Experimental Mechanics, Testing and Structural Health Monitoring

Introduction and context

Mechanical design is ultimately validated by evidence. Analytical models and numerical simulations predict how a component or structure should behave; experimental mechanics determines how it actually behaves under controlled or service conditions. Testing therefore serves several purposes: validating design assumptions, identifying failure mechanisms, estimating uncertainty, qualifying materials and products, and supplying data for model updating and structural health monitoring (SHM).

Experimental mechanics is broader than measurement alone. It includes the formulation of an experimental question, selection of measurable response variables, instrumentation, calibration, test execution, signal conditioning, data interpretation, uncertainty assessment and engineering decision-making. SHM extends this logic into operation: sensors and algorithms are used to detect, localize, characterize and assess damage while a structure remains in service.

For postgraduate mechanical engineers, the central issue is not simply how to obtain data, but how to establish whether the data are physically meaningful, statistically defensible and relevant to structural integrity.

Learning objectives

After studying this chapter, the reader should be able to:

1. Explain the principles and scope of experimental mechanics and structural testing.
2. Select suitable sensors and test methods for displacement, strain, force, pressure, temperature and vibration.
3. Distinguish static, dynamic, fatigue, fracture and environmental tests.
4. Design a measurement chain and assess calibration, resolution, sensitivity and uncertainty.
5. Interpret strain-gauge, optical and vibration measurements using appropriate mechanical models.
6. Explain SHM architectures, damage-detection levels and diagnostic algorithms.
7. Evaluate a test programme critically, including boundary conditions, repeatability, correlation and ethical responsibilities.

1. Experimental mechanics as an engineering discipline

A well-designed experiment begins with a question that can be answered by measurement. The question should identify the system, loading, response variable, operating range and decision that will follow. For example, “Does the bracket meet the design requirement?” is incomplete unless the requirement specifies allowable strain, displacement, fatigue life or failure probability.

The experimental system consists of:

• Input: force, displacement, pressure, temperature, excitation frequency or environmental exposure.
• System: material, component, assembly or structure with specified boundary conditions.
• Output: strain, stress, acceleration, crack length, deformation, temperature or failure state.
• Measurement chain: transducer, signal conditioning, data acquisition and processing.
• Decision criterion: a limit state, model-validation metric, acceptance criterion or maintenance action.

The idealized relationship between input and output may be written as

where x(t) is the applied input, y(t) is the measured response, θ represents system parameters, and ε(t) is measurement and modelling error. The relationship is not necessarily linear or time invariant. In practice, the experiment seeks to estimate either the response y, the parameters θ, or the uncertainty associated with both.

Important terminology

• Accuracy: closeness of a measurement to the accepted reference value.
• Precision: closeness of repeated measurements to one another.
• Sensitivity: change in output per unit change in input.
• Resolution: smallest input change that can be distinguished.
• Repeatability: agreement under the same operator, equipment and conditions.
• Reproducibility: agreement under changed operators, equipment or laboratories.
• Traceability: documented connection of a measurement to recognized standards through an unbroken calibration chain.
• Bias: systematic deviation from the reference value.
• Noise: unwanted random or structured variation in the signal.

A high-resolution instrument is not necessarily accurate. Similarly, a highly accurate instrument may be unsuitable if its bandwidth or environmental tolerance is inadequate.

2. Measurement principles and instrumentation

2.1 Measurement-chain architecture

A typical chain is:

physical quantity → transducer → bridge or amplifier → analogue filter → analogue-to-digital converter → software processing → engineering interpretation.

Each stage can introduce gain error, offset, drift, saturation, aliasing or phase distortion. The design should therefore begin with the expected range and frequency content of the physical quantity, rather than with the availability of a particular sensor.

For a linear sensor, the indicated output may be represented by

where x is the measurand, S is sensitivity, b is offset or bias, and n is random noise. The calibration process estimates S and b. The linear form is valid only over the specified operating range; nonlinear sensors require a calibration curve or appropriate polynomial/model identification.

2.2 Strain measurement

A resistance strain gauge changes resistance when its length changes. Its nominal relation is

where R is nominal resistance, ΔR is resistance change, ε is normal strain (dimensionless), and G is the gauge factor. For metallic gauges, G is commonly near 2, but the certified value must be used in calculations.

A Wheatstone bridge converts the small resistance change into a voltage. For a quarter bridge with one active gauge and sufficiently small strain, the approximate output is

where V_o is bridge output and V_e is excitation voltage. This approximation assumes a balanced bridge, small resistance changes and negligible lead-wire and temperature effects. Half-bridge and full-bridge arrangements improve sensitivity and can compensate for bending or temperature, depending on gauge arrangement.

For a uniaxial, linear-elastic, isotropic material under plane stress, longitudinal and transverse strains are related through Poisson’s ratio ν. Stress may then be estimated by

for uniaxial loading, where σ is normal stress and E is Young’s modulus. Under general plane stress, the constitutive relations are

where ε_x, ε_y are normal strains, γ_xy is engineering shear strain, G = E/[2(1+ν)] is shear modulus, and the assumptions are small strain, linear elasticity, isotropy and plane stress.

Practical strain-gauge errors include imperfect bonding, gauge misalignment, local stress concentrations, temperature sensitivity, moisture ingress and cable movement. Surface preparation, adhesive curing, protective coating and shunt calibration are essential controls.

2.3 Displacement, force and pressure measurement

Linear variable differential transformers (LVDTs) provide contact displacement measurement with good resolution and robust analog output. Potentiometric sensors are simple but involve sliding contact. Laser triangulation and digital image correlation (DIC) are non-contact methods, useful where contact would disturb the specimen or where full-field information is required.

Load cells generally use strain-gauged elastic elements. Their rated capacity should exceed the maximum expected load without being so large that resolution becomes inadequate. Calibration should include loading and unloading to identify hysteresis.

Pressure transducers may use diaphragms with piezoresistive, capacitive or piezoelectric sensing. Piezoelectric sensors are well suited to dynamic pressure but cannot measure a true static value indefinitely because charge leakage causes drift.

2.4 Optical and full-field methods

DIC tracks the movement of a random surface speckle pattern between images. A subset of pixels is matched through successive images, and displacement gradients provide strain. DIC can reveal strain concentrations, crack-tip fields and deformation modes that point sensors may miss. Its limitations include sensitivity to lighting, camera calibration, out-of-plane motion, pattern quality, spatial resolution and correlation parameters.

Photoelasticity reveals stress patterns in transparent birefringent models and is valuable for qualitative visualization and stress-concentration studies. Moiré methods and holographic interferometry can resolve small displacement fields but require careful optical stability.

3. Data acquisition, sampling and uncertainty

3.1 Sampling and aliasing

If a continuous signal contains frequencies above half the sampling frequency, those components can appear falsely at lower frequencies. The Nyquist condition is

where f_s is sampling frequency and f_max is the highest frequency of interest. In real systems, an anti-aliasing low-pass filter is applied before digitization, and sampling is selected with margin above the intended bandwidth. Sampling faster does not correct a poor sensor or inadequate filtering.

Quantization introduces finite resolution. For an ideal N-bit converter with full-scale span V_FS, the nominal quantization step is

This is an ideal estimate; effective number of bits is reduced by noise, nonlinearity and converter imperfections.

3.2 Filtering and signal conditioning

Low-pass filtering reduces high-frequency noise, high-pass filtering removes slowly varying offsets, and band-pass filtering isolates a frequency range. Filters alter amplitude and phase. For modal testing and transient reconstruction, phase distortion must be considered; zero-phase offline filtering is possible in some analyses but is not causal and should not be described as real-time processing.

Signal conditioning may include bridge completion, amplification, isolation, excitation, anti-alias filtering and cold-junction compensation for thermocouples. Over-ranging must be avoided because clipping can create harmonics and invalidate spectral analysis.

3.3 Uncertainty evaluation

A measurement result should be reported as an estimate plus an uncertainty statement, not as an unjustifiably precise number. For a result y = f(x₁,x₂,…,x_n), a first-order combined standard uncertainty is

where u(x_i) is the standard uncertainty of input x_i, and u(x_i,x_j) is covariance. The covariance terms are required when inputs are correlated. If inputs are independent, covariance terms are zero.

For a mean of n independent repeated observations with standard deviation s, the standard uncertainty of the mean is

This describes uncertainty in the estimated mean, not necessarily the uncertainty of an individual future observation. Systematic effects, calibration uncertainty and model inadequacy must be considered separately.

An expanded uncertainty is often reported as U = ku_c, where k is a coverage factor selected according to the desired coverage probability and statistical assumptions. A statement such as “result = 12.4 ± 0.3 mm, k = 2” is incomplete unless the measurand, method and confidence interpretation are specified.

4. Structural testing methods

4.1 Static and quasi-static testing

Static tests apply loads slowly enough that inertia and rate effects are negligible for the intended model. Typical measurements include load, displacement, strain and residual deformation. Boundary conditions must reproduce the design situation; an overly rigid fixture can produce unrealistic load paths.

A force–displacement curve reveals stiffness, yield, hardening, hysteresis and failure. The tangent stiffness is the local slope,

where F is force and d is displacement. A secant stiffness is F/d relative to a selected origin. These quantities should not be confused when nonlinear behaviour is present.

4.2 Dynamic and vibration testing

Dynamic testing characterizes response under time-varying loading. In a linear single-degree-of-freedom model,

where m is mass, c damping coefficient, k stiffness, x displacement and F(t) applied force. The undamped natural circular frequency is

and the damping ratio is

These expressions assume a linear model with constant parameters and a single dominant mode. Real structures are multi-degree-of-freedom systems; their measured resonances depend on mass distribution, boundary conditions, joints and sensor locations.

In experimental modal analysis, measured frequency response functions are used to estimate natural frequencies, damping ratios and mode shapes. A frequency response function may be defined as

where X(ω) and F(ω) are Fourier transforms of response and force. Coherence, commonly used as a quality indicator, is

where G_xx and G_yy are auto-spectral densities and G_xy is cross-spectral density. Values near one indicate a strong linear relationship under the measurement conditions, but high coherence does not prove that the model is correct.

4.3 Fatigue testing

Fatigue tests apply repeated loading to characterize life, crack initiation or crack growth. Stress-life methods use an S–N curve; strain-life methods are more suitable when plastic strain is significant. Results depend on stress ratio, surface condition, size, environment, manufacturing defects and statistical scatter.

For variable-amplitude loading, a simple linear damage rule is often written

where n_i is the number of applied cycles at stress level i, and N_i is the constant-amplitude life at that level. Failure is conventionally predicted when D ≈ 1. This is an empirical approximation, not a universal law; sequence effects, overload retardation and multiaxiality can make it inaccurate.

4.4 Fracture and failure testing

Fracture tests measure crack resistance using standardized specimen geometries and controlled crack sizes. Linear elastic fracture mechanics uses the stress-intensity factor

where σ is nominal stress, a is crack length, and Y is a dimensionless geometry factor. The equation applies when small-scale yielding and appropriate specimen validity conditions hold. A material’s critical value K_Ic is meaningful only when plane-strain and thickness requirements are satisfied; otherwise the measured value may be a conditional fracture toughness.

For fatigue crack growth, the Paris relation is commonly used over an intermediate growth regime:

where a is crack length, N is cycle count, ∆K is stress-intensity-factor range, and C and m are experimentally determined constants. It does not accurately represent threshold or near-instability regions without additional models.

5. Structural Health Monitoring

SHM is the process of observing a structure over time, extracting damage-sensitive information and making engineering decisions about its condition. It differs from a one-time inspection because it emphasizes repeated or continuous measurement and changes in structural state.

A useful four-level description is:

1. Detection: determine whether an abnormal change exists.
2. Localization: identify the region or component affected.
3. Classification: distinguish damage type, such as crack, loosened joint or delamination.
4. Quantification and prognosis: estimate severity, remaining useful life or risk.

The levels are progressively more difficult. A system may detect a change reliably but be unable to identify its cause or remaining life.

5.1 SHM architecture

An SHM system normally contains sensors, excitation if required, signal conditioning, synchronized acquisition, communication, data storage, feature extraction, a decision algorithm and a maintenance interface. Passive systems listen to operational responses; active systems inject known electrical, mechanical or ultrasonic excitation.

Sensor choice depends on damage physics. Strain gauges measure local deformation; accelerometers reveal changes in modal properties; acoustic-emission sensors detect transient waves from active crack events; guided-wave piezoelectric transducers interrogate larger areas; fibre-optic sensors provide immunity to electromagnetic interference and multiplexing capability; thermography detects thermal anomalies and subsurface effects under suitable conditions.

5.2 Model-based and data-driven methods

Model-based SHM compares measured behaviour with a physical model. A finite-element model may be updated by minimizing a residual such as

where r(θ) is the vector of differences between measured and predicted quantities, W is a weighting matrix, and θ contains uncertain model parameters. The method requires identifiable parameters and reliable uncertainty characterization. Non-unique parameter combinations can produce similar responses.

Data-driven methods learn normal behaviour from historical data. Principal component analysis, clustering, support-vector methods, autoencoders and probabilistic models may be used for novelty detection. A standardized feature may be written

where μ and σ are the training mean and standard deviation. Such normalization is valid only when operating conditions are comparable or explicitly included in the model.

A major SHM problem is environmental and operational variability. Temperature, humidity, preload, speed and payload can change sensor outputs without damage. Compensation may use measured environmental variables, cointegration, regression, domain adaptation or physics-informed models. An algorithm trained only in a laboratory may generate excessive false alarms in service.

5.3 Detection performance

A monitoring system should report more than accuracy. Important measures include probability of detection, false-alarm probability, missed-detection probability, localization error, detection latency, robustness to sensor failure and uncertainty in severity estimation. Thresholds should be established using representative healthy and damaged data, not selected after observing only a convenient test set.

Receiver operating characteristic analysis can show the trade-off between true-positive and false-positive rates. In safety-critical applications, the cost of a missed detection may greatly exceed the cost of an unnecessary inspection; threshold selection must therefore reflect risk and consequences.

6. Experimental design and test planning

A rigorous test programme normally follows these steps:

1. Define the engineering hypothesis and acceptance criteria.
2. Identify variables, constraints, failure modes and governing physics.
3. Select specimen geometry, material batch, fixtures and boundary conditions.
4. Perform uncertainty and sensitivity analysis before testing.
5. Specify sensor range, bandwidth, calibration and sampling.
6. Plan replication, randomization where appropriate and test sequencing.
7. Conduct a pilot test to identify saturation, resonance, leakage or fixture problems.
8. Record raw data, metadata, calibration certificates and deviations.
9. Validate data quality before interpreting results.
10. Compare with analytical or numerical predictions and explain discrepancies.

Replication distinguishes random scatter from a deterministic effect. Randomization reduces confounding from drift or order effects. Blocking groups tests under known environmental or material conditions. Design of experiments can efficiently identify influential factors and interactions, but statistical efficiency cannot compensate for a physically invalid test configuration.

Correlation with finite-element analysis requires consistent coordinate systems, material properties, contacts, damping assumptions, sensor mass and boundary conditions. Agreement in one response quantity does not validate every aspect of a model. Discrepancies should be diagnosed, not hidden by arbitrary parameter adjustment.

7. Illustrative worked example: strain and uncertainty

A steel tie is instrumented with a strain gauge of gauge factor G = 2.05. The bridge excitation is V_e = 5.00 V, and the measured quarter-bridge output is V_o = 2.05 mV. Estimate the axial strain and stress, assuming a linear-elastic steel modulus of E = 200 GPa.

For a quarter bridge,

Substitution gives

Thus the strain is approximately 800 με, where με denotes microstrain. The corresponding stress is

Therefore, σ = 160 MPa, provided the strain is axial, the bridge approximation is valid, temperature effects are compensated and the steel remains elastic. If the strain estimate has a relative uncertainty of 3% and the modulus has a relative uncertainty of 2%, neglecting covariance, the relative stress uncertainty is approximately

or 3.6%. The standard uncertainty in stress is therefore about 5.8 MPa, before considering model uncertainty, alignment error and residual stress.

8. Applied case: illustrative SHM programme for a wind-turbine tower

Background

Consider an illustrative steel wind-turbine tower subjected to cyclic wind loading, start–stop transients and changing temperature. Inspection has identified welded door-frame details as potential fatigue hot spots.

Problem

The operator requires early warning of crack initiation without frequent shutdowns. A laboratory-only threshold is unsuitable because vibration and strain vary strongly with wind speed, rotor speed and temperature.

Analysis

A failure-mode analysis identifies weld toe cracking, bolt loosening and sensor detachment as credible events. Strain gauges are selected near critical welds for local fatigue response, accelerometers are installed at several elevations for modal changes, and temperature sensors are added for compensation. Periodic visual and ultrasonic inspections provide reference labels.

A baseline is established over a range of healthy operating conditions. Features include strain range, spectral peaks, damping estimates and temperature-compensated residuals. A finite-element model supplies expected mode shapes and identifies regions where a crack would produce measurable changes. The monitoring algorithm first classifies the operating regime, then compares measurements with the appropriate healthy baseline.

Approach and solution

The system uses redundant sensors and records raw as well as processed data. Alerts are graded: a low-level novelty prompts data review; a persistent localized strain anomaly prompts targeted inspection; corroborated evidence of crack growth triggers controlled shutdown. Detection thresholds are selected using false-alarm and missed-detection costs, not merely overall classification accuracy.

Outcome

In the illustrative programme, the system does not claim to measure crack length directly from strain alone. Instead, it provides earlier prioritization of inspections and supports a risk-based maintenance decision. Periodic non-destructive examination remains necessary because an SHM system can fail, drift or miss damage outside its sensitivity region.

Learning points

• Environmental normalization is essential in operational SHM.
• Sensor redundancy improves confidence but does not eliminate common-mode errors.
• A physical failure-mode model guides sensor placement and feature selection.
• SHM should support, not replace, qualified inspection and engineering judgment.
• Performance must be demonstrated on representative damage and healthy variability.

9. Limitations, governance and professional responsibility

Testing can be misleading when fixtures impose unintended constraints, sensors are placed at nonrepresentative locations, or data are selectively discarded. Research records should preserve raw data, calibration information, specimen history, software versions and deviations from the plan. Results that contradict a hypothesis are valuable and must not be suppressed.

Safety-critical testing requires documented hazard analysis, interlocks, containment, emergency shutdown and competency of personnel. Fatigue and fracture tests can release stored elastic energy suddenly. High-voltage instrumentation, rotating machinery, pressure systems and environmental chambers require appropriate controls.

Standards such as ISO/IEC 17025 provide principles for laboratory competence and traceability; ASTM, ISO and sector-specific standards define many test methods. A standard is not a substitute for engineering judgment: its scope, specimen validity and acceptance criteria must be checked.

AI-assisted SHM introduces additional governance concerns. Training data may be unrepresentative, labels may be uncertain, and a model may drift as the structure ages. Safety-relevant decisions require explainability appropriate to the risk, version control, cybersecurity, audit trails, human oversight and a defined fallback when the algorithm is uncertain. Data ownership and privacy also matter when monitoring connected industrial assets.

10. Contemporary developments and best practice

Current developments include distributed fibre-optic sensing, wireless low-power sensor networks, embedded piezoelectric transducers, robotic inspection, digital twins and physics-informed machine learning. These technologies can improve coverage and reduce manual inspection, but they introduce challenges in power management, synchronization, data volume, calibration stability and verification.

Best practice is to:

• begin with damage physics and a decision requirement;
• calibrate the complete measurement chain, not only the sensor;
• document bandwidth, sampling, filtering and synchronization;
• use redundancy and independent validation for critical conclusions;
• separate training, validation and test data in data-driven SHM;
• quantify uncertainty and report limitations;
• test under realistic environmental and operational variation;
• combine monitoring with scheduled inspection and maintenance procedures;
• maintain configuration control for hardware, software and algorithms.

Chapter Summary

Experimental mechanics links physical measurement with mechanical theory, numerical modelling and design decisions. Reliable experimentation requires a clearly defined measurand, appropriate transducer, calibrated measurement chain, suitable sampling and explicit uncertainty analysis. Strain gauges, load cells, displacement sensors, accelerometers, optical methods and acoustic sensors each have characteristic ranges and limitations.

Static, dynamic, fatigue and fracture tests answer different questions and rely on different assumptions. Linear vibration models support modal interpretation, while fracture mechanics and fatigue relations are valid only within their stated regimes. Structural health monitoring extends testing into service by detecting, localizing, classifying and assessing changes in structural condition. Model-based and data-driven approaches are complementary, but both must address environmental variability, false alarms, sensor failure and uncertainty.

A professional test programme is therefore a controlled argument from evidence. It preserves traceability, protects personnel, validates models without overclaiming, and uses monitoring as a support for—rather than a replacement for—sound engineering judgment and qualified inspection.

Key Terms

Experimental mechanics: Study of mechanical behaviour through controlled observation and measurement.

Measurand: Quantity intended to be measured.

Transducer: Device that converts a physical quantity into a usable signal.

Calibration: Establishment of the relationship between instrument indication and reference values.

Sensitivity: Change in output per unit change in input.

Resolution: Smallest distinguishable change in the measured quantity.

Strain gauge: Resistive sensor used to measure mechanical strain.

Digital image correlation: Optical method that estimates displacement and strain from image patterns.

Aliasing: False frequency representation caused by inadequate sampling.

Uncertainty: Quantified doubt associated with a measurement result.

Modal analysis: Identification of natural frequencies, damping and mode shapes.

Fatigue: Progressive damage caused by repeated or fluctuating loading.

Stress-intensity factor: Crack-tip parameter used in linear elastic fracture mechanics.

Structural health monitoring: Repeated observation and assessment of structural condition during service.

Damage detection: Determination of whether a structural change or defect exists.

Model updating: Adjustment of model parameters using experimental observations.

False alarm: Indication of damage when the structure is healthy.

Probability of detection: Probability that a specified damage state will be detected.

Digital twin: Computational representation updated using data from a physical asset.

Traceability: Documented linkage of measurements to recognized standards.

Review Questions

Short Answer Questions

1. Distinguish accuracy, precision and resolution in experimental measurement.
2. State the assumptions behind the quarter-bridge strain relation.
3. What is aliasing, and how is it controlled?
4. Differentiate passive and active structural health monitoring.
5. Why must environmental variability be considered in operational SHM?

Long Answer Questions

1. Explain the complete measurement chain for a strain-based structural test, including calibration and uncertainty sources.
2. Compare static, dynamic, fatigue and fracture testing in terms of objectives, measurements and principal limitations.
3. Derive the natural frequency and damping-ratio expressions for a linear single-degree-of-freedom system and discuss their experimental interpretation.
4. Explain model-based and data-driven SHM, including the conditions under which each may fail.
5. Design a test programme for validating a finite-element model of a mechanically loaded bracket.

Analytical / Application Questions

1. A full-scale component is instrumented with strain gauges and accelerometers, but measured modal frequencies change with temperature even when inspection shows no damage. Propose a diagnostic procedure to separate environmental effects from damage.
2. A fatigue test applies 40,000 cycles at a stress level for which life is 200,000 cycles and 20,000 cycles at a second level for which life is 100,000 cycles. Calculate the linear cumulative damage estimate and discuss why the result should not be treated as a universal failure prediction.
3. Develop a sensor layout and alert strategy for detecting loosening of a bolted joint in a vibrating machine. Justify sensor type, location, sampling, baseline data and validation tests.

Multiple Choice Questions with Answers

Question 1

For a quarter-bridge strain-gauge circuit under small-strain conditions, the approximate output relation is:

A. V_o/V_e = Gε

B. V_o/V_e ≈ Gε/4

C. V_o/V_e ≈ 4Gε

D. V_o/V_e = ε/G

Correct Answer: B. V_o/V_e ≈ Gε/4

Question 2

A signal contains frequencies up to 2 kHz. Which sampling frequency satisfies the basic Nyquist condition?

A. 1 kHz

B. 2 kHz

C. 3 kHz

D. More than 4 kHz

Correct Answer: D. More than 4 kHz

Question 3

In the linear SDOF vibration model, the undamped natural circular frequency is:

A. √(m/k)

B. k/m

C. √(k/m)

D. c/(2m)

Correct Answer: C. √(k/m)

Question 4

Which SHM level identifies the region in which damage has occurred?

A. Detection

B. Localization

C. Classification

D. Prognosis

Correct Answer: B. Localization

Question 5

The stress-intensity relation K_I = Yσ√(πa) is primarily associated with:

A. Linear elastic fracture mechanics

B. Thermal conduction

C. Plastic collapse theory only

D. Signal quantization

Correct Answer: A. Linear elastic fracture mechanics

Question 6

A 12-bit ideal converter has a full-scale span of 10 V. Its nominal quantization step is closest to:

A. 0.244 mV

B. 2.44 mV

C. 24.4 mV

D. 244 mV

Correct Answer: B. 2.44 mV

Question 7

In a fatigue damage estimate D = ∑n_i/N_i, n_i denotes:

A. The material modulus

B. The applied cycles at level i

C. The critical stress intensity

D. The measured crack length

Correct Answer: B. The applied cycles at level i

Question 8

A high value of frequency-response coherence generally indicates:

A. A strong measured linear relationship under the test conditions

B. That damage is definitely present

C. That all noise has been eliminated

D. That the finite-element model is exact

Correct Answer: A. A strong measured linear relationship under the test conditions

Question 9

Which method provides non-contact, full-field displacement information from images?

A. LVDT measurement

B. Digital image correlation

C. Piezoelectric pressure measurement

D. Resistance thermometry

Correct Answer: B. Digital image correlation

Question 10

For independent inputs, the covariance terms in a first-order uncertainty combination are:

A. Always dominant

B. Equal to one

C. Zero

D. Negative by definition

Correct Answer: C. Zero