Vibration analysis of a rotating beam with variable angular velocity

A beam subjected to a constant fluid flow load is analysed assuming a solution in the form of exponential and trigonometric functions and applying the Galerkin method. The combined effect of gas velocity, angular velocity of rotation, setting angles, and hub radius is examined. Through appropriate simplifications, the fourth order nonlinear differential equations governing the problem are degenerated into a second order ordinary differential equation. It is demonstrated by numerical examples, that the constant fluid flow load can have a significant effect on the dynamic response of a rotating bea

Dynamics of multi-layered composite plates with SMA wires

In this paper certain aspects of the dynamic behavior of a multilayered, composite plate with shape memory alloys (SMA) wires have been investigated. The influence of parameters such as the orientation and location of SMA wires, the orientation and relative volume fraction of reinforcing fibers, the thickness-to-length and length-to-width ratios, and different boundary conditions, on changes in the critical load, the natural frequencies and the modes of vibrations of the plate have all been studied and discussed in the paper. The use of two different techniques, generally known in the literature as the active property tuning and active strain energy tuning methods, has also been investigated. The results presented in this paper have been obtained by the use of the finite element method and a new finite element formulated for multilayered composite plates has been applied for this purpose

A sensitivity analysis of the dynamic performance of a composite plate with embedded shape memory wires

In this paper the dynamic performance of a multi-layered composite plate with embedded shape memory alloy (SMA) wires has been investigated in terms of the changes in its relative fundamental natural frequency. A sensitivity analysis has been carried out on the influence of various geometrical parameters and material properties on the plate's dynamic performance, as well as the influence of the form of boundary condition. The use of the active property tuning (APT) method and the active strain energy tuning (ASET) method has also been discussed within the paper. The finite element method has been used for the analysis, and a new element has been exploited for modelling multi-layered composite plates. It has been found that the dynamic performance of the multi-layered composite plate with embedded SMA wires strongly depends on the plate geometry and the form of boundary condition, however, the dynamics can be successfully controlled and influenced by an optimal selection of the geometrical parameters and material properties

Genetic algorithms in health monitoring of structures

The development of real-time, in-service structural health monitoring and damage detection technique has recently attracted a large number of academic and industrial researchers. <br />The basic concept of the frequency-based structural health monitoring technique is to monitor the variations in the structural natural frequencies changes caused by the presence of damage. Through monitoring the measured natural frequencies and comparing them to a baseline measurement (for undamaged structure), we can qualitatively determine that structural damage has occurred or is imminent.<br />The lecture presents results on the identification of damage in composite structures via genetic search technique and changes in natural frequencies. Location and size of the damage are carried out by minimization of an error function involving the difference between calculated and measured natural frequencies. Simulation studies indicate that changes in natural frequencies and genetic algorithm allow to estimate delamination parameters (location and size) very accurate and fast.<br />Genetic algorithm is a search technique based on ideas from the science of genetics and the process of natural selection. Differences between conventional search techniques and the genetic algorithm (GA) can be summarised as follows: <br /> GA operate on coded form of task parameters, <br /> GA works with a population which represents numerical values of a particular variables, <br /> GA used only objective function, <br /> GA applied only probabilistic rules of selection. <br />A simple genetic algorithm consists of three basic operations: reproduction, crossover and mutation. The algorithm starts with the randomly generated initial population. The members of this population are usually binary strings (called chromosomes). Particular elements of chromosomes are called genes. In these strings are coded values of a variable or variables, which can be a solution of examining problem in the search space. These variables are then used to evaluate the corresponding fitness value which is the objective function. Objective function used in the presented examples is based on the changes in natural frequencies from measurements. Changes in natural frequencies may be called the classical damage indicators if any. They are without any doubt the most used damage indicators both formerly and nowadays. The main reason for the great popularity is, that natural frequencies are rather easy to determine with relatively high level of accuracy. In fact, one sensor placed on a structure and connected to a frequency analyser gives estimates for several natural frequencies. Further, natural frequencies are sensible to all kind of damage - local and global damage.<br />The advantages and limitations of the present technique are also discussed

Propagation of elastic waves in beams - including damping effects

No abstract available

Statics and dynamics of composite structures with embedded shape memory alloys

A new class of modern smart materials such as piezoelectric polymers and ceramics, electrorheological fluids, optical fibers and shape memory alloys have a great number of possible applications in many industrial and engineering fields. This number grows constantly encouraging scientists and engineers to study and analyze the behavior of the materials, range and ways of their best use.<br />Shape memory alloy reinforced composites are an extremely versatile class of materials. Shape memory alloys are characterized by: large internal forces, unique ability of changing its material properties, wide range of operational temperature, excellent damping properties and high durability. Mechanical and physical properties of SMA strongly depend on temperature and initial stresses. Changes in temperature and initial stresses involve changes in the volume fraction of martensite in the alloys. During the martensite transformation recovery stresses appear. These recovery stresses are not only a function of alloys temperature but also depend on initial strains. Using shape memory alloys as fibre reinforcement gives structures numerous adaptive capabilities. One of them is the controlling of motion and the vibration of structures.<br />In order to model accurately the behavior of composite structures with embedded shape memory alloy components three literature models have been carefully examined. These models have been studied according to their abilities to predict properly superelastic and shape memory effects associated with the thermomechanical behavior of shape memory alloys and special attention has been paid to the set of state variables chosen for each model (Tanaka, Liang and Rogers, Brinson)<br />The lecture illustrates stress-strain relationships for composite structures with embedded SMA fibres and their influence upon certain changes in natural frequencies and thermal buckling of selected composite structures. Governing equations based on the finite element method are formulated for beams, plates, and shells. Active frequency controlling can be used, for example, to avoid resonances in composite structures such as shafts, blades, aircraft wings, etc. The finite element analysis results are compared to those obtained from an analytical continuum solution.<br />The results of calculations demonstrate the potential effectiveness of SMA fiber- reinforcement in composite structural elements in the process of controlling the vibration. The effect of SMA fibers activation on the amplitude of vibration normalized with respect to the amplitude of the uncontrolled vibration can also be analyzed.<br />It can be clearly observed that the activation process of SMA wires involves an increase in the natural bending frequencies. This effect rises when both the temperature and initial strains are higher

The location of a concentrated mass on rectangular plates from measurements of natural vibrations

This paper presents new results for the identification of the location of a concentrated mass on isotropic plates by means of a genetic algorithm search technique based on changes in natural frequencies. The location and size of the mass are determined by minimisation of an error function, which expresses the difference between calculated and measured natural frequencies. Simulation studies indicate that changes in natural frequencies allow the estimation of mass location and magnitude at high levels of accuracy and speed. The advantages and limitations of this technique are also discussed

Dynamics of multi-layered composite plates with SMA wires

In this paper certain aspects of the dynamic behavior of a multilayered, composite plate with shape memory alloys (SMA) wires have been investigated. The influence of parameters such as the orientation and location of SMA wires, the orientation and relative volume fraction of reinforcing fibers, the thickness-to-length and length-to-width ratios, and different boundary conditions, on changes in the critical load, the natural frequencies and the modes of vibrations of the plate have all been studied and discussed in the paper. The use of two different techniques, generally known in the literature as the active property tuning and active strain energy tuning methods, has also been investigated. The results presented in this paper have been obtained by the use of the finite element method and a new finite element formulated for multilayered composite plates has been applied for this purpose

One dimensional SMA models for use with reinforced composite structures

In this paper three models of the shape memory alloy behaviour have been presented and re-investigated. The models are attributed to Tanaka, Liang and Rogers, and Brinson, and have been used extensively in the literature for studying the static or dynamic performance of different composite material structures with embedded shape memory alloy components. The major differences and similarities between these models have been emphasised and examined in the paper. A simple experimental rig was designed and manufactured to gain additional insight into the main mechanics governing the shape memory alloy (SMA) mechanical properties. Data obtained from the experimental measurements on Ni-Ti wires have been used in the numerical simulation for validation purposes. It has been found that the three models all agree well in their predictions of the superelastic behaviour at higher temperatures, above the austenite finish temperature when shape memory alloys stay in the fully austenitic phase. However, at low temperatures, when the alloys stay in the fully martensitic phase, some difficulties may be encountered. The model developed by Brinson introduces two new state variables and therefore two different mechanisms for the instigation of stress-induced and temperature-induced martensite. This enables more accurate predictions of the superelastic behaviour. In general, it can be recommended that for investigations of the shape memory and superelastic behaviour of shape memory alloy components the Brinson model, or refinements based on the Brinson model, should be applied