• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.239-263
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• 2016

The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson's ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies.

• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1241-1260
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• 2015

Any rational approach to define the configuration and size of viscous fluid dampers in a structure should be based on the dynamic properties of the system with the dampers. In this paper we propose an alternative representation of the complex eigenvalues of multi degree of freedom systems with dampers to calculate new equivalent natural frequencies. Analytical expressions for the dynamic properties of a two-story building model with a linear viscous damper in the first floor (i.e. with a non-proportional damping matrix) are derived. The formulas permit to obtain the equivalent damping ratios and equivalent natural frequencies for all the modes as a function of the mass, stiffness and damping coefficient for underdamped and overdamped systems. It is shown that the commonly used formula to define the equivalent natural frequency is not applicable for this type of system and for others where the damping matrix is not proportional to the mass matrix, stiffness matrix or both. Moreover, the new expressions for the equivalent natural frequencies expose a novel phenomenon; the use of viscous fluid dampers can modify the vibration frequencies of the structure. The significance of the new equivalent natural frequencies is expounded by means of a simulated free vibration test. The proposed approach may offer a new perspective to study the effect of viscous dampers on the dynamic properties of a structure.

• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.1-6
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• 2011

Vibration-based Structural Health Monitoring (SHM) systems use field measurements of operational signals, which are distorted by noise from many sources. Reducing this noise allows a more accurate assessment of the original "clean" signal and improves analysis results. The implementation of a noise reduction methodology for the Modal Distribution Method (MDM) is reported here. The spectral subtraction method is a popular broadband noise reduction technique used in speech signal processing. Its basic principle is to subtract the magnitude of the noise from the total noisy signal in the frequency domain. The underlying assumption of the method is that noise is additive and uncorrelated with the signal. In speech signal processing, noise can be measured when there is no signal. In the MDM, however, the magnitude of the noise profile can be estimated only from the magnitude of the Power Spectral Density (PSD) at higher frequencies than the frequency range of the true signal associated with structural vibrations under the additional assumption of white noise. The implementation of the spectral subtraction method to MDM may decrease the energy of the individual mode. In this work, a modification of the spectral subtraction method is introduced that enables the conservation of the energies of individual modes. The main difference is that any (negative) bars with a height below zero after subtraction are set to the absolute value of their height. Both noise reduction methods are implemented in the MDM, and an application example is presented that demonstrates its effectiveness when used with a signal corrupted by noise.

• Smart Structures and Systems
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• v.17 no.3
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• pp.523-539
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• 2016

The ambient vibration measurement is an output-data-only dynamic testing where natural excitations are represented, for instance, by winds and typhoons. The modal identification involving output-only measurements requires the use of specific modal identification techniques. This paper presents the application of a reliable method (the Stochastic Subspace Identification - SSI) implemented in a general purpose software. As a criterion toward the robustness of identified modes, a bio-inspired optimization algorithm, with a highly nonlinear objective function, is introduced in order to find the optimal deployment of a reduced number of sensors across a large civil engineering structure for the validation of its modal identification. The Ting Kau Bridge (TKB), one of the longest cable-stayed bridges situated in Hong Kong, is chosen as a case study. The results show that the proposed method catches eigenvalues and eigenvectors even for a reduced number of sensors, without any significant loss of accuracy.

• Smart Structures and Systems
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• v.16 no.5
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• pp.937-960
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• 2015

Tuned mass dampers (TMDs) have been a prevalent vibration control device for suppressing excessive vibration because of environmental loadings in contemporary tall buildings since the mid-1970s. A TMD must be tuned to the natural frequency of the primary structure to be effective. In practice, a TMD may be assembled in situ, simultaneously with the building construction. In such a situation, the respective dynamic properties of the TMD device and building cannot be identified to determine the tuning status of the TMD. For this purpose, a methodology was developed to obtain the parameters of the TMD and primary building on the basis of the eigenparameters of any two complex modes of the combined building-TMD system. The theory was derived in state-space to characterize the nonclassical damping feature of the system, and combined with a system identification technique to obtain the system eigenparameters using the acceleration measurements. The proposed procedure was first demonstrated using a numerical verification and then applied to real, experimental data of a large-scale building-TMD system. The results showed that the procedure is capable of identifying the respective parameters of the TMD and primary structure and is applicable in real implementations by using only the acceleration response measurements of the TMD and its located floor.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.153-159
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• 2010

This work focuses on finding a method to reduce the noise of a hermetic reciprocating compressor during start-up using an acoustical analysis. The noise of compressor during start-up, which is a higher level than that of a normal operating condition, has transient and non-stationary characteristics. The acoustical analysis of compressor cavity is performed to find an effective method to reduce the noise level. In the acoustical analysis, the shape variations of frequency response function in the neighborhood of resonances are tested for three parameters: the height of remained oil, the suction position of refrigerant and the position of driving part. As a conclusion of this result, to reduce the emission noise of compressor during start-up, the height of remained oil should be kept at 16 mm, the refrigerant should be sucked at the cross point of nodal lines of X and Y directional cavity modes, and the driving part should be positioned in the center of cavity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.184-191
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• 1997

A method, termed as the substructural sensitivity synthesis method, which utilizes the computational merits of the component mode synthesis technique is proposed to calculate design sensitivity of modal parameters of substructurally combined structures. In this method, the sensitivity analysis is combined with component mode synthesis thchnique. thus the degrees of freedom of a combined structure can be dramatically reduced. Free-interface mode method including the residual attachment modes among the component mode synthesis methods is used to calculate the modal sensitivity of the combined structure. For the design sensitivities of modal properties of structure, the Nelson's method, which is exact solving method is used. It is shown that the modal sensitivities of the entire structure can be obtained by synthesizing the substructural modal data, and the sensitivities of the modal data about the design variables of modifiable substructure. Using the proposed method, the final degrees of freedom of entire structure can be remarkably reduced to calculate the modal parameter sensitivities. With a structure composed of beams and plates, as an example, the sensitivities of the eigenvalues and eigenvectors obtained by this proposed method were compared with the exact solutions in terms of accuracy.

• Steel and Composite Structures
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• v.37 no.5
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• pp.551-569
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• 2020

Vibration of vertically aligned-monolayered-nonuniform nanorods consist of functionally graded materials with elastic supports has not been investigated yet. To fill this gap, the problem is examined using the elasticity theories of Eringen and Gurtin-Murdoch. The geometrical and mechanical properties of the surface layer and the bulk are allowed to vary arbitrarily across the length. The nonlocal-surface energy-based governing equations are established using differential-type and integro-type formulations, and solved by employing the Galerkin method by exploiting admissible modes approach and element-free Galerkin (EFG). Through various comparison studies, the effectiveness of the EFG in capturing both nonlocal-differential/integro-based frequencies is proved. A constructive parametric study is also conducted, and the roles of nanorods' diameter, length, stiffness of both inter-rod's elastic layer and elastic supports, power-law index of both constituent materials and geometry, nonlocal and surface effects on the dominant frequencies are revealed.

• Smart Structures and Systems
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• v.6 no.8
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• pp.905-920
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• 2010

Changes in temperature, loads and boundary conditions may have effects on the dynamic properties of large civil structures. Taking the Run Yang Suspension Bridge as an example, modal properties obtained from ambient vibration tests and from the structural health monitoring system of the bridge are used to identify and evaluate the modal parameter variability. Comparisons of these modal parameters reveal that several low-order modes experience a significant change in frequency from the completion of the bridge to its operation. However, the correlation analysis between measured modal parameters and the temperature shows that temperature has a slight influence on the low-order modal frequencies. Therefore, this paper focuses on the effects of the boundary conditions on the dynamic behaviors of the suspension bridge. An analytical model is proposed to perform a sensitivity analysis on modal parameters of the bridge concerning the stiffness of expansion joints located at two ends of bridge girders. It is concluded that the boundary conditions have a significant influence on the low-order modal parameters of the suspension bridge. In addition, the influence of vehicle load on modal parameters is also investigated based on the proposed model.

• Earthquakes and Structures
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• v.10 no.1
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• pp.25-51
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• 2016

In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.