Y.Y. Lee

Thermoelastic analysis of functionally graded plates using the element-free kp-Ritz method

In this paper, the static responses of metal and ceramic functionally graded plates subject to thermal and mechanical loads are investigated. The first-order shear deformation plate theory is adopted, and the displacement field is expressed in terms of a set of mesh-free kernel particle functions. It is assumed that the material property of each plate exponentially varies through the thickness. The governing equations are solved to obtain the plate displacements and axial stresses using the element-free kp-Ritz method. The effects of the volume fraction, material property, boundary conditions and length-to-thickness ratio on the plate deflection and axial stress are discussed in detail. The numerical results generated from the proposed method agree well with those in the literature.

Analysis of strongly nonlinear oscillator using the max-min approach

Recently, considerable attention has been directed towards the analytical solutions of various nonlinear equations. Numerous new techniques have been appeared in open literature, for example, the parameter-expansion method [1-3], Lindstedt-Poincare method [4], the homotopy perturbation method [5-11], the variational iteration method [12], the energy balance method[13] and some others [14,15]. A complete review is available in Refs. [16,17]. For some nonlinear problems [21-28], it is easy to find the maximal and minimal solution thresholds. In fact, these nonlinear solutions can be approximated using the ancient Chinese mathematics, He Chengtians inequality [19, 20], which has been playing an important role in the physical sciences for more than 2 thousand years. In this paper, it aims to further verify the capacity of the max-min method [18], which is modified from He Chengtians inequality to solve nonlinear problems.

The multi-level residue harmonic balance solutions of multi-mode nonlinearly vibrating beams on an elastic foundation

In this paper, an efficient analytical solution method, namely, multi-level residue harmonic balance, is introduced and developed for the nonlinear vibrations of multi-mode flexible beams on an elastic foundation subject to external harmonic excitation. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions for any desired accuracy can be obtained by solving a set of linear algebraic equations. In other words, the computation effort to find more accurate nonlinear solutions is much less. In this paper, a multi-mode formulation, which represents the nonlinear beam vibration, is derived and set up. Then, the solution procedures are developed for obtaining the nonlinear multi-mode solution. The results from the multi-level residue harmonic balance method agree well with those from a numerical integration method. The effects of various parameters such as vibration amplitude, foundation modulus coefficient, damping factor and excitation level etc., on the nonlinear behaviors are examined. A convergence study is also performed to verify the solutions. The stability analysis is conducted using the virtue of Floquet theory and steady-state solutions are investigated.

Typical Collapse Modes of Confined Masonry Buildings under Strong Earthquake Loads

Confined masonry structures are a widely applied structural system in many developing countries. During the past Wenchuan Earthquake in 2008, numerous confined masonry buildings collapsed, while many others suffered dam- age. This study reviews the construction practices of confined masonry buildings in China. Simple models and hand cal- culation methods are proposed for quantifying the tearing failure of diaphragms, the tensile failure of tie-columns and the sway-mode strength of masonry buildings. The results indicate very good agreement with field observations. The seismic measures that are stipulated in the seismic design codes are very effective for increasing the strength and integrity, but not the ductility of masonry buildings. For those buildings that survived the earthquake, strength rather than ductility pro- tected the confined masonry from collapse or serious damage. Design recommendations are suggested for preventing various types of premature failures and enhancing the lateral strength of masonry buildings.

Multi-Level Residue Harmonic Balance Method for the Transmission Loss of a Nonlinearly Vibrating Perforated Panel

This paper investigates the transmission loss of a nonlinearly vibrating perforated panel using the multi-level residue harmonic balance method. The coupled governing differential equations which represent the air mass movement at each hole and the nonlinear panel vibration are developed. The proposed analytical solution method, which is revised from a previous harmonic balance method for single mode problems, is newly applied for solving the coupled differential equations. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions to any desired accuracy can be obtained by solving a set of linear algebraic equations. The results obtained from the multi-level residue harmonic balance method agree reasonably with those obtained from a numerical integration method. In the parametric study, the velocity amplitude convergences have been checked. The effects of excitation level, perforation ratio, diameter of hole, and panel thickness are examined.

Convergence Study of Minimizing the Nonconvex Total Delay Using the Lane-Based Optimization Method for Signal-Controlled Junctions

This paper presents a 2D convergence density criterion for minimizing the total junction delay at isolated junctions in the lane-based optimization framework. The lane-based method integrates the design of lane markings and signal settings for traffic movements in a unified framework. The problem of delay minimization is formulated as a Binary Mix Integer Non Linear Program (BMINLP). A cutting plane algorithm can be applied to solve this difficult BMINLP problem by adding hyperplanes sequentially until sufficient numbers of planes are created in the form of solution constraints to replicate the original nonlinear surface in the solution space. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. The main difficulty to solve this high-dimension nonlinear nonconvex delay minimization problem using cutting plane algorithm is the requirement of substantial computational efforts to reach a good-quality solution while approximating the nonlinear solution space. A new stopping criterion is proposed by monitoring a 2D convergence density to obtain a converged solution. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The cutting-plane algorithm producing an effective signal design will become more computationally attractive with adopting the proposed stopping criterion.

Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods

The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. The results obtained from the harmonic balance and homotopy perturbation approaches verified each other. The effects of vibration amplitude, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth, on the first two resonant natural frequencies, are examined.

Nonlinear multi-modal structural/acoustic interaction between a composite plate vibration and the induced pressure

This study aims to develop a mixed finite element and classical formulation for the nonlinear multimodal structural acoustic interaction of a composite plate backed by a three dimensional cavity. The formulation is developed by adopting the nonlinear finite element modal reduction method for the two-dimensional plate and the classical solution for the three-dimensional acoustic cavity, respectively. The main advantages of the adopted approach are as follows. 1) There is no need to update the nonlinear matrices; 2) the sizes of the nonlinear matrices can be reduced drastically; and 3) the acoustic pressure that acts on the plate can be obtained from the classical solution of the three-dimensional wave equation (i.e., no boundary element is required). Hence, the proposed approach can avoid the numerical error induced from the coupling between the two dimensional finite elements and three dimensional boundary elements. The frequency ratios for the fundamental modes of the structural-acoustic system at various plate vibration amplitudes, the contribution of each linear mode to the overall plate vibration, and the effect of air cavity depth on the frequency ratios are also studied.

Periodic and Quasi-periodic Responses of Van der Pol-Mathieu System Subject to Various Excitations

Abstract This paper addresses the steady-state periodic and quasi-periodic responses of van der Pol–Mathieu system subject to three excitations (i.e., self, parametric and external excitations). Method of multiple scales and double perturbation technique are employed to study the original system. The cases of van der Pol–Mathieu oscillator with and without external excitation are considered, and periodic and quasi-periodic solutions are obtained and discussed. In the parametric study, the effects of various parameters and self, parametric and external excitations on the system behaviors are studied. Results from method of multiple scales well agree with those from numerical method.

Nonlinear Analysis of Forced Responses of an Axially Moving Beam by Incremental Harmonic Balance Method

This article analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces. The governing equation of the beam vibration is developed using Hamiltons Principle. The stable and unstable periodic solutions are obtained by employing the multivariable Floquet theory and incremental harmonic balance (IHB) method. In the solution procedure, Hsus method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.