Experimental Identification of Nonlinearities under Free and Forced Vibration using the Hilbert Transform

Abstract

In this paper we discuss the experimental identification of a nonlinear vibrating mechanical system. The system under test incorporated several spring and damping related nonlinearities. Indeed, in this paper we use data from a real laboratory device thus increasing the confidence in the proposed methods that have been previously applied mostly to simulated data. A unique feature of the identified model is that it shows the dependency of the estimated parameters on the vibration amplitude. The provided measurements of free and forced vibration motion, together with the unique signal processing, based on the Hilbert transform analysis, yield an accurate estimation of nonlinear spring and friction parameters of the vibration model. The obtained natural frequencies and friction parameters are functions rather than scalars that describe the system’s behavior under different operating conditions. This paper complements previously published Hilbert transform analytical methods with experimental and numerical results.

Xác định tham số dao động của dầm bằng phương pháp Rayleigh

“…Năm 2008, P. Frank Pai cùng cộng sự [8] trình bày xử lý tín hiệu phi tuyến trên cơ sở biến đổi Hilbert Huang để xác định hệ động lực học tham số và không tham số. Năm 2009, M. Feldman cùng cộng sự [9] sử dụng biến đổi Hilbert kết hợp với dao động cưỡng bức và dao động tự do để xác định tham số hệ phi tuyến. Năm 2010, H.A.…”

A Stepped Frequency Sweeping Method for Nonlinearity Measurement of Microresonators

“…Combining with SSA, the procedure of FREEVIB algorithm is modified as follows:

Calculate the instantaneous amplitude A ( t ) and the instantaneous phase θ ( t ) from the free vibration signal x ( t ) by the Hilbert transform: $A(t)=\sqrt{x^2(t)+{\tilde{x}}^2(t)};\theta (t)=\arctan (\stackrel{false^}{x}(t)/x(t));$

Figure out the instantaneous frequency f ( t ) after the differential operation on θ ( t ), and the expression is f ( t ) = 0.5 π −1 dθ ( t )/ dt . The estimation of IA and IF, indicated by A ( t ) SSA and f ( t ) SSA respectively, are obtained by processing A ( t ) and f ( t ) with SSA algorithm.

Compute the normalized damping coefficient h ( t ) by A ( t ) SSA , f ( t ) SSA and their derivatives [19]. f estd ( t ) is figured out by the above mentioned parameters, and the FRF curve is further obtained.…”

“…Compute the normalized damping coefficient h ( t ) by A ( t ) SSA , f ( t ) SSA and their derivatives [19]. f estd ( t ) is figured out by the above mentioned parameters, and the FRF curve is further obtained.…”

A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges

“…Time-frequency methods, e.g., those based on continuous wavelet transform (CWT), are powerful tools used in applications such as vibration absorbers that are broadly used in naval architecture, rotor-bearing systems, and constructions [ 62 ]. In addition, HT was employed in applications such as unbalance of rotating machines, ship movement control, and damage detection of RC beams based on free vibration measurements for nonlinear damping determination [ 63 ]. Modal methods are considered particularly useful in the field of structural dynamics and damage identification.…”