Vibration Consultants


Our dedicated team of experienced engineers provide noise and vibration consulting services nationally and worldwide. Our vibration consulting services commonly involve vibration testing, monitoring, and analysis, and culminates in a report summarizing our findings with recommendations, clear explanations, and practical solutions. 

Our Vibration Consulting Services include:

  • Vibration Testing Services, both on-site and in our lab, experimental design, instrumentation selection and installation.

  • Vibration Analysis Services, we use our decades of experience and analysis techniques to bring the key elements of the puzzle into view so that problems can be understood and practical solution options compared.  We work with facility and system design teams, to address sources, sensitive tools and facilities, to minimize the risk that the vibration criteria will be exceeded.  This work often involves providing Finite Element Analysis Services to model the anticipated vibration response performance of the system or the facility to expected disturbances.

  • Experimental Design and Vibration Testing Implementation, including selection and use of vibration equipment and instrumentation selection, spectral analysis and digital signal processing techniques, data interpretation, and development of problem solutions and recommendations.

  • Modal Testing and Resonance Testing Services, to gain understanding the system dynamics needed to diagnose and fix challenging problems.

  • System and Facility Vibration Monitoring Services, involving characterization in the time and frequency domain, with multiple measurement types, with trends though time, for system or facility disturbance.

  • Noise and Vibration Control Services, including source identification testing and associated design of isolation systems and mitigation measures to control excessive vibration.

Photo links below provide specific information by topic

​Our extensive Client list showcases our extensive experience in successfully addressing a diverse range of vibration issues for a wide range of industries.

Our Team Of Vibration Consultants is extremely experienced and is headed up by:

  • Reuben Hale, P.E., our resident, founded Response Dynamics over 35 years ago.  Reuben also loves the outdoors, and kayaks over 100 times a year, most frequently in the San Francisco Bay. 

  • Henry Bittner, MSME, our VP of Engineering, has been a key part of our company for more than 26 of these years.  When Henry gets a chance, he loves family time at the beach as well as camping, surfing and hang-gliding.  

  • Susan Reno, MSE, Senior Engineer, has been a key part of our Engineering Team for more than 12 years.  Among her favorite free-time enjoyments are crafting activities and playing board games.

  • Campbell Dixon, BSME, is a comparatively new member of our team, providing brilliant insights and great energy in our work place, working on his treadmill-mounted computer system, after riding miles up into the Oakland hills to our offices (on his 2-speed unicycle!), and frequently spends his lunch hours at the climbing gym.

We love what we do, and are at the very top of our unique field.

Company Background

Response Dynamics was founded in 1984, by Reuben Hale P.E., and is now in our 36th year of providing vibration consulting services, and acoustic consulting services, on all related issues associated with the design, development, and testing of critical systems and facilities.

Response Dynamics consults extensively, as a part of the R&D teams, on the design and development of hundreds of critically sensitive systems.  Critically sensitive systems that we have helped develop include:

scanning electron (SEM) microscopes (SEM), telescopes, MRImagnetic resonance imaging (MRI) systems, optical inspection systems, confocal microscopes systems, chromatographic analyzers, atomic force microscopes (AFM), genomic sequencers, biomedical fluorescent array analyzers, optical interferometers, ion mills, nuclear magnetic resonance (NMR) spectrometers, stylus profilometers, film thickness analyzers, tunneling electron microscopes, critical dimension measurement systems, defect optical detection systems, industrial turbines, power generation steam turbines, industrial fans blowers, motors, paper mill rollers, and industrial conveyors (for food and minerals).   

Often it is necessary for us to quickly develop an understanding of vibration problems and implement solutions so that our client companies can begin shipping their multi-million dollar systems (such as electron microscopes, etc.).  For example, in order to meet the stringent performance requirements for inspection interferometers, we developed a revolutionary method for restraining vibration of their optical components (and was awarded U.S. Patent # 5,822,136.) 

Upon completion of a critical system’s design and fabrication we perform testing to quantify the system’s sensitivity to external environmental disturbance of vibration and acoustic noise.  This testing provides the essential basis for the creation of the system’s specification of allowable facility floor vibration and acoustic noise.

Response Dynamics also provides vibration consulting services extensively for the end users of sensitive equipment and industrial systems, ranging from semiconductor production facilities to academic and commercial research laboratories, to commercial power plants running steam turbines, to mineral processing facilities, running large vibratory conveyors, etc..  We consult on existing facilities as well as on the design of new facilities to address issues associated with providing the necessary environment (with appropriate levels of floor vibration and acoustic noise and stray magnetic fields) required for optimal performance of their sensitive equipment, 

For example, work we have performed related to the design and/or performance of new or existing critical facilities includes:

  • Hitachi Global Storage Technologies –Advanced Materials Research Lab - We were hired by Hitachi’s A/E to take the lead role in addressing new facility design issues associated with minimizing floor vibration, acoustic noise and stray magnetic fields, all of which can disturb sensitive equipment such as electron microscopes, etc.  We worked with the team to address floor foundation issues, in order to mitigate vibration disturbance. We specified wall, ceiling, door design and HVAC details, as well as wiring details, in order to meet stringent acoustic and EMF specifications. We made on site visits to verify that the often subtle (yet very important) construction details were being implemented effectively.

  • University of California Irvine –Stem Cell Research Facility – We addressed floor design issues as a vibration consultant to the UCI design team.  This work involved the direct measurement and analysis of footfall forces associated with walking. We then performed finite element analyses (FEA) in which these footfall forces were analytically applied to numerous alternative designs of floor systems.  Using this approach, we were able to design a floor system that meets the project requirements without excessive over-design.

  • Kaiser Hospital – New Hospital Facility with Microsurgery Operating Rooms – We performed monitoring of floor vibration in response to footfall and to HVAC systems operation, we provided recommendations of vibration isolation mounting of HVAC systems, and we performed modal analysis testing of the floor system (testing that measures resonant frequencies and mode shapes), to assure that the new operating rooms would meet their stringent demands.  

  • Pharmaceutical Manufacturer – performed vibration monitoring of baseline pre-construction vibration levels and provided ongoing vibration monitoring (with email/phone notification of alarm conditions) during building seismic retrofit construction.


For both new and existing facilities, Response Dynamics identifies and recommends mitigation measures for unavoidable internal disturbances such as HVAC equipment, specialized manufacturing systems (with significant moving masses), footfall and external sources such as heavy construction or vehicle/train traffic in the vicinity of the facility.  This often involves computer modeling of various mitigation alternatives to aid in the development of the preferred solution. 

Response Dynamics performs site evaluation measurements of vibration, acoustic noise and stray magnetic fields (we have measured many hundreds of sites and evaluated in the U.S. and internationally), including on-site testing for new and existing critical equipment.  The site evaluation measurements involve making floor vibration, stray magnetic field and acoustic noise measurements to determine whether the proposed locations are suitable for adequate operation of critical equipment.  If a facility is found to have excessive floor vibration, acoustic noise, or stray magnetic field, then we work closely with the facility owners to identify the most cost-effective solution.  The solution may involve reduction/isolation of the disturbance source, active cancellation of the disturbance at the sensitive tool, modification of the floor system, or tool improvement (such as with custom designed tuned mass dampers, etc.), or tool relocation.

Additionally, under contract with SEMATECH (consortium of Semiconductor Manufacturers) we developed a state-of-the-art facility vibration and magnetic field monitoring system that performs simultaneous continuous 24/7 monitoring and analysis of dozens of locations, and performs spectral analysis of the measured signals and continually compares the vibration and magnetic field amplitudes measured at each frequency with the allowable values for each sensitive tool at each frequency.  Since then Response Dynamics has continued developing improvements to the VMS1 system to meet the evolving needs of high-tech facilities monitoring.  


Vibration Sensors:

In our vibration consulting work we use a wide variety of sensors to meet the requirements of each project.  Vibration can be measured using either an absolute inertial reference frame or can be measured relative to another location.  However, different sensors are used.  

  • Sensors used to measure absolute vibration include accelerometers (based on piezoelectric and MEMS technologies) and geophone velocity sensors (which generate signals from a suspended coil moving in a fixed magnetic field)

  • Sensors used to measure vibration relative displacement (gap) are based on a variety of non-contact sensor technologies, and include eddy current proximeters, capacitive gages, and optical / laser sensors


Vibration Measurement and Analysis Units

Vibration is defined as an oscillation of a solid (or fluid).  A given oscillatory motion results in vibratory displacements, velocities and accelerations.  These parameters are mathematically interrelated (via differentiation or integration) and can each describe the same vibratory motion.  They have different units as follows:  

  • Vibration displacements are typically expressed in units of nanometers, microns, millimeters or meters, or micro-inch, mils, or inches

  • Vibration velocities are typically expressed in units of microns/second, millimeters/sec or meters/sec, or micro-inch/sec, or inches/sec

  • Vibration accelerations are typically expressed in units of micro-g or g, or meters/sec^2, or inches/sec^2.  Note 1 g = 9.81 m/sec^2 or 386.4 inch/sec^2


Vibration Time Records and Corresponding Frequency Spectra

Vibration can be described based on the motion versus time (vibration time record, commonly plotted with a horizontal axis of seconds) or the same vibration may be described based on its amplitudes of the vibration at each frequency (vibration frequency spectrum, commonly plotted with a horizontal axis of Hz, or cycles/sec, or RPM, rotations per minute).  Intuitively, one can think of a frequency spectrum as the “recipe” which tells us the amplitudes and frequencies of each of the simultaneous sine waves that must be added together to create a given time waveform.

On a recent vibration consulting project, we provided in-depth vibration monitoring services and vibration analysis services for a site being evaluated for potential construction of a highly vibration-sensitive research facility.  We continuously monitored the vibration from more than 60 sensors at selected locations around the site (some located indoors, others outdoors and other underwater at the bottom of drill holes). We monitored the vibration continuously for a 1 month period using our Response Dynamics VMS1 Vibration Monitoring Systems.  Example data from this project can be used to explain fundamental aspects of vibration monitoring data analysis and interpretation and the associated terminology.   

The following 3 plots all show a single 4 second “snapshot” of the ground vibration caused by a distant train.  The same vibration data is presented in the 3 different formats most commonly used to present vibration data, as follows: 

  • Vibration Time Record: The 1st plot is the raw plot of vibration velocity versus time, with the horizontal time axis going from 0 to 4 seconds.  This time record shows classic “beating” (a modulated sine waveform) that results when there are 2 sinewaves at closely spaced oscillation frequencies.  You can see that there are about 4 peaks per second and you can see that the overall amplitude modulates from high to low to high, about once every second.  

  • Vibration Spectrum, in Narrowband (or FFT) Format: The 2nd plot is the corresponding vibration spectrum that was computed from this same 4 second time record, with a horizontal frequency axis which goes from 0 to 100 Hz.  This FFT spectrum shows that the vibration is dominated by 2 closely spaced spectral peaks, at about 3.5 Hz and 4.5 Hz, which results in the beating observed in the time record plot.  Note that FFT spectra contain amplitude information for a linearly spaced set of frequencies (in this example spaced every 0.25 Hz from 0 Hz to 100 Hz). 

  • Vibration Spectrum, in 1/3 Octave Band Format: The 3rd plot is the corresponding vibration spectrum presented in 1/3 octave band format that was computed from this same 4 second time record, with a logarithmic horizontal frequency axis which goes from 1 to 100 Hz.  The term “octave” simply means a factor of 2 in frequency, and is commonly used in music. For example, the piano’s A4 key, at 440 cycles per second (= 440 Hz), is at twice the frequency (an octave higher) than the A3 key (at 220 Hz).  Thus, there are three 1/3 octave bands per octave, resulting in 1/3 octave bands that are centered at about 1, 1.25, 1.6, 2, 2.5, 3.1, 4, 5, 6.25, 8, 10, 12.5, 16, 25, 31.5, 40, 50, 63, 80, 100 Hz, etc.  Note that the frequency of every 3rd band is 2X higher in frequency (e.g., 2.5, 5, 10, 20, 40, and 80 Hz each differ by 2X).  This also means that the 20 Hz band is twice as wide as the 10 Hz band, due to this logarithmic spacing.

The vertical axis of spectra can be displayed in linear or logarithmic or dB formats.  The vibration amplitudes (shown on the vertical axis of time records and frequency spectra) can be expressed in terms of peak amplitude (or peak-to-peak) or rms amplitude (root-mean-squared).  For a sine wave the peak amplitude is about 1.4X the rms amplitude.  

Using the VMS1’s trend analysis capabilities we were able to post-process the data (using our digital signal processing algorithms) to get a handle on the vibration levels that occurred at each location on the site during the entire duration of the train passing.  A trend of the overall rms vibration velocity levels measured during a 10 minute period at a selected location is presented in the next plot. You can see that the horizontal axis is time of day for the 10 minute period, and that the total duration of significantly elevated vibration levels caused by the train passing was about 4 to 5 minutes.  With the highest vibration intensity measured just before 10:04. The prior 3 plots show the data for this 4 second time period with the highest vibration intensity that occurred just before 10:04.

Types of Vibration Time Waveforms and Their Corresponding Vibration Spectra

Vibration motion can be almost perfectly sinusoidal and steady-state, or random (non-repeating / non-periodic), or short duration transients or shocks.  Examples include:

  • A spinning imbalanced shaft can create steady-state sine vibration at the frequency of the shaft rotation.  An imbalanced shaft rotating at 1740 rpm (=29 rotations per second) will create once per revolution vibration at 29 Hz (1 Hz = 1 cycle per second).  Shaft misalignment, such as between a motor shaft and a fan shaft, also results in cyclic (periodic) vibration but often contains energy at exact multiples of the shaft rotation rate (harmonic vibration). 

  • Random vibrations are non-repeating (non-periodic) waveforms that can be caused by turbulent airflow, like on the tail of an aircraft in flight, and typically has vibrational energy spread out over a wide range of frequencies (also called broadband vibration).

  • Short duration vibration transients can be produced many ways including by motion actuation of servo controlled XY control stages, or by vehicles hitting road bumps, etc.

  • Shock transients are extremely short duration vibration transients such as those that result on a hard object, like a smartphone, when it is dropped onto a hard surface like concrete, often result in very high acceleration amplitudes of greater than 100 g.


Resonant System Vibration Response

Physical objects have resonances.  There are modal parameters associated with each resonance consisting of its natural frequency, damping and deformation shape (also called mode shape).  These modal parameters are dependent upon on the object’s distribution of mass, stiffness and damping as well as on how the object is mounted (also referred to as the boundary conditions).  

As vibration consultants we work on structures and systems, big and small, that all have resonances, such as a skid-mounted power generator set, or the floor of an upper-floor surgical operating room, or a semiconductor inspection system, or a guitar, etc.. These resonances act to amplify vibration from forced excitation at frequencies near a resonant frequency. 

All acoustic musical instruments have resonances that are typically tuned to have natural frequencies at the frequencies of the desired musical note for which it is tuned.  For example, strings on a piano are carefully tuned to each resonate at its specified musical frequency. Thus, when a piano’s A4 key is struck, it actuates a padded hammer that strikes a stretched piano wire, thereby exciting vibration of the wire at its tuned frequency (of 440 cycles per second = 440 Hz), which in turn radiates sound which grows quieter over time as the wire vibration undergoes ring-down (exponential decay) due to energy loss (damping).

Resonant amplification is at the root of numerous vibration problems.  For example, consider the Tacoma Narrows Bridge collapse of 1940, caused by resonant amplification of wind excitation forces which resulted in 8 meters of vibration displacement prior to collapse!  As vibration consultants, we also work with product R&D teams to address resonance amplification that occurs in very sensitive critical systems, such as atomic force microscopes and electron microscopes, in which 8 nanometers of vibration results in unacceptable image performance (a billion times less motion than the bridge but still unacceptable for the application requirements).

In order to solve a vibration it is necessary to develop an understanding of the resonance(s) that are resulting in excessive vibration.  We do this by performing modal testing and operating deflection shape testing.  

Modal testing involves measuring the system’s response to forced excitation, such as that we apply through an attached shaker, in order to directly measure the systems frequency, damping and shape of each of the resonances of concern.  

Operation deflection shape testing involves using a system’s vibration response to its own normal operating conditions (such as operation of a fan, motor, pump, steam turbine, etc.) or under ambient conditions (such as bridge or building response to wind loading).  

Once, the results of our testing provide the required understanding of the problem resonance(s) we then work with the team to develop a practical cost-effective modification of the system, which may involve changes to its mass, stiffness and/or damping to improve the vibration performance.  In some instances, the best solution involves us designing custom tuned mass dampers to extract vibration energy from the system, thereby lowering its response amplitudes.


Vibration Specifications

Typically, we determine which vibration specification or target vibration levels are applicable for the project.  In some instances no specification exists for a new sensitive system and we perform the vibration sensitivity testing and vibration analysis to develop an appropriate specification of its allowable facility floor vibration.  

Some specifications are relevant for operating industrial machines and others are for human comfort or for the performance of sensitive systems like electron microscopes or semiconductor manufacturing systems.  

For industrial machines, an ISO standard, such as the ISO 10816-3 vibration specification is often used for in-situ vibration testing of large industrial rotating machines (i.e. for pump vibration and fan vibration).

For sensitive systems, such as electron microscopes, system-specific floor vibration specifications, or generic VC curves (Vibration Criteria, as published in the ASHRAE handbook) are often used for determining the suitability of a floor vibration environment to meet the requirements for human comfort or for the performance of vibration-sensitive systems.  These sensitive systems are commonly sensitive to vibration at levels far lower than the threshold of human perception (which is about 100 micron/second rms).  

The determination of the suitability of a given vibration level is made based on comparison of the measured severity from our vibration testing results (site survey or vibration monitoring ) with the project specifications.

Some critical rotating machines systems (like steam turbines) are monitored continuously and have both an operating vibration alarm limit (for immediate shutdown) and a lower warning level (for reliability, indicating maintenance is due at the next scheduled shutdown).


Please contact us to discuss how we can assist your team on your project to address your vibration-related issues.

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