A robust damage detection method based on multi-modal analysis in variable temperature conditions

•Robust, reliable and insensitive to temperature changes, damage detection method.•Beams with fixed-fixed ends and elastic constrains boundary conditions.•Developing temperature dependent coefficients to calculate natural frequency in variable temperatures.•Mathematical expressions to cancel the effect of temperature on the frequency shift. This paper proposes a method, based on multi-modal analysis, which permits assessing damages in beams subjected to axial forces induced by temperature changes. The effect of temperature is eliminated by employing adjustmentcoefficients, individually developed for each mode of vibration. If the beam is supported by elastic supports, these coefficients consider also the relative displacement at the beam ends. These coefficients can be used for the intact beam, as well as, for the beam with transverse cracks. Predictive models describing the vibration behavior of beam-like structures in healthy and damaged states are developed based. Numerical simulations and experimental tests were completed on beams with fixed ends to check the practical applicability of the proposed method in variable temperature conditions. The results validate the developed method that employs adjusting coefficients, which can be used for perfectly clamped beams, even if restraints allow a small longitudinal displacement.