Showing papers by "Yiu-Yin Lee published in 2016"
TL;DR: In this paper, the effect of cavity length on the natural frequency of a nonlinear panel coupled with an extended cavity was examined and the multi-level residue harmonic balance method was used to solve this nonlinear problem.
Abstract: This article addresses the free vibration analysis of a nonlinear panel coupled with extended cavity. In practice, the cavity length of a panel-cavity system is sometimes longer than the panel length. Therefore, this study examines the effect of cavity length on the natural frequency of a nonlinear panel coupled with extended cavity. The multi-level residue harmonic balance method, which was recently developed by the author and his research partners, is used to solve this nonlinear problem. The present harmonic balance solution agrees reasonably well with the results obtained from a previous classical solution and shows that the cavity length is a very important factor that significantly affects the panel vibration and should not be ignored in the modelling process. The natural frequency of a panel-cavity system is very sensitive to the cavity length and decreases significantly when the cavity is longer, due to its larger volume or weaker stiffness. Moreover, when the cavity is very long and its resonant frequencies are close to that of the panel, multiple frequency solutions are obtained.
25 citations
TL;DR: 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.
Abstract: 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 ...
17 citations
TL;DR: In this article, the authors investigated the effect of leakage on the sound absorption of a nonlinear perforated panel backed by a cavity with leaking edges, and proposed a multi-level residue harmonic balance method to compute the nonlinear vibration responses.
16 citations
TL;DR: In this paper, 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) were investigated.
Abstract: 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.
11 citations
TL;DR: In this article, the transmission loss of a nonlinearly vibrating perforated panel using the multi-level residue harmonic balance method was investigated. And the results obtained from the multilevel solution method agree reasonably with those obtained from a numerical integration method.
Abstract: 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.
5 citations
01 Feb 2016
3 citations
TL;DR: In this paper, a modified harmonic balance solution method with Vieta substitution technique for nonlinear multimode damped beam vibration is presented, which can be used to calculate the vibration amplitudes without the need of nonlinear equation solver for the nonlinear algebraic equations generated in the harmonic balance processes.
Abstract: This paper presents a modified harmonic balance solution method incorporated with Vieta’s substitution technique for nonlinear multimode damped beam vibration. The aim of the modification in the solution procedures is to develop the analytic formulations, which are used to calculate the vibration amplitudes of a nonlinear multimode damped beam without the need of nonlinear equation solver for the nonlinear algebraic equations generated in the harmonic balance processes. The result obtained from the proposed method shows reasonable agreement with that from a previous numerical integration method. In general, the results can show the convergence and prove the accuracy of the proposed method.
3 citations
TL;DR: In this article, the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries is addressed, and the results obtained from the proposed method and numerical method are generally in good agreement.
Abstract: This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. The structural–acoustic modal formulations are developed from the Duffing differential equation and wave equation, which represent the large-amplitude structural vibration of a flexible panel coupled with a cavity. This problem considers both non-rigid acoustic boundary and structural cubic nonlinearity. The multi-level residue harmonic balance method is employed for solving the nonlinear coupled differential equations developed in the problem. The results obtained from the proposed method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter, etc., are examined.
2 citations
TL;DR: In this article, the multi-level residue harmonic balance method was used for vibro-acoustic systems with one flexible panel only (or 2D enclosures), whereas Fahy's and Pretlove's techniques are used for systems with multiple flexible panels.
Abstract: Fahy’s and Pretlove’s modelling techniques for a vibro-acoustic system have been employed in many research works. This is the first article addressing the differences between these modelling techniques for a nonlinear vibro-acoustic system. Pretlove’s technique is used for vibro-acoustic systems with one flexible panel only (or 2D enclosures); Fahy’s is applied to vibro-acoustic systems with multiple flexible panels (or 3D enclosures). The main difference between them is that all acoustic boundary conditions can be satisfied in the 2D modelling technique, while only rigid acoustic boundary conditions can be satisfied in the 3D modelling technique. The multi-level residue harmonic balance method, which was recently developed and modified from the classical harmonic balance method, is employed here. The advantage of this method is that it requires less computation effort when solving the nonlinear equations generated in the entire solution process. The comparisons between various transmission loss and nonlinear vibration results generated from the two models are investigated.
1 citations
18 Nov 2016
TL;DR: In this paper, the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries was performed using the multi-level residue harmonic balance method.
Abstract: This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.