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Since 1984 - Now in Our 35th Year
Contact Us:
Reuben Hale, P.E.
Ph: (510) 507-1300


- High Tech Consulting

- Heavy Industry Consulting

- Facility Design Consulting

- Product Vibration & Noise

- Emergency Solutions

- Vibration Consulting

- Acoustic Consulting

- Vibration & Noise Monitoring

- Construction Monitoring

- Site Testing & Analysis

- Diagnostic Testing

- Sensitivity Testing

- Vibration & Noise Isolation

- Modal & Resonance Testing

- Finite Element Modeling

- Shake Table Testing

- Strain Gage Testing Services

- Servo Control Consulting

- Thermal Testing & Design

- Magnetic Field / EMF / EMI

About Us / Partial Client List

Overview Vibration Characterization Dynamic Testing Damping Treatments Time Domian Analysis
Dynamics Testing: Frequency Response Function Measuremnt: Coupling of structures, Resonance, Damping, Stiffness, Mass, Relative Motion Between parts, Sensitivity to Disturbance, Load path identification, Basic modal testing, Our most powerfull debugging tool
- Vibration Consulting : Dynamic Testing Vibration Testing: Dynamic Testing

Dynamic testing is the backbone of all of our work, it is the basis of vibration analysis and Modal Analysis testing, and the way we show cause & effect in our Diagnostic Testing.

Most everyone will tap on an object to determine what it is made of, if its broken and cracked, if its hollow or solid, if its full or half full, hard and resilient, or soft and damped, just by the feel and the resulting sound. Dynamic testing is simply a highly advanced extension of this basic human investigative impulse.
Image showing an overlay of a structural resonance with modifications that produce a progressively stiffer structure.  The resonance shift is proportional to the square root of the modal stiffness change.  This is what I do as a vibration consultant in testing our design modifications and performing vibration analysis to verify that our modifications produce the desired dynamic properties An image of a representation of a semiconductor inspection tool for animating modal analysis results and showing the estimated mode shapes associated with each resonance. As vibration consultants we often perform these modal tests on physical systems to determine what is causing performance problems, image disturbances, and measurement errors.
Structural modifications to improve the stiffness of an optical structure, the torsional resonance is increased by making progressive improvements to the backbone frame structure. Computer representation of a semiconductor tool used for animation of mode shapes from dynamic testing on the physical system

Consider that when you strike a bell you apply an impulsive force with energy at a broad and continuous range of frequencies. The bell, however, responds according to its inherent dynamics with its resonant response that we hear as a very narrow ringing tone centered at a particular frequency. This is the frequency at which the bell will store mechanical energy and build up to high amplitudes of motion. A different bell may have a different resonant frequency.

The Frequency Response Function (FRF) - Dynamic testing involves measurement of the response at a given point on a structure to a measured input force at another point. The ratio of the response to the input force as a function of frequency is called the Transfer Function, or the Frequency Response Function (FRF). We can use a measured impulse (like a tap) to excite a structure, or use an electromagnetic shaker using full spectrum force excitation. the FRF is the response per unit force applied as a function of frequency. Measurement of the frequency response function (FRF) is our most powerful tool. It is the finger print of the inherent structural dynamics of a system.

The image below shows the time domain waveform of an impulse delivered by a small instrumented force hammer (bottom trace). The ringdown response of the structure is shown in the middle trace. The periodic ringing shows some beating, or modulation, which suggests the interaction of two different but closely spaced resonances. The upper trace is the resulting FRF computed from the Fourier transform of input force and response acceleration. In the FRF we see the peaks of the two resonances, the width of the peaks tells us of the damping, the low frequency portion of the FRF tells us about the stiffness relating the input and output measurement locations.
An image showing three plots, the top plot is the frequency response function, or transfer function, that is calculated from the complex division of the FFT of the response-input cross power spectrum divided by the FFT of the input wave form.
Top trace is the Frequency Response Function (FRF), with a peak at the resonant frequency,
relating the response per unit input. The middle trace is the response of the structure ringing down
at its resonant frequency, the bottom trace is a measurement of the the input force impulse

Dynamics Parameters - The resonant parameters can be extracted numerically from these FRFs and include the resonant frequencies, the local stiffness, mass, and damping. We can show the coupling between structures, debug disturbance path issues, and estimate sensitivity to disturbance (which is what an FRF essentially is). The way force and response are measured using digital signal processing allows us to average out external disturbances that is not caused by the measured applied input force. This is a powerful tool for showing cause and effect in the trouble shooting process.

Below is a plot showing the frequency response function (top blue trace) measured on a structure on a scanning electron microscope (SEM) that involved many important resonances. These resonances can be seen to dominate the ambient response of the tool (middle green trace). We hit the jackpot with this measurement because this one FRF identified a structure responsible for the amplification of the bulk of the disturbance to this sensitive inspection tool. The ambient environment, however, was relatively flat, both in the floor vibration (purple trace) and in the acoustics noise (red trace), making for a particularly easy "imprint" of the shape of these resonances from the FRF in the ambient spectra (middle green trace). We made a couple hundred such measurements before finding this unique FRF. Often important resonances will be found in a handful of FRF measurements.
An image showing the importance of dynamics testing in understanding vibration issues. The top trace is the Frequency Response Function (FRF) showing the resonant peaks of the structure.  The next trace is the floor acceleration spectra, the tool response spectra showing that the tool response is dominated by the resonances show in the top FRF measurement. The bottom trace is the spectrum of the acoustic noise around the tool.
Overlay of the FRF, showing the resonances of the structure (Blue Trace), the floor vibration spectra (Purple Trace), the System Response dominated by the structural resonances (Green Trace), the acoustic spectrum (Red Trace)

Resonance and Mode Shape - Many engineers will recall that the peaks in the FRFs (transfer functions) correspond to the resonances of the structure. This is a very valuable concept that helps predict at what excitation frequencies we should expect large motions. What most people don’t think about as often is what the deformation shape looks like as the system oscillates at resonance?

We spend much of our time thinking about just that. The fascinating thing about these resonances is that each resonant peak corresponds to a unique deformed shape called a mode shape. In other words, a mode shape is the unique deformed shape a structure will take as it oscillates at a unique resonant frequency. The resonant frequency and mode shape are collectively referred to as a mode.

Dynamic testing and Frequency Response Function (FRF) measurement are used in a systematic way to collect the data for a Modal Analysis which is used to create visualizations of these unique mode shapes. The modes can show how and why these resonances form and what can be done to change them so that the tool will have less sensitivity to environmental disturbance. Change the mode shape and we change the resonance frequency, the input and response relationship, and the product, facility, or tool performance. The modes can be superimposed to approximate the possible deformed motions of the structure. The characterization of a sub-set of these modes is often all that is necessary to gain a full understanding of the deformations that dominate a vibration and/or acoustic problem. A more detailed discussion of the very powerful concepts of Modal & Resonance Testing are given under that title.

AFM Modal Analysis Mode5-72 Hz
Excited by Cooling Fan
FRF showing Resonance ID in Scanning Electron Microscope Image
Disturbance Issue

The plot below is a set of FRFs measured on a bio-tech device that originally had very poor image quality due to structural resonances of the sample holder. We used dynamic testing and the FRF to characterize the improvements in resonant behavior for various structural modifications and Damping Treatments, quantifying our analysis, and allowing our client to predict image disturbance for given external excitations, such as environmental chamber vibration. These measurements and calculations can then be used to engineer isolation of sources of the environmental chamber, etc.
As vibration consultants we engineer a wide range of unique customized damping treatments for all types of products and structures, this image shows the frequency response functions before and after attaching a custom tuned mass damper we designed for a biotech product
Damping Treatments Include Tuned Mass
Dampers When Appropriate

By taping at various locations we can quickly get a larger picture of the structural dynamics, causes of resonant amplification, and the nature of the disturbance transmission path. With this understanding we can often quickly narrow down on the possible nature and scope of the problem and a solution to the vibration problem can be designed quickly and efficiently.

Whether making a few dynamics measurements, or a full modal analysis, we use the concepts relating to the FRF and modal analysis to understand dynamic problems. We have over 30 years of experience making these measurements and solving structural dynamics issues. Our VP of Engineering, Henry Bittner, MSME, has been with our company, and in the field solving structural dynamics issues, for over 24 years. We love what we do and are at the very top of our unique field.

- Vibration Consulting Topics Include:
Overview, Vibration Characterization, Dynamic Testing, Damping Treatments, Time Domian Analysis

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