The electromechanical analogy method for characterization of the rheological properties of polymer materials

Abstract

Three-parameter and four-parameter models of mechanical systems were analyzed to assess the physicomechanical properties of polymer materials. An electromechanical analogy method was developed for characterizing the physicomechanical properties of polymer and fibre materials; one feature of the method is the physical directivity, i.e., representation of the elements of mechanical systems in the form of equivalent electrical circuits. The quadrupole method was used for creating electrical models of the mechanical systems examined, which consisted of elastic, inertial, and friction elements.Let us consider the widely used Frenkel mechanical model proposed in [1]. Spring e 2 models the elasticity of a fibre, the parallel connection of spring e 1 and damper S t1 models the elasticity, while damper S t2 models the plasticity.According to the well-known rules of equivalent transformation of elements, we determine the complex modulus of elasticity for the model indicated above:1/e(p) = 1/e 2 (p) + 1/(e 1 + S ò1 ð) + 1/(S ò2 ð); e(p) = e 2 S ò2 (ð)(å 1 + S ò1 ð)/[S ò1 S ò2 ð 2 + (å 1 S ò2 + å 2 S ò2 + å 2 S ò1 )ð + å 1 å 2 ].Dividing the numerator and denominator in the last relation by e 1 e 2 and introducing the notation T 1 = S t1 /e 1 , T 2 =

A novel adjustable magnetorheological fluid gradient material of low frequency vibration isolation: a theoretical and experimental study

“…Therefore, a set of differential equations based on the micro-mechanical model of MRF cannot solve the mechanical impedance of the adjustable gradient material constituted by MRF under the action of the TMF. In contrast, the differential equations can be transformed into algebraic equations through the machine-electric analogy theory, which can significantly simplify the process of solving the mechanical impedance [36,37]. Although the mechanical vibration of a mechanical system and the electromagnetic oscillation of an electrical system are different physical phenomena, they have the same manifestation mathematically.…”