S. Olutunde Oyadiji

Identification of cracks in beams with auxiliary mass spatial probing by stationary wavelet transform

This paper proposes a new approach based on auxiliary mass spatial probing by stationary wavelet transform (SWT) to provide a method for crack detection in beamlike structure. SWT can provide accurate estimation of the variances at each scale and facilitate the identification of salient features in a signal. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to the change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore, the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitate the identification and location of damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is difficult to locate the crack directly from the graphical plot of the natural frequency versus axial location of auxiliary mass. This curve of the natural frequencies can be decomposed by SWT into a smooth, low order curve, called approximation coefficient, and a wavy, high order curve called the detail coefficient, which includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams with auxiliary mass used are computed using the finite element method (FEM). Sixty-four cases are studied using FEM and SWT. The efficiency and practicability of the proposed method is illustrated via experimental testing. The effects of crack depth, crack location, auxiliary mass, and spatial probing interval are investigated. From the simulated and experimental results, the efficiency of the proposed method is demonstrated.

A mechanical model representation of the in vivo creep behaviour of muscular bulk tissue

In vivo mechanical properties of bulk tissue have not yet been explored sufficiently. One of the major problems researchers face is the lack of agreement between the constitutive models and the standardised methodologies for experimental studies. The object of this study was to obtain bulk modulus of the upper arm under relaxed and controlled contraction that was 25% of the maximum voluntary contraction. A new testing machine was designed to generate constant load on the upper arm and measure the deformation over time. This device is effectively a cuff that applies controllable pressure on a 47-mm wide band of the upper arm. Six different loads (10, 20, 30, 40, 50 and 60 kgf) were applied over a time of up to a maximum of 120 s. The deflection-time curves obtained show strongly non-linear responses of the bulk tissue. The non-linearity manifested by these deflection-time curves is in terms of both time- and load-dependency. A specific mechanical model was developed to represent the creep behaviour of the bulk tissue. The creep behaviour of the upper arm can be simulated by using four Voigt viscoelastic models in series. The three obvious soft tissues of the upper arm, namely skin, fat and muscle, were modelled in series. The effects of blood vessels and connective tissue were also modelled in series with the previous ones. A mechanical model would provide a more controlled method of studying the mechanical properties of the bulk tissue. The purpose of the current research, therefore, was to develop a mechanical model, which would predict the non-linear, viscoelastic behaviour of the human muscular bulk tissue.

Modal electromechanical optimization of cantilevered piezoelectric vibration energy harvesters by geometric variation

The design studies of cantilevered piezoelectric vibration energy harvesters have been focused on the optimization of the power output of rectangular cantilevered beam vibration energy harvesters. However, without clarifying the influences of the modal electromechanical coupling and mechanical behaviour clearly, the power outputs cannot be adequately optimized. In this article, a distributed parameter electromechanical model is used to predict the power output with resistive loads, and the parameters are derived using the finite element method. First, a parametric study is presented to investigate the effects of the two factors on the volumetric power of cantilevered vibration energy harvesters. Then, an optimization strategy is implemented to investigate the modal electromechanical coupling coefficient and mass ratio separately using geometric parameter study. Mass ratio represents the influences of modal mechanical behaviour on the power density directly. The findings indicate that the convergent and divergent tapered cantilevered and rectangular cantilevered beam designs with partial coverage of piezoelectric layer are able to generate higher electromechanical coupling coefficient than conventional rectangular cantilevered designs with full coverage. Besides, using convergent tapered cantilevered designs can actually decrease the power density significantly. Both using divergent tapered cantilevered structures and attaching reasonable extra masses with varied locations on vibration energy harvesters can generate larger power density.

Mathematical modeling, analysis, and design of magnetorheological (MR) dampers

Most magnetorheological (MR) fluid dampers are designed as fixed-pole valve mode devices, where the MR fluid is forced to flow through a magnetically active annular gap. This forced flow generates the damping force, which can be continuously regulated by controlling the strength of the applied magnetic field. Because the size of the annular gap is usually very small relative to the radii of the annulus, the flow of the MR fluid through this annulus is usually approximated by the flow of fluid through two infinitely wide parallel plates. This approximation, which is widely used in designing and modeling of MR dampers, is satisfactory for many engineering purposes. However, the model does not represent accurately the physical processes and, therefore, expressions that correctly describe the physical behavior are highly desirable. In this paper, a mathematical model based on the flow of MR fluids through an annular gap is developed. Central to the model is the solution for the flow of any fluid model with a yield stress (of which MR fluid is an example) through the annular gap inside the damper. The physical parameters of a MR damper designed and fabricated at the University of Manchester are used to evaluate the performance of the damper and to compare with the corresponding predictions of the parallel plate model. Simulation results incorporating the effects of fluid compressibility are presented, and it is shown that this model can describe the major characteristics of such a device-nonlinear, asymmetric, and hysteretic behaviors-successfully.

Modal optimization of doubly clamped base-excited multilayer broadband vibration energy harvesters

Piezoelectric vibration energy harvesters with doubly clamped base-excited multilayer structures have been developed. The vibration energy harvesters consist of stacked H-shaped configurations including up to three beams and two extra masses. One beam is doubly clamped as a base layer. The extra masses are attached between the base layer and the other two beams to connect them together. By altering mass positions and the thickness of the base layer, the vibration energy harvesters can generate considerable power output in up to five modes of vibrations. An optimization strategy is established for multi-resonance broadband vibration energy harvesters designs. The strategy is based on a modal approach, which can determine the modal performance of vibration energy harvesters using mass ratio and electromechanical coupling coefficient. In particular, mass ratio is used to represent the influence of modal mechanical behaviour on the power density. The design strategy is executed by selecting the multilayer configurations with close resonances and preferred values of mass ratios in multiple modes. These configurations have optimal or near-optimal structural performance for broadband power output. The finite element method and a distributed electromechanical parameter model are used to derive the required modal parameters and power output with resistive loads.

Experimental Testing and Validation of a Magnetorheological (MR) Damper Model

The focus of this paper is on the experimental validation of a mathematical model that was developed for the flow of magnetorheological (MR) fluids through the annular gap in a MR damper. Unlike previous work by other researchers, which approximate the flow of the MR fluid through this annulus as a flow of fluid through two infinitely wide parallel plates, the model presented represents accurately the annular flow. In this paper, the mathematical model is validated via experimental testing and analysis of a double-tube MR damper fabricated at the University of Manchester, UK. The experimental setup and the procedures for executing the tests on the MR damper according to established standards for the testing of conventional automotive dampers are given. This involved sets of many isofrequency sinusoidal tests of various displacement amplitudes. Predictions from theoretical simulations based on the mathematical model are validated using the data collected from the experiments. It was found that the modeling procedure represents the MR damper very satisfactorily.

Wavelet-based Structural Damage Detection

In this paper, a new wavelet-based approach for crack identification in beam-like structures is presented and applied to simply-supported beams with single or multiple cracks. A novel damage index, based on finding the difference between two sets of detail coefficients obtained by the use of the Stationary Wavelet Transform (SWT) of two reconstructed sets of modal displacement data of the cracked beam-like structure, is proposed for single crack detection or multiple crack detection. These two sets of mode shape data represent the left half and the modified right half of the modal data of the structure. Currently, SWT is widely used in the field of image processing for image noise reduction and image quality improvement. However, because it can provide an accurate estimate of the variances at each scale and facilitate the identification of salient features in a signal, SWT has great potential in the field of structural damage detection. In this paper, the modal responses of the damaged simply supported beams used are computed using the finite element method (FEM). The modal data generate is decomposed by SWT into a smooth curve, called approximation coefficient, and detail coefficient. It is shown that the detail coefficient includes crack information that is useful for structural damage detection. Therefore, a novel damage index, the difference of the SWT detail coefficients of two reconstructed sets of modal displacement data, is proposed and employed. The numerical simulation results show that the proposed wavelet-based method has a good anti-noise ability and it does not require the modal parameters of an intact structure as a baseline for crack detection. Therefore, it can be recommended for real applications in structural health monitoring and damage detection.Copyright

Applications of the fractal-like finite element method to sharp notched plates

The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.Copyright

Design of polymer-based mechanical filters for shock-measurement accelerometers

Shock measurement accelerometers require protection from the high frequency components of input shock spectra which often cause irreversible damage to these transducers. The resonance frequencies of shock accelerometers are usually designed to be much greater than the highest frequency of their operating range. It is not unusual, however, for input shock waveforms to contain spectral components whose frequencies are much greater than the resonance frequencies of shock accelerometers. This is particularly true for shock waveforms of very short duration whose shape approach that of the classical Dirac delta function. Consequently, there is a need for mechanical filters which will isolate the accelerometers from the highest frequency components of shock loadings applied to structures. In this paper, the design of a mechanical filter comprised of metal discs, metal housing and viscoelastic elements is examined using the finite element method. The transformation of the frequency domain complex Youngs modulus data to the time domain extensional relaxation function using collocation method is described. The procedures for the derivation of the Prony series coefficients from the time data for input into the finite element analysis code are presented. It is shown that effective mechanical filters can be designed using viscoelastic materials of optimal properties.

Predicting the vibration characteristics of elements incorporating incompressible and compressible viscoelastic materials

In order to predict accurately the vibration characteristics of viscoelastic elements and viscoelastically damped structures, the use of frequency-dependent parameters such as complex modulus and Poissons ratio is important. Several techniques have been developed for measuring the frequency-dependent complex modulus of viscoelastic materials. However, the accurate determination of Poissons ratio of viscoelastic materials is much less developed. This quantity is important as its commonly quoted value of 0.5 can be very different when a viscoelastic material is in its transition or glassy region or if the material is compressible. In this paper, prismatic viscoelastic samples are employed to predict the value of Poissons ratio using the finite element method (FEM). The transmissibility characteristics of these prismatic samples are established experimentally and FEM is used in conjunction with measured complex Youngs modulus and iterated values of Poissons ratio such that the predicted FEM results agree as well as possible with the experimental data. It is shown that the method suggested is able to predict accurately the Poissons ratio of incompressible and compressible viscoelastic materials.