. 22:54the driver's seat is not is experiencing
  683. 22:57lower or moderate vibrations which are
  684. 22:58under the
  685. 23:00regulated guidelines
  686. 23:04yeah going further let's talk more about
  687. 23:08damping and what is done exactly in a
  688. 23:11eigen value analysis or a modal analysis
  689. 23:14so
  690. 23:15damping is nothing but dissipation of
  691. 23:18energy from a system
  692. 23:19and as discussed in the first slide
  693. 23:21itself it's going to play a
  694. 23:24major role in terms of attenuating the
  695. 23:28amplitude of vibration so if you can
  696. 23:32if you can see the image on the right
  697. 23:33side here
  698. 23:35there are three different dampings which
  699. 23:36are provided so the first one
  700. 23:40has a very light damping the second one
  701. 23:43has
  702. 23:43a critical damping and the third one has
  703. 23:46heavy dumping what do you mean by
  704. 23:48those three terms so if the first one
  705. 23:51by light damping it means that the
  706. 23:53system is free to vibrate
  707. 23:55okay and it is going to come to rest in
  708. 23:58a slow
  709. 23:58and a phased manner and if you can plot
  710. 24:01a graph of it
  711. 24:02this is how the behavior will be and it
  712. 24:04will come slowly to rest
  713. 24:06okay and critical damping is the one
  714. 24:09where
  715. 24:11the vibration will come to rest in the
  716. 24:13minimum or the shortest possible time
  717. 24:15and that is what you can see here that
  718. 24:17the vibration started
  719. 24:19and then it damped out and there is no
  720. 24:21hydration now there is no amplitude
  721. 24:23and the third one is heavily damped
  722. 24:27okay so here the
  723. 24:30rate at which it is going to come to
  724. 24:32zero is going to be very very slow
  725. 24:34so all the three have different set of
  726. 24:37applications in the industry
  727. 24:39uh one of the applications for the or
  728. 24:41the heavy dumping case which i can give
  729. 24:43is the
  730. 24:45the dampers which we use on the doors in
  731. 24:47offices so if you have seen them
  732. 24:49whenever you open the door and you leave
  733. 24:51it so it will come back
  734. 24:54slowly and it will respect to its
  735. 24:55original position and that is one of the
  736. 24:57examples of
  737. 24:59heavily damped system so critically
  738. 25:03damped systems uh
  739. 25:05the example which i can give would be
  740. 25:06those of
  741. 25:08missile systems wherein after the
  742. 25:09missile is shot or after the after the
  743. 25:11gunshot
  744. 25:12the system has to quickly recoil and
  745. 25:14come back to its original position
  746. 25:17otherwise imagine what would happen if
  747. 25:18it keeps on recoiling like this
  748. 25:21the soldiers will never be able to
  749. 25:22reload it back
  750. 25:24so different damping conditions help in
  751. 25:27arresting
  752. 25:28the amplitude of vibration to the
  753. 25:30desired level
  754. 25:31so there are different mathematical
  755. 25:33equations which are formed
  756. 25:35for the damping and how is damping going
  757. 25:38to
  758. 25:39play a role in analysis so what we saw
  759. 25:42in the previous slide was the
  760. 25:44natural frequency omega n and
  761. 25:48that was nothing but is equal to root of
  762. 25:50k by m
  763. 25:52but whenever you talk about damping
  764. 25:54damping is
  765. 25:55going to reduce the natural frequency to
  766. 25:58a certain level and that formula is
  767. 26:00given by
  768. 26:01the last one here the damping frequency
  769. 26:03is going to be
  770. 26:04omega natural frequency multiplied by
  771. 26:06root of 1 minus
  772. 26:07tau of tau square and what is tau tau is
  773. 26:10nothing but
  774. 26:11the damping factor divided by the
  775. 26:12critical damping
  776. 26:14and if you closely observe now critical
  777. 26:16damping is nothing but a function of
  778. 26:17constant multiplied by root of again
  779. 26:20mass
  780. 26:21and spring stiffness so
  781. 26:25they're all interrelated everything is
  782. 26:27going to revolve around
  783. 26:28the mass and stiffness of the body and
  784. 26:32damping as damping is going to play a
  785. 26:35important role
  786. 26:36as per this equation which is provided
  787. 26:39now coming down to eigenvalue analysis
  788. 26:42what what
  789. 26:43are the different types of analysis that
  790. 26:45can be carried out
  791. 26:47here in modal analysis you can carry out
  792. 26:49a free free analysis
  793. 26:51of the body so what do you mean by free
  794. 26:53free analysis here
  795. 26:54in a preview analysis there is no
  796. 26:55forcing function or no force involved
  797. 26:58you are just going to allow the body to
  798. 27:00freely vibrate
  799. 27:01and then you are you are going to figure
  800. 27:04out what are the natural frequencies of
  801. 27:05the system
  802. 27:06and what are the different mode shapes
  803. 27:07which are going to be exhibited by the
  804. 27:09system uh one of the main applications
  805. 27:12of a free free analysis especially in
  806. 27:14assembly setting is to understand
  807. 27:17the model integrity so let us say you
  808. 27:20have number of
  809. 27:21components of automated components
  810. 27:23connected to each other and if you run a
  811. 27:25free free analysis
  812. 27:27you should get six rigid modes for the
  813. 27:29complete
  814. 27:30component or complete body or the
  815. 27:32complete assembly of the vehicle
  816. 27:34if you get more than that it means that
  817. 27:36there is there is some mismatch
  818. 27:38in the way you have connected the
  819. 27:40different components with each other and
  820. 27:42that is going to make your complete
  821. 27:45whole of the analysis
  822. 27:46uh to be invalid so a free free run will
  823. 27:50usually give you
  824. 27:51the the six rigid modes and your seventh
  825. 27:54mode will be
  826. 27:55by rigid modes i mean that the frequency
  827. 27:57will be tending almost standing to zero
  828. 28:00and from the seventh mode onwards you
  829. 28:02will have a positive
  830. 28:03frequency value which will be termed as
  831. 28:04the first fundamental frequency of the
  832. 28:07system under test

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