**Applications** Random vibration and shock are important in most engineering applications where the product is exposed to vibration and shock during transport and service. The need to understand the effects of vibration and shock on product reliability is paramount today where electronic/computer components are part of almost every product.

**For Whom Intended** Many engineers need specialized education to properly understand this generally unfamiliar environment and to reproduce it in environmental test laboratories. This course is for design engineers and project managers. It also helps quality and reliability specialists. It is designed to serve the needs of personnel in a wide range of industries where equipment problems may be encountered during the shipment and use of their product.

The instructor maintains good balance between theory and practical applications. Project personnel, structural and packaging engineers learn how to take the effects of vibration and shock into account in the design process.

**Brief Course Description** The course commences with an introduction to vibration and then covers basic dynamics theory including relationships between displacement, velocity and acceleration. Dunkerley's and Rayleigh's methods are introduced, with examples. Damping, transmissibility ratio and resonance stacking are addressed. The course then covers basic structural theory: tension, compression, stress, strain, torsion and moments of inertia. Examples show the torsional shape factors of different structures. The instructor then addresses frequency and stiffness of beams, plates and gussets, providing useful graphs, formulas and examples.

Modal analysis is then discussed, with mention of multi-degree-of-freedom systems, modes and complex systems. Measurement and fixturing for modal analysis and testing are covered before moving on to a brief discussion of random vibration, including power spectral density theory. The concept of RMS acceleration is discussed. Mechanical shock and its design implications are then discussed. Methods of isolating assemblies from shock and vibration are covered.

Fatigue is covered, including discussion of crackgrowth rates, fracture mechanics, the SN curve, and the use and abuse of accelerated testing, including Miner's hypothesis.

Material selection is then covered, with information on overall and design-limiting material properties. Tools are provided for comparing different materials. The course concludes with chassis analysis and general design suggestions, such as methods for increasing natural frequencies.

**Prerequisites** Prior participation in TTi’s Fundamentals of Vibration or the equivalent would be helpful. Participants will need first-year college mathematics (or equivalent experience) and some facility with fundamental engineering computations. Some familiarity with electrical and mechanical measurements will be helpful. Supervisors are invited to telephone or write to TTi on prospective attendees' backgrounds and needs.

**Diploma Programs** This course is a required course for TTi’s Electronic Design Specialist (EDS) and Mechanical Design Specialist (MDS) Diploma Program and may be used as an optional course for any other TTi Specialist Diploma Program.

**Related Courses** This course is equivalent to the mechanical design portion of Course 157-5, Vibration and Shock Test Fixture Design, which runs concurrently.

**Text** Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks are available for an additional fee.

**Course Hours, Certificate and CEUs** Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.

**Internet Complete Course** 310 features over 17 hours of video as well as more in-depth reading material. All chapters of course 310 are also available as OnDemand Internet Short Topics. See the course outline below for details.

Click for a printable course outline (pdf).

- Laws of Motion
- Weight vs. Mass
- Gravity
- Density
- Force, Mass and Acceleration
- Degrees of Freedom
- Displacement
- Velocity
- Acceleration
- Natural Frequency
- Sinusoidal Waveform
- Modeling Complex (MDoF) Systems
- Dunkerley's and Rayleigh's Methods
- Transmissibility
- Isolation
- Damping
- Examples

- Material Properties
- Tension and Compression
- Stress and Strain
- Shear
- Torque
- Moments of inertia
- Torsional Stiffness
- Torsional Shape Factors
- Bending Stiffness
- Instability of beams and flanges

- Natural frequency and stiffness graphs for various structures
- Beam Formulas
- Plate frequency parameters, examples
- Column Resonance
- Axial Resonance
- Example: Stresses in a Loaded Beam

- Preload
- Data on Bolts
- Design of Bolted Joints
- Stiffness Data
- Required flange material area
- Material thickness, stiffness

- Applications
- Modes, Natural Frequencies
- Fixturing for Impedance and Modal Testing
- Finite Element Analysis (FEA)
- Example

- Demonstrations-Sinusoidal Vibration, Complex Waveform, Random Vibration
- Probability Density
- Power Spectral Density (PSD)
- Shaker Power Spectral Density Response
- Equalization
- Calculating the RMS Acceleration from Spectral Plot

- Causes of Shock, Effects and Remedies of Shock
- Transient or Shock Tests
- Shock Pulse shapes, Shock Isolation Example

- Fatigue-Crack-Growth Rate
- How Materials Behave: The S-N Curve
- Factors Influencing Fatigue Behavior
- Stress Concentration
- Photoelasticity
- Fracture Mechanics
- Fracture Toughness of Some Common Materials
- Crack Propagation
- Crack Growth Rate
- Example of a Fracture Surface
- Fracture Surfaces

- Forensics
- Failure Models
- Failure Mechanism
- Time-Dependent Failures
- First Passage Model (Time to Failure)

- The Goodman Diagram
- The Constant Life Diagram
- Exceeding a Critical Stress During Random Vibration
- Inverse Power Law Model - Time to Failure
- Fatigue Damage Model Based Upon S-N Curve - Number of Cycles to Failure
- Idealized S-N Curve for Structural Materials

- Fatigue Damage Model Based on Crack Growth Rate
- Crack Growth Rate vs. Stress Intensity Factor
- Stress Intensity Factors

- Miner's Hypothesis for Fatigue Damage Accumulation
- Miner's "Rule" Cautions
- Determination of Effective Excitation
- Fatigue, Miner’s Rule Example

- Typical Endurance Limits
- "S-N" Curve from Fatigue Testing
- Fatigue Case Study
- Example: Rating a Printed Circuit Board

- Overall & Design-Limiting Material Properties
- Application-Specific Material Properties
- Example: Optimization of Shaker Table

- Chassis Dynamics, Section Properties
- Increasing Resonant Frequency, Torsion
- Rotational Inertia