Abstract
An online algebraic estimation technique for natural and forcing frequencies for a class of uncertain and lumped-parameter vibrating mechanical systems with n degrees of freedom is described. In general, realistic vibrating systems can be affected by unknown exogenous excitation forces with multiple and independent frequency harmonic components. Hence, natural frequencies as well as excitation force frequencies can be simultaneously computed from an algebraic approach into a small interval of time during online operation of the mechanical system. Measurements of an available output signal, associated with some specific degree of freedom, are only required for frequency estimation in time-domain. Information on mass, stiffness and damping matrices are not necessary for multifrequency estimation algorithms. Some analytical, numerical and experimental results on a cantilever Euler–Bernoulli beam are described to show and validate the acceptable estimation of multiple frequencies in forced multiple degrees of freedom vibrating systems.
Highlights
Several techniques for mainly offline modal parameter identification on vibrating mechanical systems have been proposed [1,2,3,4,5]
Fast Fourier Transform (FFT), spectral estimation, Kalman filtering, linear regression, least squares and zero-crossing techniques have been applied for estimation of frequency parameters in oscillating signals [6,7,8]
Some popular experimental modal analysis techniques based on Frequency Response Functions (FRF) are peak picking, mode-picking, circle-fit and curve fitting [1,2]
Summary
Several techniques for mainly offline modal parameter identification on vibrating mechanical systems have been proposed [1,2,3,4,5]. Real-time information on natural frequencies and/or excitation force frequencies can be used to implement efficient vibration control schemes in a wide variety of vibration engineering systems [18,19,20] In this context, active vibration control on flexible smart structures, based on modal control techniques, requires information on the existing natural frequencies with a reasonable accuracy [20]. In contrast with other parameter identification techniques, in this multifrequency estimation approach natural and excitation frequencies are computed from an algebraic approach, online, in time-domain and using information of some simple and measurable signal. A novel algebraic technique for online estimation in time-domain of multiple natural frequencies for an important class of forced and uncertain lumped-parameter vibrating mechanical systems of n degrees of freedom is proposed.
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