This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

Damage identification in beam-type structures: frequency-based method vs mode-shape-based method

This paper is concerned with the free vibration problem for micro/nanobeams modelled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

http://iopscience.iop.org/article/10.1088/0957-4484/18/10/105401/pdf

Vibration of nonlocal Timoshenko beams

In this paper, an efficient and simple higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton’s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

Implementing wind turbines in a tall building for power generation: A study of wind loads and wind speed amplifications

Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances

This paper is a study of snap-through properties of a non-linear dynamic buckling response to sinusoidal excitation of a clamped—clamped buckled beam. Using a simple formula, the highly non-linear motion of snap-through and its effects on the overall vibration response have been studied. The non-linear governing equation obtained here is solved using the Runge—Kutta (RK-4) numerical integration method. Critical parameters at the onset of the snap-through motion, which vary with different damping coefficients and linear circular frequencies of a flat beam, are studied and given in terms of the excitation level and response displacement. The relationships between static and dynamic responses at the start of the snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. (a) small oscillations about the buckled position, (b) chaotic motion of intermittent snap-through and (c) large oscillations of continuous snap-through motion crossing the ...

Yiu-Yin Lee

Papers

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

Implementing wind turbines in a tall building for power generation: A study of wind loads and wind speed amplifications

Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances

Dynamic stability of a curved beam under sinusoidal loading

Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate