Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

Abstract

The nonlinear model of torsion pendulum is presented by considering the nonlinear damping force and nonlinear restoring force. The analytic solution of the nonlinear model is calculated to analyze the relationship between the characteristics of torsion pendulum and the nonlinear factors. The instantaneous characteristics of nonlinear torsion pendulum are analyzed by instantaneous undamped natural frequency and instantaneous damping coefficient. The instantaneous characteristics can be used for the parameter estimation of nonlinear torsion pendulum system. The nonlinear characteristics of the torsion pendulum are validated by the torsion pendulum based on the air-hovered turntable. The parameter estimation method based on the instantaneous characteristics is validated by the moment of inertia measurement system based on the torsion pendulum.

Inertia property determination by spectrum analysis of damped oscillation detection signal

“…IET Science, Measurement & Technology published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology ing use of the fact that the MoI about the torsion axis is proportional to the square of the oscillation period. Although a high-precision torsion pendulum measuring system is usually equipped with an advanced air bearing for the torsion rod, which significantly reduces the frictional damping of the bearing [27], the influence of air resistance caused by the complex shape of the measured object and internal damping of the torsion rod still cannot be ignored [28]. Furthermore, the use of air bearing greatly increases the complexity of the measurement system and the economic cost of measurement.…”

“…When using empirical mode decomposition (EMD) algorithm [35] to denoise the detection signal, the damped torsional oscillation component can be regarded as a typical intrinsic mode functions (IMF) component. Therefore, the EMD algorithm is commonly used to pre‐process the oscillation detection signal [28]. However, the EMD algorithm often fails to achieve ideal denoising, as do some improved mode decomposition algorithms.…”

Duality of Complex Systems Built from Higher‐Order Elements

“…The system can therefore be described by the set of charge-type equations of motion ( 16), ( 17), ( 32), (33), and (34). However, it seems that we cannot derive from them a single explicit differential equation such as in the case of the voltage-controlled elements in Section 3.1 (see the TIF-type equation ( 24)).…”

“…Note that the methodology of drawing up equations of motion of systems built from HOEs, described in Section 4, can conversely be used for the synthesis of the so-called predictive models of systems or phenomena of most varied nature from HOEs as the building blocks [30]. For example, the nonlinear equation of motion of torsion pendulum from [33] is…”

A spatial–temporal analysis approach for flutter predictions using decoupled and fully-coupled methods

“…In addition, the classical peak-based log-dec has been shown to be less accurate and not desirable for certain nonlinear configurations [19]. To overcome this problem, the time-varying characteristics are used by some researchers to estimate the nonlinear system [20,21], although these methods do not provide information of the locally spatial characteristics.…”