Mastering Structural Dynamics: Building the Foundations of Structural Dynamics in NVH

Today, Engineers continue to expedite their testing while capturing potential issues early on in the development phase of their product life cycle. As such, HEAD acoustics GmbH recently updated a 4-part series to their customers promoting the use of ArtemiS SUITE in Structural Dynamics Testing. This article will highlight some of the details in Part 1 of the Application Note providing some benefits of structural dynamics, as well as start off with the glossary of terms to consider with advancing your investigations.

Understanding the dynamic response of structures enables the optimization of mechanical vibrations through constructive measures. This optimization extends to improving structure-borne sound transmission and radiation behavior. Moreover, minimizing vibrations not only decreases the load on the structure but also enhances the service life of components or machines.

Many important insights can be gained by analyzing structural dynamics very early on in the product development cycle.

Insights from Structural Dynamics:

• How a structure vibrates during excitation under real conditions
• The sound radiation to be expected from the surfaces of a structure (e.g., a machine) and ways to avoid it.
• Finding the root cause of sound and vibration problems and optimize the transmission paths throughout the product.
• Optimization of the structural system for sound and vibration applications
• The expected dynamic stress and associated material fatigue.
• Determine points of weaknesses in the structure with regard to dynamic stress and evaluate solutions
• Advanced prediction of the effects of modifications and bypass the trial-and-error approach to solving existing vibration problems, thus reducing time and cost of implementing design changes
• Validate and adjust the mathematical models of the structure

The aim is to adjust a structure in such a way that its natural frequencies do not coincide with the excitation frequencies, thus reducing or even eliminating dynamic influences.

Procedures Used with Structural Analysis

EMA (experimental modal analysis, also known as modal tests): EMA is a method for analyzing the dynamic proper- ties of linear, time-invariant structures. In EMA, the structure is ex- cited with an impact hammer or shaker(s) and the structure’s response is measured with sensors (usually accelerometers). The ac- quired data and further analyses allow the determination of the modal quantities (natural frequencies, damping, eigenmodes).

Curve Fitting: Curve Fitting is a mathematical process for generating a curve that matches a target curve as closely as possible. In structural analysis, curve fitting refers to the recreation of a transfer function. Natural frequencies and damping of the structure are extracted. Various methods have been developed for curve fitting. Using curve fitting for several transfer functions at the same time, the natural frequencies and the corresponding characteristics can be determined.

OMA (operational modal analysis or output-only modal analysis): OMA is a method for determining modal parameters in which structural excitations present in operation are used for modal analysis. It is used, for example, if it is not possible to apply sufficient excitation energy to the structure by using a hammer or shaker. Furthermore, OMA can be used if the structure to be investigated needs to be analyzed in assembled condition (e.g., an installed powertrain). Also with OMA, specific software is used to extract modal quantities. A broadband form of excitation is the mathematical prerequisite for calculating the modal parameters in case of unknown excitation.

The problem with OMA is to achieve a broadband uniform excitation of the structure without tonal components due to operating forces.

ODS analysis (operational deflection shape analysis): An operational deflection shape analysis examines the vibration behavior of a structure in operating condition. For this purpose, the vibration of the structure during operation is recorded at numerous points (the excitation forces are not explicitly measured). Modal parameters such as natural frequencies and modal damping cannot be determined by operational deflection shape analysis. The deflection shapes determined by ODS usually do not correspond to the individual modes, but reflect the response behavior of the structure to an (unknown) excitation induced by operation. The deflection shapes are usually composed of several individual modes.

Using a visualization model, the operating deflection shapes can be displayed in animated form as a function of time or frequency.

Measurement Methods

SISO (single input - single output): SISO measurements include modal analysis with a hammer or shaker (single input) and an accelerometer (single output).

This measurement method is suitable for smaller structures; it is a very cost-effective measurement, since little measurement equipment is needed.

SIMO (single input - multiple outputs): SIMO measurements include modal analysis with a hammer or a shaker (single input) and multiple accelerometers (multiple outputs).

MIMO (multiple inputs - multiple outputs): MIMO measurements include, for example, modal analysis with multiple shakers (multiple inputs) and multiple accelerometers (multiple outputs). An advantage of MIMO measurements is that the injected energy is distributed over multiple locations in the structure. This provides a more uniform vibration behavior of the structure, especially for large and complex structures and those with strong damping. MIMO measurements can be used, for example, if the test structure has closely spaced or coupled modes.

These measurements acquisition times can be significantly reduced by using multiple accelerometers.

Roving Hammer: In the roving hammer method, the structure is excited with a hammer at various points. The structural response is measured with one or more accelerometers at a fixed position in each case. This has the advantage that the mass influence of the sensors does not change between the individual measurements.

• The roving hammer method is particularly suitable for smaller structures and can be performed with relatively little measurement equipment. The roving hammer method can only be used if all required positions can be struck with the impact hammer.

• Roving Accelerometer: In the roving accelerometer method, the structure is excited with a hammer or shaker at a fixed position. The structural response is measured with one or more accelerometers, the position(s) of which is/are changed after each measurement. If several accelerometers are used, data acquisition can be accelerated considerably, since the transfer function for several measurement points can be determined simultaneously with one measurement. The roving accelerometer measurement should be used if not all points can be easily reached for excitation with the impact hammer. On the other hand, when evaluating the data, it has to be taken into account that moving the sensor(s) will change the mass influence on the structure and can lead to differences between the measurements.

Other Key Points / Phrases:

Natural frequency: The natural frequency f0 is the frequency at which an oscillating single degree of freedom system oscillates after a single, broadband excitation (free oscillation).

• In the case of a periodic excitation with the frequency fa, the system oscillates with the frequency fa (forced oscillation). If the frequency fa of the excitation is the same as the system’s natural frequency f0, the system responds with high amplitudes (resonance case).
• A structure’s natural frequency is an inherent property and depends on the structure’s geometry, composition and material properties.

Frequency response function, FRF or transfer function): The frequency response function describes the frequency-dependent ratio of the vibration response of a structure to the excitation. For structures that behave linearly, the system response can be calculated directly from the excitation signal and the frequency response function.

• A frequency response function contains information on the natural frequencies and modal damping, and a set of frequency response functions also includes information on the corresponding eigenmodes of the system.

• The frequency response functions provide information on the dynamics of the system: mass, rigidity and damping or natural frequencies, eigenmodes and modal damping.
• The frequency response function is a complex-valued function that can be represented by real and imaginary parts or magnitude and phase. In the so-called Bode diagram, the magnitude and phase of the frequency response function are shown as a function of frequency.

Phase: The time shift between the input signal (load force) and the system response changes depending on the frequency. This shift can be represented in the form of the phase response (phase over frequency). The phase response provides information on the relative direction of oscillation, the mode shape and existing natural frequencies. The system response below the natural frequency is in phase with the excitation. When the natural frequency f0 is reached, the phase curve tilts. Above the natural frequency, the input and output signals are shifted by 180°.

Coherence: Coherence describes the linear dependence between two signals in the frequency domain (e.g., between excitation signal and system response). The coherence between the input and the output signal allows for the identification of response components that are not causally based on the input signal, but were caused by additional external excitations. It also allows for the detection of non-linearities of a system.

The coherence can assume values between 0 and 1 and is plotted over frequency.

The actual coherence values depend very much on the practical application. In the realm of natural frequencies, the coherence should be very close to 1. With anti- resonances, the signal-to-noise ratio is poor, and coherence breaks down at these points. However, this does not allow any conclusions to be drawn about the quality of the measurement.

When calculating the coherence, it must be taken into account that meaningful results can only be obtained by averaging several measurements. Without averaging, the coherence assumes the value 1 over the entire frequency range.

If the system was excited with several input sources (e.g., with multiple shakers), the partial or multiple coherence must be determined in order to evaluate the quality of the measurement.

1. Partial coherence describes the linearity between a single input signal and the output signal. The linear influence of other input channels is removed in the calculation. This presupposes that the input channels are as uncorrelated as possible.
2. Multiple coherence provides a statement on the common linear dependence between several input signals and the output signal.

To find out even more terminology or details involved in Part 1 of this Application Note - Feel free to check out the listing on our webpage www.HEADacoustics.com

For questions about this article. Please contact BCremeans@HEADacoustics.com or Imke.Hauswirth@HEAD-acoustics.com