Vibration and Constitutive Relations of Viscoelastic Cantilever Beam of HTPB Propellant

Abstract

A cantilever beam test specimen of a viscoelastic material, which is sourced from the hydroxy-terminated polybutadiene (HTPB) propellant, has been made. The traditional experimental modal analysis (EMA) is performed using the SIEMENS TESTLAB software to obtain the first six orders of modal frequencies based on the Poly MAX method, thereby determining the frequency range associated with the frequency domain analysis. The relaxation modulus of this viscoelastic material is first measured using a thermo-viscoelasticity analyzer (DMA); subsequently, the relaxation modulus is adopted to fit the 19-parameter Prony series of conformational models that characterize this viscoelastic material. Sinusoidal frequency sweep is then conducted on the SIEMENS TESTLAB platform, and the corresponding measured signals are obtained. Using the finite element method, a transient analysis simulation of the experimental conditions is performed. The dynamic response of this viscoelastic material under sinusoidal frequency sweep is evaluated by comparing it with the experimental data. It is observed that the overall acceleration peak error and the finite element simulation result are less than 3%. This study verifies that the obtained static constitutive equation (19-parameter Prony series) can describe the dynamic responses at low frequencies (<80 Hz).