The Effects of the Stiffness Mistuning on the Dynamic Response of Periodic Structures under a Harmonic Force

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

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Theoretical and experimental analysis of the exact receptance function of a clamped-clamped beam with concentrated masses

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/14628 ◽

2020 ◽

Author(s):

Nguyen Viet Khoa ◽

Dao Thi Bich Thao

Keyword(s):

Dynamic Response ◽

Numerical Simulations ◽

Experimental Analysis ◽

Arbitrary Point ◽

Peak Position ◽

Numerical Results ◽

Experimental Results ◽

Harmonic Force ◽

Concentrated Masses

This paper establishes the exact receptance function of a clamped-clamped beam carrying concentrated masses. In this paper, the derivation of exact receptance and numerical simulations are provided. The proposed receptance function is convenient to apply for predicting the dynamic response at arbitrary point of the beam acted by a harmonic force applied at arbitrary point. The influence of the concentrated masses on the receptance is investigated. The numerical simulations show that a peak in the receptance decreases when there is a mass located close to that peak position. The numerical results have been compared to the experimental results has to justify the theory.

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Dynamic response of a bi-axially pre-stressed bi-layered plate resting on a rigid foundation under a harmonic force

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219886328 ◽

2019 ◽

Vol 234 (3) ◽

pp. 784-795

Author(s):

Ahmet Daşdemir

Keyword(s):

Mathematical Model ◽

Dynamic Response ◽

Three Dimensional ◽

Dimensionless Frequency ◽

Rigid Foundation ◽

Layered Plate ◽

Harmonic Force ◽

Time Harmonic ◽

Linearized Theory ◽

Complete Contact

This study aims to investigate the forced vibrations caused by a time-harmonic force from a pre-stressed bi-layered plate resting on a rigid foundation under the action of a time-harmonic pointwise loading. Our investigation was conducted according to a piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies. Throughout this study, we assumed that there is complete contact between the plate and the rigid foundation. The purpose of this study is threefold: the development of a mathematical model to investigate the dynamic response of the pre-stressed bi-layered plate, the analysis of the frequency response of the plate under consideration, and finally, demonstrating the relationship between the initial stress and the dimensionless frequency of the plate. We solved the mathematical model by employing the finite element method. We present our numerical results on the dynamic behavior of the plate. In particular, we have shown that an increase in the values of the aspect ratio of a plate under fixed thickness leads to a decrease in the normal stress resonance values.

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The Response of Mechanical Systems to Random Excitation

Journal of Applied Mechanics ◽

10.1115/1.4011504 ◽

1957 ◽

Vol 24 (2) ◽

pp. 248-251

Author(s):

W. T. Thomson ◽

M. V. Barton

Keyword(s):

Dynamic Response ◽

Mechanical Systems ◽

Random Excitation ◽

Fixed Frequency ◽

Harmonic Force ◽

Instantaneous Values ◽

Random Nature

Abstract Mechanical systems are not always excited by a harmonic force of fixed frequency and amplitude. Often the excitation input is of random nature, and the response of the system displays no orderly trends. Instantaneous values and phase are meaningless in such cases, and the problem must be treated statistically. It is the purpose of this paper to outline such an approach as related to the dynamic response of structures.

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Vibration Absorbers for Hysterically Damped Mass-Loaded Beams

Journal of Vibration and Acoustics ◽

10.1115/1.2930145 ◽

1991 ◽

Vol 113 (1) ◽

pp. 116-122 ◽

Cited By ~ 34

Author(s):

D. N. Manikanahally ◽

M. J. Crocker

Keyword(s):

Dynamic Response ◽

Cross Section ◽

General Procedure ◽

Space Structure ◽

Graphical Form ◽

Variable Cross ◽

Vibration Absorbers ◽

Harmonic Force ◽

Beam System ◽

Force Excitation

A procedure for designing dynamic vibration absorbers for a general mass-loaded beam system of variable cross-sectional area, when it is subjected to an arbitrarily distributed simple harmonic force excitation, is presented. The procedure gives flexibility for choosing the number of absorbers depending upon the number of significant modes to be suppressed. The beam is assumed to be hysteretically damped and each absorber is a spring-mass-damper system. For each absorber, for a selected mass, the stiffness and damping coefficients are optimized so as to minimize the dynamic response corresponding to the resonance frequency at which they are tuned to operate. The interaction between the absorbers is also accounted for in the analysis. This general procedure for designing vibration absorbers is then applied to a space structure modeled as a mass-loaded free-free beam, to suppress the first two resonances when it is subjected to a concentrated simple harmonic force excitation. The frequency response is presented in a graphical form. Furthermore, it is also shown that optimizing the beam system first and then designing vibration absorbers for this beam system will result in a small dynamic response. Although the analysis is general enough to cover beams of nonuniform cross-section, the examples presented in this paper of the above simplified model of the space structure have been restricted to beams of uniform cross-section.

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Preliminary Experimental Results of a Masonry Building Prototype Subject to Harmonic Forces of Different Intensity

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.446-449.3405 ◽

2012 ◽

Vol 446-449 ◽

pp. 3405-3411 ◽

Cited By ~ 2

Author(s):

Donato Cancellara ◽

Fabio de Angelis ◽

Vittorio Pasquino

Keyword(s):

Experimental Study ◽

Dynamic Response ◽

Laboratory Test ◽

Experimental Results ◽

Structural Behavior ◽

Masonry Building ◽

Floor Plan ◽

Harmonic Force ◽

Seismic Input ◽

Structure Test

In the present paper an experimental study has been performed on a masonry building prototype and some preliminary experimental results are illustrated for analyzing the structural behavior of a masonry building prototype subject to harmonic forces of different intensity. The physical model used for the laboratory test is a two-story masonry building characterized by a regular floor plan. The structure test is subjected to a harmonic force input supplied by a vibrodyne. The experimental results are aimed at characterizing the dynamic response of the masonry building subject to harmonic forces in order to describe the bahaviour of the masonry building under the predominant actions of a seismic input.

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SEA Subsystem Property Identification by Periodic FEM Approach

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.94-96.1979 ◽

2011 ◽

Vol 94-96 ◽

pp. 1979-1982

Author(s):

Jie Gao ◽

Ke An Chen

Keyword(s):

Dynamic Response ◽

High Frequency ◽

Periodic Structures ◽

Low Frequency ◽

Engineering Method ◽

Complex Structures ◽

High Frequency Range ◽

Frequency Range ◽

Remarkable Improvement ◽

Property Identification

A study on SEA properties of periodically stiffened structure was accomplished based on the periodic theory. With application of certain software, a simulation was performed on a common periodically stiffened fuselage structure. The results indicate such modeling approach reflects relatively accurate property of subsystem in mid and high frequency range, while a remarkable improvement could also be expected in low frequency range, especially for complex structures. Such approach was approved as one reliable engineering method for solving dynamic response of periodic structures.

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Dynamic Response of Adhesively Bonded Beams Subjected to Harmonic Peeling Loads

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8147 ◽

1999 ◽

Author(s):

H. R. Hamidzadeh ◽

J. L. Prescher ◽

H. Nayeb-Hashemi

Keyword(s):

Dynamic Response ◽

Natural Frequency ◽

System Response ◽

Shear Stresses ◽

Harmonic Force ◽

Factors Affecting ◽

Initiation And Propagation ◽

Stress Changes ◽

Bonded Joint ◽

Out Of Plane

Abstract The only viable method to join some components is by using adhesive. These components are often subjected to dynamic loading, which may cause initiation and propagation of failure in the joint. In order to insure the reliability of these structures, their dynamic response and factors affecting their response must be understood. Dynamic response of a single lap joint subjected to an out of plane harmonic force is evaluated. The bonded joint is modeled as Euler Bernoulli beams joined with an adhesive and constrained at one end and subjected to a harmonic force at the free end. The results show that the system response is not sensitive to the damping characteristic of the adhesive. In contrast, the elastic properties, and geometry of adhesive and adherends dominate the response. Significant peel and shear stresses develop in the over lap. These stresses are confined to the edge of the overlap and their magnitude increases as the frequency approaches the natural frequency of the system. The results show that the direction of the shear stress changes as the frequency of applied load sweeps over the first natural frequency. In contrast the peeling stress direction does not change as result of sweeping frequency over the first natural frequency.

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Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2017-0034 ◽

2017 ◽

Vol 22 (3) ◽

pp. 521-537 ◽

Cited By ~ 2

Author(s):

A. Daşdemir

Keyword(s):

Dynamic Response ◽

Initial Stress ◽

Equations Of Motion ◽

Three Dimensional ◽

Layered Plate ◽

Harmonic Force ◽

Time Harmonic ◽

Governing System ◽

Plate Strip ◽

Complete Contact

AbstractThe forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

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