Analogy between dynamics of thermo-rheological and piezo-rheological pendulums

Abstract

The constitutive stress-strain relations of the standard thermo-rheological and piezo-rheological hereditary element in differential form as well as in two different integro-differential forms are defined. The considered problem of a thermo-rheological hereditary discrete system nonlinear dynamics in the form of thermo-rheological double pendulum system with coupled pendulums gets the significance of two constrained bodies in plane motion problem, as a problem important for studying a sensor dynamics or actuator dynamics in active structure dynamics. System of the averaged equations in the first approximation for amplitudes and phases are derived and qualitatively analyzed. Analogy between nonlinear dynamics of the double pendulum systems with thermo-rheological and piezo-rheological properties between pendulums is pointed out.