A multiple scales method solution for the free and forced nonlinear transverse vibrations of rectangular plates

Shooshtari, A.,Khadem, S.E. Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.24 No.5

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

Dynamic Analysis of Harmonically Excited Non-Linear System Using Multiple Scales Method

Moon, Byung-Young,Kang, Beom-Soo The Korean Society of Mechanical Engineers 2002 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.16 No.6

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear systems. This method is based on the substructure synthesis formulation and a MS (multiple scales) procedure, which is applied to the analysis of nonlinear responses. The proposed procedure reduces the size of large degrees-of-freedom problem in solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated with the nonlinear rotating machine system as an example of large mechanical structure systems. In addition, its efficiency for nonlinear response prediction will be shown by comparison of other conventional methods.

Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core

Kamran Foroutan,Liming Dai 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.48 No.3

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin–Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke’s law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

Nonlinear primary resonance of multilayer FG shallow shell with an FG porous core reinforced by oblique stiffeners

Kamran Foroutan,Liming Dai 국제구조공학회 2024 Structural Engineering and Mechanics, An Int'l Jou Vol.91 No.5

The present research examines the primary resonance (PR) behaviors of oblique stiffened multilayer functionally graded (OSMFG) shallow shells featuring an FG porous (FGP) core under an external excitation. The research considers two distinct types of FGP cores: one characterized by uniform porosity distribution (UPD) and the other by non-uniform porosity distribution (NPD) along the thickness direction. Furthermore, the study explores two types of shallow shells: one with external oblique stiffeners and one with internal oblique stiffeners, which might have angles that are similar or different from each other. Using the stress function alongside the first-order shear deformation theory (FSDT), the research establishes a nonlinear model for OSMFG shallow shells. The strain-displacement relationships are obtained utilizing FSDT and von-Kármán’s geometric assumptions. The Galerkin approach is utilized to discretize the nonlinear governing equations, allowing for the analysis of stiffeners at varied angles. To validate the obtained results, a comparison is made not only with the findings of previous research but also with the response of PR obtained theoretically with the method of multiple scales, using the P-T method. Renowned for its superior accuracy and reliability, the P-T method is deemed an apt selection within this framework. Additionally, the study investigates how differences in material characteristics and stiffener angles affect the system’s PR behaviors. The results of this study can be used as standards by engineers and researchers working in this area, and they can offer important information for the design and evaluation of the shell systems under consideration.

Dynamic analysis of magnetorheological elastomer sandwich MEMS sensor under magnetic field

Hossein Akhavan,Javad Ehyaei,Majid Ghadiri 국제구조공학회 2022 Smart Structures and Systems, An International Jou Vol.29 No.5

In this paper, the effect of magnetic field on the vibration behavior of a Magnetorheological elastomer (MRE) sandwich MEMS actuated by electrostatic actuation with conductive skins are examined within the multiple scales (MMS) perturbation method. Magnetorheological smart materials have been widely used in vibration control of various systems due to their mechanical properties change under the influence of different magnetic fields. To investigate the vibrational behavior of the movable electrode, the Euler-Bernoulli beam theory, as well as Hamilton's principle is used to derive the equations and the related boundary conditions governing the dynamic behavior of the system are applied. The results of this study show that by placing the Magnetorheological elastomer core in the movable electrode and applying different magnetic fields on it, its natural vibrational frequency can be affected so that by increasing the applied magnetic field, the system's natural frequency increases. Also, the effect of various factors such as the electric potential difference between two electrodes, changes in the thickness of the core and the skins, electrode length, the distance between two electrodes and also change in vibration modes of the system on natural frequencies have been investigated.

한국어 수용성 판단의 실험방법론 비교 연구

조용준(Yong Joon Cho),전문기(Moon Gee Jeon) 언어과학회 2015 언어과학연구 Vol.0 No.72

The main purpose of this study is to investigate the differences among three experimental methods that have been widely used in the areas of experimental syntax and psycholinguistics. Specifically, this study examined the differences among Likert Scale (LS), Magnitude Estimation (ME), and Thermometer Task (TT) that were applied to analyze the multiple accusative construction in Korean. In this study, a total of 104 participants were randomly assigned to the three experimental conditions and the data was analyzed with several statistical methods. The findings of this study showed that there were significant differences statistically among the three experimental methods. These results have implications for the experimental syntax.

Combination resonance analysis of FG porous cylindrical shell under two-term excitation

Habib Ahmadi,Kamran Foroutan 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.2

This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

Dynamic combination resonance characteristics of doubly curved panels subjected to non-uniform tensile edge loading with damping

Udar, Ratnakar. S.,Datta, P.K. Techno-Press 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.25 No.4

The dynamic instability of doubly curved panels, subjected to non-uniform tensile in-plane harmonic edge loading $P(t)=P_s+P_d\;{\cos}{\Omega}t$ is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to simple resonances in parametrically excited doubly curved panels. Analytical expressions for the instability regions are obtained at ${\Omega}={\omega}_m+{\omega}_n$, (${\Omega}$ is the excitation frequency and ${\omega}_m$ and ${\omega}_n$ are the natural frequencies of the system) by using the method of multiple scales. It is shown that, besides the principal instability region at ${\Omega}=2{\omega}_1$, where ${\omega}_1$ is the fundamental frequency, other cases of ${\Omega}={\omega}_m+{\omega}_n$, related to other modes, can be of major importance and yield a significantly enlarged instability region. The effects of edge loading, curvature, damping and the static load factor on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which the curved panels cannot become dynamically unstable. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.

Reconfigurable Intelligent Surface assisted massive MIMO systems based on phase shift optimization

Xuemei Bai,Congcong Hou,Chenjie Zhang,Hanping Hu Korean Society for Internet Information 2024 KSII Transactions on Internet and Information Syst Vol.18 No.7

Reconfigurable Intelligent Surface (RIS) is an innovative technique to precisely control the phase of incident signals with the help of low-cost passive reflective elements. It shows excellent potential in the sixth generation of mobile communication systems, which not only extends wireless coverage but also boosts channel capacity. Considering that multipath propagation and a high number of antennas are involved in RIS in assisted mega multiple-input multiple-output (MIMO) systems, it suffers from severe channel fading and multipath effects, which in turn lead to signal instability and degradation of transmission performance. To overcome this obstacle, this essay suggests an improved gradient optimization algorithm to dynamically and optimally adjust the phase of the reflective elements to counteract channel fading and multipath effects as a strategy. In order to overcome the optimization problem of falling into local minima, this paper proposes an adaptive learning rate algorithm based on Adagrad improvement, which searches for the global optimal solution more efficiently and improves the robustness of the optimization algorithm. The suggested technique helps to enhance the estimate of channel efficiency of RIS-assisted large MIMO systems, according to simulation results.

Nonlinear vibration characteristics of accelerating viscoelastic membrane

Mingyue Shao,Jing Wang,Jimei Wu,Jiajuan Qing,Zhicheng Xue 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.10

Considering the viscoelastic characteristics of the accelerating viscoelastic membrane in roll-to-roll manufacturing, the nonlinear vibration characteristics of the accelerating viscoelastic membrane were investigated. The mechanical model of the accelerating viscoelastic membrane was established. Considering geometric nonlinearity, the equation of nonlinear vibration of the accelerating viscoelastic membrane was deduced. The ordinary differential equation of moving membranes was obtained using the Bubnov-Galerkin method and solved using the method of multiple scales. Numerical analyses reveal the effects of constant average speed, the speed fluctuation amplitude, the elastic modulus, the viscosity coefficient, and other parameters on the amplitude of vibration and the amplitude-frequency characteristics of moving membranes. Results provide theoretical guidance for the reasonable selection of printing parameters.