Zhikun Hou

An overview of vibration and seismic applications of NiTi shape memory alloy

Shape memory alloys (SMAs) exhibit peculiar thermomechanical, thermoelectrical and thermochemical behaviors under mechanical, thermal, electrical and chemical conditions. Examples of these materials are Cu-based SMAs, NiTi SMAs, ferrous SMAs, shape memory ceramics and shape memory polymers. NiTi SMAs in particular, have unique thermomechanical behaviors such as shape memory effect and pseudoelasticity, which have made them attractive candidates for structural vibration control applications. Numerous studies have been conducted in modeling and applications of NiTi SMAs in structural vibration control. Several active, passive and hybrid energy absorption and vibration isolation devices have been developed utilizing NiTi SMAs. In this paper we present an overview of NiTi behaviors, modeling and applications as well as their limitations for structural vibration control and seismic isolation.

A Wavelet Packet Based Sifting Process and its Application for Structural Health Monitoring

This article presents an innovative wavelet packet based sifting process to decompose a signal into its components with different frequency contents by examining the energy content in the wavelet packet components of a signal and imposing certain decomposition criteria. A new method is illustrated for simulation data of a linear three-degree-of-freedom spring-mass-damper system and the results are compared with those obtained using the empirical mode decomposition (EMD) method. Both methods provide good approximations, as compared with the exact solution for modal responses from a conventional modal analysis and both show relatively greater errors at the beginning and ending parts of the signal due to the well-known end effects. A comparison study is also provided to illustrate differences between two sifting processes of the proposed approach and the EMD, by using a harmonic signal with a sweeping frequency and the impulse response of a linear single-degree-of-freedom system with viscous damping. Incorporated with the classical Hilbert transform, the proposed sifting process may be effectively used for structural health monitoring, including both detecting abrupt loss of structural stiffness and monitoring development of progressive stiffness degradation, as demonstrated by two case studies. Results from a preliminary study for experimental data from a shaking table test of a full-size two-story wooden building structure are also presented to show great promise of the proposed method in practical applications of health monitoring of real structures.

Using NiTi SMA tendons for vibration control of coastal structures

Hurricane damage inflicted upon coastal structures, particularly residential structures, results in millions of dollars in financial damage and loss of life each year. A major cause of this damage usually begins with roof uplifts of coastal structures; prevention of roof uplift helps mitigate damage to coastal structures by hurricanes. Development of more effective fastening mechanisms for the connections between the walls and the roofs of these structures will aid in damage reduction to coastal structures. Recent developments in the new field of auto-adaptive materials offer promising opportunities for developing radically new fastening mechanisms. One of the classes of materials in this category is shape memory alloys (SMAs). SMAs are very attractive for structural application because of their major constitutive behaviors such as pseudoelastic characteristics. The pseudoelastic behavior of NiTi SMAs is a unique hysteretic energy dissipation behavior which, combined with a very long fatigue life, makes NiTi a viable candidate for developing new fasteners. However, as a first step it is important to develop an in-depth understanding of NiTi behavior under dynamic loads. Research carried out in this area has been very limited in scope. Therefore, in this paper, eight different configurations of bracing systems, divided into two categories, are explored on a single degree of freedom (SDOF) structure to investigate the feasibility of developing devices for the mitigation of hurricane damage. These bracing devices basically utilize the hysteretic energy dissipation of NiTi resulting from its pseudoelastic characteristic. Since the main goal of this ongoing research is to develop a thorough understanding of the pseudoelastic and hysteretic behavior of SMAs under severe dynamic loading/excitation, a series of earthquake data has been considered as the source of excitation. Through this analysis both the damping and stiffening characteristics of NiTi wires and the effect of these dynamic characteristics on changing the dynamic response of the structure are studied. In the first category the NiTi wires are not pre-strained, while in the second category they are pre-strained. In each category, four different combinations of wire length and modeling of pseudoelastic behavior of NiTi wire are considered. A bilinear stress-strain model is used for representing the pseudoelastic behavior of NiTi tendons, capable of representing internal yield, internal recovery and trigger line concepts. This study establishes that hybrid tendons have the highest damping and stiffening effects on the structure. It is also concluded that, when the amplitude of excitation is small, tendons act as stiffening devices. Once the amplitude of the excitation is large enough to initiate stress-induced phase transformations, tendons act as energy absorption devices. These findings provide very useful information for the development of more effective fastening devices that can withstand severe dynamic loads, such as hurricane loadings.

Stability and Performance of Feedback Control Systems with Time Delays

Abstract This paper investigates the time delay effects on the stability and performance of active feedback control systems for engineering structures. A computer algorithm is developed for stability analysis of a SDOF system with unequal delay time pair in the velocity and displacement feedback loops. It is found that there may exist multiple stable regions in the plane of the time delay pair, which contain time delays greater than the maximum allowable values obtained by previous studies. The size, shape and location of these stable and unstable regions depend on the system parameters and the feedback control gains. For systems with multiple stable regions, the boundaries between the stable and unstable regions in the plane of the time delay pair are explicitly obtained. The delay time pairs that forms these boundaries are called the critical delay time pairs at which the steady-state response becomes unbounded. The conclusions are valid for both large and small delay times. For any system with multiple stable regions, preliminary guidelines obtained from an explicit formula are given to find the desirable delay time pair(s). When used, these desirable delay time pair(s) not only stabilize an unstable system with inherent time delays, but also significantly reduce the system response and control force. For any system with multiple stable regions, these desirable delay time pair(s) are above the maximum allowable delay times obtained by previous studies. Numerical results, for both steady-state and transient analysis, are given to investigate the performance of delayed feedback control systems subjected to both harmonic and real earthquake ground motion excitations.

Vibration Suppression of Structures Using Passive Shape Memory Alloy Energy Dissipation Devices

The paper presents a preliminary study on feasibility using shape memory alloy (SMA) passive devices for vibration suppression of building structures. A one-story prototype-building model is used. The structure is subjected to a base excitation and is strengthened by SMA diagonal bracing wires. Constitutive behavior of SMA wires used in the study was experimentally characterized to properly model the SMA super- or pseudoelastic material properties and results were compared with the numerical simulation based on theoretical SMA constitutive models by Lexcellent and Bourbon ((1996). Thermodynamical model of cyclic behavior of Ti-Ni and Cu-Zn-Al shape memory alloys under isothermal undulated tensile tests. Mechanics of Materials, 24: 59-73) and Brinson ((1993). One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. Journal of Intelligent Material Systems and Structures, 4: 229). The Single-degree-of-freedom structural system was also experimentally calibrated to determine the structural parameters. Both the experimentally calibrated structural model and SMA constitutive model were then employed in numerical simulation to predict dynamic response of the building structure with SMA bracing wires subjected to a base input and results showed a good agreement with experimental data. The results were also compared with both cases of conventional steel bracing wires and no bracing at all. The results showed that SMA passive devices maybe effectively used to suppress vibration by introducing additional stiffness to shift the system natural frequency away from the resonance and/or providing additional energy dissipation by its superelastic hysteresis. The SMA damping is adaptive and is especially attractive for the case when the loading is random in nature. When an unexpected excitation causes excessive vibration, more energy will be dissipated through larger SMA superelastic hysteretic loops and therefore, the vibration will eventually be mitigated. Numerical simulation also showed that the SMA device dissipated more energy than the viscous damping in the case studied.

Modeling and random vibration analysis of SDOF systems with asymmetric hysteresis

This study focuses upon SDOF systems having non-linear, hysteretic stress-strain behavior which is asymmetric about the initial linear elastic relationship. Differences between tensile and compressive strength witnessed in various materials, particularly in the unique stress-strain properties of the shape-memory alloy Nitinol, motivate the need for mathematical models capable of simulating asymmetric response. Two models are presented, and the specific capabilities of each are explored. Both models follow the rate-type format of the Bouc-Wen model, and offer previously unavailable stress-strain relationships. Response statistics under Gaussian White Noise input are obtained using the method of equivalent linearization. For asymmetric systems, a need for non-zero-mean analysis is evident, even under zero-mean input.

First-passage study and stationary response analysis of a BWB hysteresis model using quasi-conservative stochastic averaging method

The quasi-conservative stochastic averaging (QCSA) method is applied to a Bouc-Wen-Baber hysteretic system (BWB) under Gaussian white noise excitations. The stationary probability density of the systems response amplitude and energy is obtained for different excitation levels and different damping ratios. These results are compared with the studies presented by Cai and Lin in A New Solution Technique for Randomly Excited Hysteretic Structures, Technical Report on Grant No. NCEER-88-0012, State University of New York, Buffalo, NY, 1988. The first-passage time problem for the hysteretic system is also studied using the method of QCSA. The results for the expected time to failure as a function of the initial total energy are shown, for different excitation levels and for different threshold values of energy. The relationship between the expected time to failure when initial total energy is zero and excitation level is shown for a wide range of hysteresis shape parameters.

Random vibration studies of an SDOF system with shape memory restoring force

Abstract Intelligent and adaptive material systems and structures have become very important in engineering applications. The basic characteristic of these systems is the ability to adapt to the environmental conditions. A new class of materials with promising applications in structural and mechanical systems is shape memory alloy (SMA). The mechanical behavior of shape memory alloys in particular shows a strong dependence on temperature. This property provides opportunities for the utilization of SMAs in actuators or energy dissipation devices. However, the behavior of systems containing shape memory components under random excitation has not yet been addressed in the literature. Such a study is important to verify the feasibility of using SMAs in structural systems. In this work a nondeterministic study of the dynamic behavior of a single-degree-of-freedom (SDOF) mechanical system, having a Nitinol spring as a restoring force element is presented. The SMA spring is characterized using a one-dimensional phenomenological constitutive model based on the classical Devonshire theory. Response statistics for zero mean random vibration of the SDOF under a wide range of temperature is obtained. Furthermore, nonzero mean analysis of these systems is carried out.

SPECTRAL DENSITY OF A NON-LINEAR SINGLE-DEGREE-OF-FREEDOM SYSTEM'S RESPONSE TO A WHITE-NOISE RANDOM EXCITATION: A UNIQUE CASE OF AN EXACT SOLUTION

Abstract A SDOF vibro-impact system with a one-sided rigid barrier is considered for the case of a perfectly elastic impact and stationary zero-mean Gaussian white-noise excitation. Special piece-wise-linear transformation of the systems state variables is applied, which effectively reduces the original problem to one without impacts. Moreover, for the special case, where position of the barrier coincides with that of the systems static equilibrium, the transformed equation of motion is found to be linear, implying Gaussian transition probability densities of the transformed state variables. Thus, the non-linear random vibration problem is reduced to one with “inertialess” non-linearity only. The above transformation is used to obtain an exact explicit expression for the response autocorrelation function, thus leading to quadrature expression for spectral density of the response.

A stationary model for periodic excitation with uncorrelated random disturbances

Abstract The paper presents a stationary model for periodic excitations with random amplitude and phase disturbances for linear and nonlinear random vibration analysis. The disturbances are modeled as uncorrelated stationary white noise processes. Application of the model is demonstrated by stationary moment response of a linear single-degree-of-freedom system subject to such excitations. To find moment responses, an equivalent augmented system subject to parametric white noise excitations under certain constraint conditions is studied. Numerical results for the second and fourth-order moment responses are presented. The probability density function of the response is calculated based on thhe cumulant-neglect closure method. NonGaussianity of the response is discussed in terms of the excess factor. The results show that the random amplitude disturbance can significantly increase system moment response. The random phase modulation may increase or reduce the system moment response, depending on the value of relative detuning berween the system natural frequency and the mean excitation frequency. The response may become Gaussian in the sense of up to the fourth-order moment for sufficiently large random phase or relative detuning.