Search

In this section, first, wave propagation in elementary laminated composite beams is discussed. The main objective is to bring out the effect of stiffness and inertial coupling on the overall wave response behavior. Next, the same is discussed for higher order composite beams. Here, the effect of lateral contraction is also introduced. The method of treating various damping schemes is addressed. The last part of this chapter deals with the spectral element formulation of layered composite tube. A number of numerical examples are provided to highlight the wave behavior. For many examples, comparisons of spectral solutions with regular FEM are provided. [ABSTRACT FROM AUTHOR]

It is now well-known that the homogeneous plane wave has the form u = Aej(k·x−ωt), where the wave amplitude A and the wave vector k are real. When A and k become complex numbers, as happens for the linear and dissipative (visco-elastic) system, A decreases with propagating distance and u is called an inhomogeneous wave [24]. Although the inhomogeneous wave is defined in a strict sense for two- or three-dimensional media, the definition can be extended to the one-dimensional situation. [ABSTRACT FROM AUTHOR]

The concept of broadband control in flexible structure has evolved over recent times. Tremendous technological success in the field of smart structures and MEMS has laid the path towards implementation of such concepts. Structures made of multi-functional composites have provided a wide range of platforms for precision sensing, distributed actuation and control related applications. Most of the mathematical frameworks behind the control systems normally use the frequency domain characteristics of the system. Since the basic foundation of SFEM is in the frequency domain, these aspects will be fully exploited in the present chapter, while developing a finite element model with integrated control algorithm for the control of a distributed flexible structure. The approach uses SFEM developed earlier to model the dynamics of the host structures. The control element, namely the sensor and the actuator, will be modeled through an active spectral finite element (ASFE). This chapter supplements Chapter 2 in giving a complete overview of the constituent models for different smart sensors/actuators. Towards the end, a case study of helicopter cabin noise reduction is presented. [ABSTRACT FROM AUTHOR]

In this chapter the damage model derived in Chapter 9 will be used to develop numerical algorithms for damage detection studies. This chapter will present four such algorithms, namely, spectral power flow, the damage force indicator, genetic algorithms and the artificial neural network (ANN). [ABSTRACT FROM AUTHOR]

Structural Health Monitoring (SHM) is a class of inverse problem wherein the state of structures requires to be determined using a predefined input and the measured output(s). In composite structures, delamination is the common type of failure. If the size of the delamination is very small, it results in negligible loss of stiffness and hence lower vibrational modes will be least affected. Hence, SHM studies require high frequency content inputs (loads) and SFEM provides a very efficient mathematical model for this purpose. The main requirements of SHM are simplified damage models and efficient damage detection studies. While the former is addressed in this chapter, the later is dealt with in the next chapter. In this chapter, various simplified damage models for single and multiple delaminations, fiber breakage, surface breaking cracks and degraded zones are formulated. Numerical examples are provided to show the wave scattering due to a crack front. [ABSTRACT FROM AUTHOR]

The aim of the present chapter is to use the formulated spectral elements of the previous chapters to solve some difficult practical problems of great industrial significance. To start with, one important application of the spectral formulation is in solving inverse problems, e.g., source identification and parameter estimation. Because of the frequency domain formulation of spectral elements, where the input and output responses are algebraically connected through the transfer function, force (external disturbance) reconstruction can be performed with relative ease compared to any FE based methods. Similarly, material property identification by a classical optimization based method, which requires multiple evaluation of the objective function (in this case spectral solution), is computationally feasible because of small spectral system sizes. The SLE developed in Section 6.1 is used in the following example to reconstruct the applied broadband force. Similarly, the SLE developed in Section 7.1 for inhomogeneous layered media is used to identify background homogeneous material properties and inhomogeneous parameters. [ABSTRACT FROM AUTHOR]

In the previous chapter we discussed the development of SFE and wave propagation aspects of layered homogeneous anisotropic media. In this chapter, inhomogeneous (isotropic or anisotropic) layered media are studied using a different set of SFEs. [ABSTRACT FROM AUTHOR]

Layered media are encountered in various natural (soil, wood, tissue, etc.) and artificial (bi-material, fibre reinforced composite, graded materials etc.) structural systems. Composite structural components are made up of a stack of layers (called ply or lamina) to form a laminate. These classes of materials can be both anisotropic and inhomogeneous. Further, these systems are required to resist harsh environments, such as impact load, high temperature load, etc. in their lifetime. Hence, analysis of these layered systems for such loading is important and requires critical attention. [ABSTRACT FROM AUTHOR]

In this chapter, all the necessary tools required for the spectral element formulation are derived. The most important of these is the determination of wavenumbers and wave amplitudes. An nth-order differential equation will yield an nth-order characteristic equation for the wavenumbers, which are normally difficult to solve. Here, we adopt some traditional techniques based on the theory of linear algebra to solve for wavenumbers and wave amplitudes. This chapter also describes the general spectral finite element formulation procedure, which is applied to form elements for isotropic waveguides. [ABSTRACT FROM AUTHOR]

In this chapter, a very brief introduction to composite materials, the evaluation of material properties and their homogenization techniques are given. Also, a brief introduction is given to smart composites and the basic constitutive models for composites, where a few standard smart materials can be embedded. Towards the end of the chapter a brief description of how to obtain constitutive models for inhomogeneous materials, such as functionally graded materials, is presented. [ABSTRACT FROM AUTHOR]

Dynamic analysis in structural engineering falls into two different classes, one involving low frequency loading and the other involving high frequency loading. Low frequency problems are categorized as Structural Dynamics problems while those involving high frequency loading fall into the category of Wave Propagation problems. In structural dynamics problems, the frequency content of the dynamic load is of the order of a few hundred hertz (Hz) and the designer will be mostly interested in the long-term (or steady-state) effects of the dynamic load on the structures. Hence, the first few normal modes and natural frequencies are sufficient to assess the performance of the structure. The phase information of the response is not critical here. Most of the dynamic problems in structures will fall into this category. On the other hand, for wave propagation problems, the frequency content of the input loading is very high (of the order of kilohertz (kHz) or higher) and hence, short-term effects (transient response) become very critical. Further, many higher order modes will participate in amplifying the dynamic response. Impact and blast-type of loading fall into this category. The multi-modal nature of wave propagation makes one parameter very important, and that is the phase information. [ABSTRACT FROM AUTHOR]