In this stud y, we attempt to analyse free nonlinear vibrations of buckling in laminated composite beams. Two new methods are applied to obtain the analytical solution of the nonlinear governing equation of the problem. The effects of different parameters on the ratio of nonlinear to linear natural frequencies of the beams are studied. These methods give us an agreement with numerical results for the whole range of the oscillation amplitude.
The acoustic properties of the sitar string are studied with the aid of a physical model. The nonlinearity of the string movement caused by the bridge acting as an obstacle to the vibrating string is of special interest. Comparison of the model's audio output to recordings of the instrument shows interesting similarities. The effects dispersion and bridge have on the sound of the instrument are demonstrated in the model.
This paper presents experimental observation of nonlinear vibrations in the response of a flexible cantilever beam to transverse harmonic base excitations around its flexural mode frequencies. In the experimental setup, instead of manual control of the signal excitation frequency and amplitude, a closed-loop vibration system is used to keep the excitation amplitude constant during the frequency sweep and to increase confidence in the experimental results. The experimental results show the presence of the third mode in the response when varying the excitation frequency around the fourth mode. The frequency-response curves, response spectrum and Poincaré plots were used for characterization of nonlinear dynamic behaviour of the beam.
Active Noise Control (ANC) of noise transmitted through a vibrating plate causes many problems not observed in classical ANC using loudspeakers. They are mainly due to vibrations of a not ideally clamped plate and use of nonlinear actuators, like MFC patches. In case of noise transmission though a plate, nonlinerities exist in both primary and secondary paths. Existence of nonlinerities in the system may degrade performance of a linear feedforward control system usually used for ANC. The performance degradation is especially visible for simple deterministic noise, such as tonal noise, where very high reduction is expected. Linear feedforward systems in such cases are unable to cope with higher harmonics generated by the nonlinearities. Moreover, nonlinearities, if not properly tackled with, may cause divergence of an adaptive control system. In this paper a feedforward ANC system reducing sound transmitted through a vibrating plate is presented. The ANC system uses nonlinear control filters to suppress negative effects of nonlinearies in the system. Filtered-error LMS algorithm, found more suitable than usually used Filtered-reference LMS algorithm, is employed for updating parameters of the nonlinear filters. The control system is experimentally verified and obtained results are discussed.
Vibrating plates can be used in Active Noise Control (ANC) applications as active barriers or as secondary sources replacing classical loudspeakers. The system with vibrating plates, especially when nonlinear MFC actuators are used, is nonlinear. The nonlinearity in the system reduces performance of classical feedforward ANC with linear control filters systems, because they cannot cope with harmonics generated by the nonlinearity. The performance of the ANC system can be improved by using nonlinear control filters, such as Artificial Neural Networks or Volterra filters. However, when multiple actuators are mounted on a single plate, which is a common practice to provide effective control of more vibration modes, each actuator should be driven by a dedicated nonlinear control filter. This significantly increases computational complexity of the control algorithm, because adaptation of nonlinear control filters is much more computationally demanding than adaptation of linear FIR filters. This paper presents an ANC system with multiple actuators, which are driven with a single nonlinear filter. To avoid destructive interference of vibrations generated by different actuators the control signal is filtered by appropriate separate linear filters. The control system is experimentally verified and obtained results are reported.
In this paper, nonlinear free vibration analysis of micro-beams resting on the viscoelastic foundation is investigated by the use of the modified couple stress theory, which is able to capture the size effects for structures in micron and sub-micron scales. To this aim, the gov-erning equation of motion and the boundary conditions are derived using the Euler–Bernoulli beam and the Hamilton’s principle. The Galerkin method is employed to solve the governing nonlinear differential equation and obtain the frequency-amplitude algebraic equation. Final-ly, the effects of different parameters, such as the mode number, aspect ratio of length to height, the normalized length scale parameter and foundation parameters on the natural fre-quency-amplitude curves of doubly simply supported beams are studied.