Laboratory for Dynamics of Machines and Structures 
Strain Experimental Modal Analysis of an Euler-Bernoulli Beam Based on the Thermoelastic Principle
 K. Zaletelj, J. Slavič, J. Šonc and M. Boltežar
Mechanical systems and signal processing, 2023

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More research on: optical methods, vibration fatigue,
The strain mode shapes can be utilized as an indicator of vibration fatigue-hotspots and are utilized for predicting the distribution of damage intensity. However, the conventional approach for measurement, which involves using strain sensors, does not offer the necessary high spatial density required for accurately identifying critical locations or creating a comprehensive map of damage intensity. Non-contact methods have been employed to indirectly determine the full-field strain shapes, but when measuring kinematic quantities, a relation between kinematics and stress/strain must be known. For Euler-Bernoulli beam, the double spatial derivative is required which introduces a significant uncertainty. In contrast, by leveraging the thermoelastic principle, the full-field stress/strain response of an arbitrary structure can be directly measured using a high-speed infrared (IR) camera. The thermoelastic principle has not been extensively researched for strain experimental modal analysis (EMA). In this study, the hybrid EMA (based on one high-dynamic range sensor) was researched for thermoelastic identification of an Euler-Bernoulli beam. The minimum stress/temperature variation required to achieve accuracy comparable to scanning-laser kinematics-based strain mode shapes was investigated. The findings demonstrate that even when the noise floor is significantly higher than the signal, full-field strain mode shapes can be identified using IR cameras and the hybrid EMA method. By considering the minimum stress/temperature variation determined in this research (for aluminum and steel), the accuracy of thermoelasticity-based strain shapes can be evaluated during the experiment-design stage. While this research is theoretically and experimentally based on Euler-Bernoulli beam, generalization of the thermoelastic principle to arbitrary structure is feasible.


Klemen Zaletelj, PhD

  Ladisk, Faculty of Mechanical Engineering, University of Ljubljana
  +386 1 4771 228
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Janko Slavič, PhD

  Ladisk, Faculty of Mechanical Engineering, University of Ljubljana
  +386 1 4771 226
jankoslavic     jankoslavic    
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Miha Boltežar, PhD

  Ladisk, Faculty of Mechanical Engineering, University of Ljubljana
  +386 1 4771 608
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