Hysteretic Stiffness Research Articles

Identification of the stick and slip motion between contact surfaces using artificial neural networks

The paper presents work related to nonlinear system parameters identification. The research is focused on systems with hysteretic stiffness characteristics. The identification procedure is developed with use of artificial neural networks. The presented method assumes two separate clusters of neural networks, which are supported by additional signal processing block. Such approach gives an advantage over the conventional identification methods due to its small restrictions. The validation process considers structural responses in time and frequency domains as well as the restoring force plane of the dynamic structure. First, verification of the identification method is performed on the numerical simulation of the system with hysteretic stiffness. Next, the identification of the real dynamic system with contact-related nonlinearity is carried out. The steel samples with contacting surfaces were used in the experiment. Electromagnetic shaker was used to excite the structure and enforce a relative shear motion between surfaces in contact. The system response was recorded using the Polytec laser vibrometer.

Nonstationary Seismic Responses of Nonlinear Structural Systems to Modulated Earthquake Excitations

AbstractA simple structure under earthquake ground motion is modeled as single-degree-of-freedom systems with nonlinear or hysteretic stiffness subjected to modulated Gaussian white noise excitatio...

Experimental investigation of hysteretic stiffness related effects in contact-type nonlinearity

The paper presents experimental works related to contact nonlinearities. The research is focused on effects derived from hysteresis stiffness characteristics and vibro-impacts generated during the relative movement of two surfaces. The modeling of the contact nonlinearities was divided in two parts. First, the parameters of the system were identified based on modal analysis test. Next, the model was created and verified with experimental data. The experimental works were performed on steel samples with prepared contact surfaces. Electromagnetic shaker was used to produce relative motion between surfaces in contact. The response of the system was acquired by noncontact laser vibrometer. Both displacement and velocity of vibration were measured. Additionally, the impedance head measures the force and acceleration. The experimental data were used to validate the created models.

Nonlinear Control Algorithm for Improving Settling Time in Systems With Friction

A nonlinear control algorithm that greatly reduces settling time in precision instruments with rolling element bearings is proposed. Reductions of 80.5%-87.4% in settling time were achieved when settling to within 3-100 nm of the commanded position. Final settling of such systems is typically impacted by the nonlinearity in the pre-rolling friction regime, which manifests as a hysteretic stiffness. Consequently, the integral term in the controller can take a long time to respond. In this paper, a nonlinear integral action settling algorithm is presented. The nonlinear integral gain takes the form of a Dahl friction model. Since the integral gain mimics hysteretic stiffness, the output of the integral control term is instantaneously set to a large value after each direction change, greatly improving settling response. A nearly first-order error dynamic results, which has a user-definable time constant. Before the algorithm can be implemented, the Coulomb friction and initial contact stiffness in the Dahl model must be experimentally determined for the stage. A sensitivity study is performed on the initial contact stiffness, which was found in other works to dictate the stability of the algorithm.

Structural Performance of Typical Beam-Column Joints in Yingxian Wood Pagoda - An Experimental Study

Yingxian Wood Pagoda, built in 1056, is located in the town of Yingxian County, Shanxi Province, China. It is the oldest and highest standing ancient wood structure in China. The pagoda is octagon-shaped in plan, with a total height of 67.31m and a base diameter of 30.27m. It appears as a five-storeyed structure, but actually consists of nine storeys, with four shorter but stiffer storeys hidden between the five apparent storeys. Yingxian Wood Pagoda was built without any metal connectors like nail, screw, or bolt. Instead, Tenon-Mortise connections and Dou-Gong brackets were used to connect all posts and beams. Tenon-Mortise connections and Dou-Gong brackets have been playing a vital role for the pagoda to resist severe winds, earthquakes and some human-induced disasters for nearly a thousand years. To evaluate the safety of the pagoda, it is, therefore, useful to investigate the structural performance of the beam-column joints, most important for Yingxian Wood Pagoda to resist lateral load. In this study, two models of typical beam-column joints of the pagoda, MBCJ-I and MBCJ-II, were manufactured following a ratio of 3.4 to the prototype of the joints. Non-destructive cyclic loading test of the models under different vertical load and destructive cyclic test of the models under vertical load of 20kN were conducted. The hysteretic stiffness of MBCJ-I was lager than MBCJ-II, and increased linearly with vertical load N. The relationship between and N was obtained by regression of the test results using the least square method. The stiffness of model joint under vertical load was 70.6kN/mm. The failure modes, energy-dissipation performance, moment resistance and bending stiffness of both model joints were derived and discussed.

Small and Large Displacement Dynamic Analysis of Frame Structures Based on Hysteretic Beam Elements

In this work, a beam element is proposed for the nonlinear dynamic analysis of frame structures. The classical Euler-Bernoulli formulation for the elastic beam is extended by implicitly defining new hysteretic degrees of freedom, subjected to evolution equations of the Bouc-Wen type with kinematic hardening. A linear interpolation field is employed for these new degrees of freedom, which are regarded as hysteretic curvatures and hysteretic axial deformations. By means of the principle of virtual work, an elastoplastic hysteretic stiffness relation is derived, which together with the hysteretic evolution equations fully describes the behavior of the element. The elemental stiffness equations are assembled to form a system of linear global equations of motion that also depend on the introduced hysteretic variables. The solution is obtained by simultaneously solving the entire set of governing equations, namely the linear global equations of motion with constant coefficient matrices, and the nonlinear local ...

Control of uncertain non-linear systems via adaptive backstepping

Models of physical non-linear systems are prone to different kinds of uncertainties. This paper presents a backstepping-based adaptive control designed for a class of one degree-of-freedom uncertain non-linear systems. The true system does not need to be known for the control design. A functional description is assumed with uncertain coefficients and an uncertain residual function. These uncertainties are bounded and lump the discrepancies between the adopted description and the real behaviour. The adaptive controller is able to handle these uncertainties and make the closed loop globally uniformly ultimately bounded when the system is subject to an unknown excitation from which a bound is known. One goal is that the transient and asymptotic performances depend explicitly on the design parameters. This feature of the control scheme establishes the main difference with other control methods used to control non-linear systems, in particular chaotic systems. The efficiency of the approach is tested by numerical simulations on Duffing oscillators and systems with non-linear and hysteretic stiffness under external loads.