# Structural dynamics

All structures large and small are subject to physical forces that affect their performance. From a wind turbine blade vibrating in an offshore gale, an aircraft experiencing turbulence during flight to machinery exposed to self-generated vibration, these forces test the integrity of structures. Yet, while structures must be resilient and rigid, over-engineering them can be both unnecessary and costly – especially when weight is an issue. And some structures, such as engine mounts, must not be too rigid. They must absorb vibration in order to maximize comfort. Understanding how structures behave in service enables engineers to optimize their designs, monitor structural integrity, and maximize performance.

## Structural characterization

Structural dynamics is about the characterization of structural properties and the behaviour of structures. Structural properties are expressed in a set of modal parameters, each consisting of a mode shape with an associated natural (resonance) frequency and damping value. The modal parameters are derived from a mathematical model describing the relationship between the inputs and outputs and can be obtained using classical modal analysis or operational modal analysis (OMA).

In classical modal analysis, the structure is excited using impact hammers or modal exciters (modal shakers), whereas in operational modal analysis, natural excitation is used. In both cases, the response is typically measured using accelerometers.

Determining how shocks affect a structure is a special type of structural characterization. For this purpose, the shock response spectrum (SRS) calculated from transients in the time domain is used.

Structural behaviour is observed using techniques such as operating deflection shapes (ODS) analysis for determining the vibration patterns of structures under various operating conditions or using permanent structural health monitoring (SHM) to follow the structural state continuously and determine the required health management of the structure.

## Integrating test and simulation

Structures are often designed using finite element (FE) models, and their geometry models and results predictions are very useful for optimizing the tests. Importing detailed FE models not only allows you to create simpler test models that are highly accurate, but also helps you to define optimal excitation and response DOFs to get the best possible test results. FE predictions can be correlated with the test results, and the test data can be imported back into the simulation tools for updating the FE models.

Recorded webinar: Introduction to Structural Dynamics Measurements and Analysis

Operating deflection shapes (ODS) analysis is a very versatile application for determining the vibration patterns of machinery and structures under various operating conditions. The vibration patterns are shown as animated geometric models of the structure that display a combination of the forcing function acting on the structure and the dynamic properties of the structure.

The forcing function depends on the operating conditions, which for machinery, can be influenced by factors such as engine speed, load, pressure, temperature and flow. For civil engineering structures, ambient forces from wind, waves and traffic might also apply.

ODS analysis can be divided into three types – time ODS, spectral ODS and run-up/down ODS.

#### System suggestion

Brüel & Kjær’s scalable ODS systems provide complete guidance through the set-up, measurement and animation for each ODS type.

Our systems cover the entire measurement and analysis chain including accelerometers, tacho probes, LAN-XI data acquisition hardware and BK Connect® software.

Recorded webinar: Operating Deflection Shapes Analysis - Determination of Vibration Patterns Under Operating Conditions

In classical modal analysis, a model of a structure’s dynamic properties is obtained by exciting the structure with measurable forces and determining the response/excitation ratio.

Classical modal analysis ranges from simple mobility tests with a roving impact hammer and a fixed accelerometer to multi-shaker testing of large structures using hundreds of accelerometers. It is used in a vast range of tests including design verification and optimization, certification testing, troubleshooting and benchmarking.

#### System suggestion

Our classical modal analysis solutions guide you through the complete set-up, measurement and analysis in simple and intuitive steps, and provide you with accurate and reliable results even in the most demanding situations, with a targeted set of best-in-class modal parameter estimators and validation tools.

Our solutions cover the entire measurement and analysis chain including accelerometers and force transducers, impact hammers, modal exciter systems, LAN-XI data acquisition hardware and BK Connect® software for pre-test analysis, measurement, analysis and Finite Element model correlation. Our solutions are also expandable so they can grow with your requirements.

Video: Brüel & Kjær Stepped Sine

Virtual simulation has dramatically accelerated the overall aircraft development process. However, physical testing remains a critical contributor to both model validation and the understanding of structural characteristics of new materials and manufacturing processes.

Aircraft ground vibration testing (GVT) is used to determine the modal parameters of the complete aircraft and is typically performed very late in the development process. The outcome is used to update the aircraft’s analytical models to predict the flutter boundaries (combinations of altitude and speed) and establish a safe flight envelope before the first test flight. Following the test flights, the analytical models are updated, the final flutter calculations made, and the aircraft obtains its airworthiness certification.

GVT is mandatory for new aircraft and for existing aircraft that undergo modifications.

#### System suggestion

A typical GVT system consists of modal exciter systems, modal accelerometers and LAN-XI data acquisition hardware. Measurements and post-processing are carried out with BK Connect® software. The test geometry is defined based on a Finite Element (FE) model of the test object. The FE model also provides the basis for a pre-test analysis to define excitation and response DOFs (Degree-Of-Freedoms), and for investigation of target modes.

This system is scalable, depending on the size of the test object, and especially for larger objects, the LAN-XI data acquisition hardware can be distributed, to minimize cabling.

In operational modal analysis (OMA), only the output of a structure is measured using the ambient and operating forces as unmeasured input. OMA is used instead of classical modal analysis for accurate modal identification under actual operating conditions, and in situations where it is difficult or impossible to artificially excite the structure.

Many civil engineering and mechanical structures are difficult to excite artificially due to their physical size, shape or location. Civil engineering structures are also loaded by ambient forces such as the waves against offshore structures, the wind on buildings, and traffic on bridges, while mechanical structures such as aircraft, vehicles, ships and machinery exhibit self-generated vibration during operation.

In OMA, these forces, which would produce erroneous results in classical modal analysis, are instead harnessed as input forces. As OMA can be performed in situ during normal operation, set-up time is reduced, and downtime can be eliminated.

#### System suggestion

For an integrated, easy-to-use modal test and analysis system, use BK Connect® Time Data Recorder for geometry-guided data acquisition, and then transfer data to PULSE Operational Modal Analysis software for analysis and validation.

To achieve the optimal OMA solution, you can select from Brüel & Kjær’s complete measurement and analysis chain including accelerometers, LAN-XI data acquisition hardware and measurement and post-processing software.

Video: Brüel & Kjær Operational Modal Analysis

Recorded webinar: Operational Modal Analysis - Modal Parameter Identification under Operating Conditions

Structures degrade over time due to use, harsh environmental conditions and accidental events. Using continuous, long-term Structural Health Monitoring (SHM) makes it possible to follow the structural state and determine the required health management of the structure such as organization of maintenance and repair.

SHM is a very important objective for end-users, manufacturers and maintenance teams as it:

• Allows for optimal use of structures
• Minimizes downtime
• Can avoid catastrophic failures
• Helps improve design of structures
• Helps optimize the organization of maintenance services

#### System Suggestion

Our SHM solutions cover the complete measurement and analysis chain. They include automatic data upload and processing, mode tracking, damage detection and drift analysis. Notification (alert) services such as visual, auditive, email and web services can be configured.

Our damage detection algorithms work in the physical domain using state space models instead of in the reduced modal domain. This gives a more robust detection with highest possible accuracy.

Video: Brüel & Kjær Structural Health Monitoring

Video: Structural Health Monitoring of a Wind Turbine Blade

Video: Predictive Structural Health Monitoring of Wind Turbine Blades

Integration of test and finite element analysis (FEA) is a core discipline in structural dynamics. Integrating testing and FEA helps to cut development costs, reduces the number of physical prototypes, and shortens the time from concept to production – all by optimizing strategies for testing structures and improving the development of finite element (FE) models.

Using baseline FE models, you can optimize your structural tests early in a project and then improve these FE models using the enhanced test results.

BK Connect® offers powerful tools to gain better confidence in the test and simulation results and to improve essential engineering judgement skills, benefiting test engineers, analysts and management.

#### System suggestion

BK Connect offers one platform for test planning (pre-test analysis), structural measurements and analysis and FE model correlation.

FE models can be imported from leading FEA programs such as Nastran® (MSC, NX, NEi), ANSYS® and ABAQUS® into BK Connect Modal Analysis for performing test planning by investigating the simulation results in terms of frequency range of interest, mode density, mode order, critical modes, etc.

The simulation results can, furthermore, be used to optimize the number and locations of excitation and response DOFs, and an accurate test geometry decimated from the FE model is easily created. Once the modal test has been done, the results can be compared with the simulation results for validation.

BK Connect Correlation Analysis lets you go a step further by performing a complete visual and numerical correlation analysis to identify shortcomings in the modal tests and any areas of insufficient modelling quality in the FE models. It is a strong tool for designing optimal test conditions and evaluating different modelling strategies.

A single transient shock event such as pyroshock or a structural impact can damage components in a structural system. Similarly, earthquakes can cause catastrophic failures in bridges and buildings. And with any motion input into a system, the response can be amplified by structural resonances, increasing the damage. By calculating the shock response spectrum (SRS) it can be determined how shocks affect a structure.

#### System suggestion

BK Connect Shock Response Spectrum Analysis software supports all five SRS models described in the ISO 18431-4:2007 standard. Combined with the nine ordinary criteria for amplitude calculations (shock instances), up to 45 response types can be calculated to match your requirements.

Special shock accelerometers for high-level and high-frequency measurements are part of our complete measurement and analysis chain.

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