product resource whitepaper

A 6-DOF Vibration Specification

Multiple degree of freedom (MDOF) excitation systems and MDOF vibration control systems
continue to improve, and are now standard equipment in many dynamic test laboratories. This paper concentrates on the often overlooked process of determination of an input specification for such MDOF (6-DOF) systems.


Two techniques were introduced for consideration in establishing an input specification for a MDOF system. It was shown that simple enveloping techniques are not appropriate when considering CSD terms, due to the sensitivity of such operations associated with maintaining a physically realizable reference. The resulting SDM references yielded through the process outlined are fully populated SDMs. Importing the fully populated SDM into the MDOF control system in an efficient manner is essential due to the volume of information involved.

While synthesizing a drive signal with CSD characteristics of the field data is desired, it is recognized that the mechanical impedance of the laboratory configuration is highly unlikely to match that of the field data. Therefore, it will be difficult to maintain CSD characteristics across the spectral bandwidth of  interest, and thus the control hierarchy will generally place emphasis on the ASD terms. Also, it is not uncommon in MDOF tests for a specific mechanical degree of freedom to consist of a very small percentage of the composite energy across all mechanical degrees of freedom. In such cases, the associated error for the low DOF will often be higher than the desired test tolerances, and it may be necessary to consider global test tolerances.

Care was taken in the examples provided to limit conservatism in the VSD process. Conservatism is cumulative across degrees of freedom and, if not managed carefully, will yield test levels significantly higher than the measured environment. Unlike the common technique of essentially adding 3dB to all measurements prior to conducting averaging or enveloping techniques in the 1-DOF arena per reference 7, all weighted averages in the 6-DOF examples shown were based on raw averaged data. Conservatism to account for variables such as fleet variability and mission scenario omissions were added in the final step.

Magnitude amplification associated with time compression techniques was limited to no more than maximum measured levels. Also, on the subject of tolerances, one may find it reasonable to define phase and coherence tolerances over only a portion of the test bandwidth. In the example provided, the coherence dropped off considerably at frequencies above 50 Hz. Since the phase term is essentially a random variable for low coherence, setting tolerances for frequencies greater than 50 Hz would not be recommended for the example shown.


1. Smallwood, D.O. 2008. A Proposed Method to Generate a Spectral Density Matrix for a MIMO Vibration Test. Proceedings of the 81st Shock & Vibration Symposium, Orlando, Florida, USA.

2. Methodology Study, Final Report of MIMO Vibration Specification Guidance. 2010. DTC/RTC Methodology Study, March 2010.

3. Hale, Michael and Marcos A.Underwood. 2008. MIMO Testing Methodologies. Proceedings of the 79th Shock & Vibration Symposium, Orlando, Florida, USA.

4. Fitz-Coy, N., Hale, M, and V. Nagabhushan. 2010. Benefits and Challenges of Over-Actuated Excitation Systems. Shock and Vibration Journal 17 (3).

5. Underwood, M. and T. Keller. 2006. Applying Coordinate Transformations to Multi-DOF Shaker Control. Sound and Vibration (January) 22-27.

6. Nobel, Ben and James W. Daniel. 1988. Applied Linear Algebra. Third Ed. Englewood Cliffs, NJ: Prentice-Hall.

7. NATO Allied Environmental Engineering and Test Publication (AECTP) 200, Leaflet 2410, June 2009.

8. Test Operations Procedure (TOP) 1-2-602. 2011. Laboratory Vibration Test Schedule Development for Multi-Exciter Applications, August 2011.

9. Underwood, Marcos A. 2002. Multi-Exciter Testing Applications: Theory and Practice. Proceedings of the Environmental Sciences and Technology, ESTECH2002, May 1, 2002, Anaheim, CA.

10. Conversation with Dr. Marcos Underwood, January 2011. 


Sales Administration

Tarin was born and raised in Wisconsin, graduated from the University of Wisconsin-Stout and received a Bachelor of Science degree in Business Administration. Prior to Vic Myers she worked in the hospitality industry 20+ years as a Sales Analyst/Administrator.

In her spare time, Tarin enjoys spending time with her family, traveling to historical sites throughout the United States, reading, going to movies and concerts. On the weekends you will find Tarin at her nephews’ band concerts and baseball games. In addition, music and dance have been a part of her life with musical contrasting influences ranging from Prince to Olivia Newton-John.  Tarin is located in our Arizona office.


Sales Engineer

Richard was born and raised in Arizona. Attended Arizona State University with a focus in Mechanical Engineering and then fell into Technical Project Management. After 12 years of managing large budget projects spanning system integrations and upgrades, he transitioned into the role of Field Sales Engineer with VMA.

Richard has a deep passion for building relationships with his clients and principals, and supporting them to problem solve and develop innovative solutions. Outside of the office, Richard can be found volunteering as a mentor and coach of high school students at his church, running and hiking the extensive trails of Arizona, and spending time with his wife, 2 boys, 2 girls, and 2 grandkids. Richard is located in our Arizona office.


Field Sales Engineer

Taylor is a Texas native, and grew up in the small town of Boerne, Texas.  He attended Texas A&M University, where earned his bachelor’s degree in Engineering.  After college he was recruited by a Manufacturer’s Rep Firm, where he spent the first 7 years of his career. Initially hired on as an inside salesperson, Taylor quickly accelerated within the organization and expanded into various other roles such as Distribution Manager, and Field Sales Engineer.  Taylor then spent the following 7 years working for an electronic component distributor named Electro Enterprises that almost exclusively supported the mil/aero market.

Taylor worked as a Field Sales Engineer supporting the Texas, Utah and New Mexico territory, Product Manager, as well as Director or Business Development where he managed a team of 10 Field Sales Professionals across the entire United States.  Gathering from his previous experiences, Taylor has now taken on the role of Field Sales Engineer with Vic Myers supporting the Texas, Oklahoma, Louisiana, and Arkansas territory.  Outside of the office you will usually find Taylor either spending time with his wife and two young children, or out on the lake bass fishing.


Field Sales Engineer

Felecia Stivers, a native of Rockford, IL, now excels as a Field Sales Engineer at VMA in our Arizona office. Holding a BSEE from Arizona State University, she draws from her extensive background at Medtronic, Orbital Sciences, General Dynamics, and Northrop Grumman.

Specializing in high-reliability applications, Felecia stands out for her proficiency in relationship-building and innovative problem-solving. Whether contributing to medical devices or playing a vital role in rocket launches, her work has had a tangible impact on saving lives and safeguarding the nation.

Beyond her professional pursuits, Felecia enjoys time with her two teenagers, finds joy in travel, and actively engages with her local church. Driven by a passion for helping customers navigate cutting-edge technology, she is committed to delivering dependable solutions in fast-changing environments.


People and Culture Specialist

Karen has been a part of Vic Myers Associates team since February 2023. Prior to her position as People and Culture Specialist, she worked in the Science & Technology field as an HR Manager & Project Lead for SAIC and LANL. In the short time with VMA she has learned a lot and looks forward to knowing our business even better in support of all of our employees. She values her church community, her two sons who happen to be engineers, volunteering, and golf. Karen is located in our Albuquerque, NM office.


Natalie Myers

Inside Sales Administration

Natalie Myers joined Vic Myers Associates in September 2021 and is excited to be part of the team. She received her bachelor’s in business administration from the University of Phoenix and prior to her position as Inside Sales Administration she worked in the Hospitality Industry for over 15 years as a Senior Sales Administrator. In her free time, she enjoys spending time with her husband, daughter, family and friends along with watching sporting events, traveling, hiking and cheering on her daughter in dance and basketball! Natalie is located in our Arizona office.


Can’t find what you’re looking for?