## MEC E 451 Vibrations **Subject & Number:** MEC E 451 **Title:** Vibrations and Sound **Course Career** **Units**: 2 **Approved Hours:** 3-0-1 **Fee index:** 8 **Faculty:** [Faculty of Engineering]{.mark} **Department:** Mechanical Engineering **Typically Offered:** either term or Spring/Summer ### Calendar Description Free and forced vibration of single degree of freedom systems with and without damping, vibration isolation, free vibration of multi degrees of freedom systems, vibration absorption, beam vibrations, sound waves, sound sources, subjective aspects of noise. Prerequisites: MEC E 250 and. ### Course Objectives & General Content MAJOR TOPICS: Free and forced vibration of single degree of freedom systems with and without damping, vibration isolation, free vibration of multi degree of freedom systems,, beam vibrations, ### Learning outcomes 1. Determine equations of motion for single degree of freedom vibrating systems using Newton\'s laws, energy methods or other techniques 2. Determine the transient and steady state response of single degree of freedom vibrating systems 3. Determine equations of motion, natural frequencies and mode shapes for multiple degree of freedom vibrating systems 4. Determine equations of motion, natural frequencies and mode shapes for continuous beams 5. basic concepts in acoustics including sound propagation, sound pressure and power levels and the role of psychoacoustics ### Textbooks and References Course notes are provided as pdf [Recommended:]{.underline} Mechanical Vibrations: SI edition by Singiresu Rao is recommended ### Assessment Details +-------------------+----------------------+---------------------+--------------+ | > **Activity** | > **(A)Synchronous** | > **Due/Scheduled** | > **Weight** | +-------------------+----------------------+---------------------+--------------+ | > Assignments | | > Friday evenings | > 30% | | | | > 11:59 PM on | | | | | > eClass after | | | | | > assigned | | +-------------------+----------------------+---------------------+--------------+ | > Labs | > Synchronous | | > 20% | +-------------------+----------------------+---------------------+--------------+ | > Final exam | > Synchronous | > As per beartracks | > 50% | +===================+======================+=====================+==============+ ### Course Accreditation Units The current total and individual Accreditation Unit (AU) counts for this course are: ------------------------------------------------------------- Total Math NS ES ED CS ------------- ------------- ------- ---------- ------- ------ 44.1 44.1 ------------------------------------------------------------- ### ### Course Graduate Attributes The Graduate Attributes (GAs) developed in this course are: ------------------------------------------------------------ \# Graduate Attribute Level (I, D, A) ----- ------------------------------------------ ----------- 1 A knowledge base for engineering (KB): A 2 Problem analysis (PA): D 3 Investigation (IN): 4 Design (DE): 5 Use of engineering tools (ET): 6 Individual and team work (TW): 7 Communication skills (CS): 8 Professionalism (PR): 9 Impact of engineering on society and the environment (IS): 10 Ethics and equity (EE): 11 Economics and project management (EP): 12 Life-long learning (LL): ------------------------------------------------------------ ### Course Schedule +-------------+------+------------------------------------------------+ | > September | > 6 | > Introduction | +-------------+------+------------------------------------------------+ | > September | > 8 | > Undamped SDOF system‐standard form of | | | | > equation of motion (FBD focus) | +-------------+------+------------------------------------------------+ | > September | > 9 | > Undamped SDOF system‐standard form of | | | | > equation of motion | +-------------+------+------------------------------------------------+ | > September | > 11 | > Undamped SDOF system -- free vibrations | +-------------+------+------------------------------------------------+ | > September | > 13 | > Undamped SDOF system -- energy methods | +-------------+------+------------------------------------------------+ | > September | > 15 | > Undamped SDOF system -- measurement from | | | | > equilibrium, effective mass/stiffness | +-------------+------+------------------------------------------------+ | > September | > 18 | > Damped SDOF systems ‐ underdamped | +-------------+------+------------------------------------------------+ | > September | > 20 | > Damped SDOF systems -- critically damped and | | | | > overdamped | +-------------+------+------------------------------------------------+ | > September | > 22 | > Undamped SDOF forced vibrations ‐ frequency | | | | > response, resonanace | +-------------+------+------------------------------------------------+ | > September | > 25 | > Undamped SDOF forced vibrations ‐ base | | | | > excitation | +-------------+------+------------------------------------------------+ | > September | > 27 | > Undamped SDOF forced vibrations ‐ | | | | > Transmission ratio, Force transmissibility | +-------------+------+------------------------------------------------+ | > September | > 29 | > Damped SDOF forced vibrations ‐ damped | | | | > spring‐mass system, graphic representation | +-------------+------+------------------------------------------------+ | > October | > 2 | > Damped SDOF forced vibrations ‐ | | | | > Transmissibility in damped systems, rotating | | | | > imbalance, base excitation | +-------------+------+------------------------------------------------+ | > October | > 4 | > Damped SDOF forced vibrations ‐ relative | | | | > motion between base and system, | | | | > accelerometers, seimometers | +-------------+------+------------------------------------------------+ | > October | > 6 | > Non‐harmonic forcing functions ‐ Fourier | | | | > Analysis | +-------------+------+------------------------------------------------+ | > October | > 9 | > **THANKSGIVING** | +-------------+------+------------------------------------------------+ | > October | > 11 | > Non‐harmonic forcing functions, **review of | | | | > material to date** | +-------------+------+------------------------------------------------+ | > October | > 13 | > Transient vibrations ‐ response to a step | | | | > input, impulse response, other functions | +-------------+------+------------------------------------------------+ | > October | > 16 | > Transient vibrations ‐ convolution | +-------------+------+------------------------------------------------+ | > October | > 18 | > MDOF systems -- equations of motion, matrix | | | | > form | +-------------+------+------------------------------------------------+ | > October | > 20 | > MDOF systems -- mode shapes | +-------------+------+------------------------------------------------+ | > October | > 23 | > MDOF systems -- coordinates and coupling | +-------------+------+------------------------------------------------+ | > October | > 25 | > MDOF systems -- coordinates and coupling, | | | | > semi‐definite systems | +-------------+------+------------------------------------------------+ | > October | > 27 | > MDOF systems -- influence coefficients | +-------------+------+------------------------------------------------+ | > October | > 30 | > MDOF systems -- Eigenvalue problem, forced | | | | > vibration of MDOF systems, vibration | | | | > absorbers | +-------------+------+------------------------------------------------+ | > October | > 1 | > MDOF systems -- forced vibration of MDOF | | | | > systems, vibration absorbers | +-------------+------+------------------------------------------------+ | > November | > 3 | > Approximate methods for MDOF systems, | | | | > Kinetic and potential energies | +-------------+------+------------------------------------------------+ | > November | > 6 | > Approximate methods for MDOF systems, | | | | > Rayleigh\'s Quotient | +-------------+------+------------------------------------------------+ | > November | > 8 | > Approximate methods for MDOF systems ‐ | | | | > Dunkerley\'s formulas for highest and lowest | | | | > natural frequencies | +-------------+------+------------------------------------------------+ | > November | > 10 | > Continuous systems ‐ equations of motions of | | | | > a cable, solution to equations of motion, | | | | > axial vibration of a bar | +-------------+------+------------------------------------------------+ | > November | > 13 | > **READING WEEK** | +-------------+------+------------------------------------------------+ | > November | > 15 | > **READING WEEK** | +-------------+------+------------------------------------------------+ | > November | > 17 | > **READING WEEK** | +-------------+------+------------------------------------------------+ | > November | > 20 | > Continuous systems ‐ axial vibration of a | | | | > bar | +-------------+------+------------------------------------------------+ | > November | > 22 | > Continuous systems ‐ lateral vibrations of | | | | > beams | +-------------+------+------------------------------------------------+ | > November | > 24 | > Approximate methods for continuous systems | | | | > ‐potential and kinetic energy in lateral | | | | > vibration of beams | +-------------+------+------------------------------------------------+ | > November | > 27 | > Approximate methods for continuous systems ‐ | | | | > Rayleigh quotient and extention for beams | +-------------+------+------------------------------------------------+ | > December | > 29 | > Sound and Acoustics ‐ sound propagation, | | | | > frequency and wavelength, RMS pressure, | | | | > superposition | +-------------+------+------------------------------------------------+ | > December | > 1 | > Sound and Acoustics ‐ Sound pressure levels, | | | | > multiple sources, sound power leve | +-------------+------+------------------------------------------------+ | > December | > 4 | > Sound and Acoustics ‐ Frequency analysis, | | | | > psychoacoustics, fluctuating noise levels | | | | > and equivalent | +-------------+------+------------------------------------------------+ | > December | > 6 | > **REVIEW** | +-------------+------+------------------------------------------------+ | > December | > 8 | > **REVIEW** | +=============+======+================================================+ +----------------------------------------------------+--------------+ | **Lab Topic** | **Date** | +----------------------------------------------------+--------------+ | > Lab 1: Laboratory equipment overview and dample | > 2023-09-26 | | > free SDOF | | +----------------------------------------------------+--------------+ | > Lab 2: Forced Damped SDOF Vibration | > 2023-10-10 | +----------------------------------------------------+--------------+ | > Lab 3: MDOF Systems | > 2023-10-24 | +----------------------------------------------------+--------------+ | > Lab 4: Continuous Systems | > 2023-11-28 | +====================================================+==============+ ###