Determination of the complex moduli of viscoelastic structural elements by resonance and non-resonance methods

Abstract

The successful prediction of the vibration transmissibility characteristics of viscoelastic structural elements is strongly dependent upon the use of fairly accurate estimates of the complex moduli, which are frequency and temperature dependent functions. Two methods, namely the standing wave resonance and the non-resonance (dynamic stiffness) methods, which are based on longitudinal forced vibration procedures, are used to investigate frequency and temperature dependent characteristics of the complex Young's modulus of a composite viscoelastic pipe. It is shown that in the case of the standing wave resonance method, the use of the simple classical frequency equation for the determination of the complex modulus of a viscoelastic prismatic element from the modal values of frequency and transmissibility results in an absolute error of less than 8% for loss factors of up to 0·4. Also, it is shown that as the loss factor increases the number of modes for which the classical frequency equation is applicable decreases and criteria for establishing the range of validity of the classical frequency equation are described. Complex moduli data obtained from experimental tests are then used with the method of reduced variables to produce master curves and equations of reduced dynamic Young's modulus and loss factor which cover many decades of frequency.