• Earthquakes and Structures
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• v.13 no.2
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• pp.103-118
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• 2017

In vertical seismic isolation (VSI), a building is partitioned intentionally by vertical layers into two dynamically different substructures for seismic response reduction. Initially, a 1-story frame was partitioned into two substructures, interconnected by viscous and visco-elastic links, and seismic responses of the original and the vertically isolated structures (VIS) were obtained, considering a large number of stiffness and mass ratios of substructures with respect to the original structure. Color contour graphs were defined for presentation and investigation of large amounts of output results. Dynamic characteristics of the isolated structures were studied by considering the non-classical damping of the system, and then the effects of viscous and visco-elastic link parameters on the modal damping ratios were discussed. On this basis, three states of mass isolation, interactional state, and control mass were differentiated. Response history analyses were performed by Runge-Kutta numerical method. In these analyses, interaction of isolation ratios and link parameters, on response control of VIS was studied and the appropriate ranges for link parameters as well as the optimal ranges for isolation ratios were suggested. Results show that by using the VSI technique, seismic response reduction up to 50% in flexible substructure and even more in stiff substructure is achievable.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.679-698
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• 2002

In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction concept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.271-286
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• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.695-708
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• 2011

Based on the multiple-time-scale (MTS) method, a general formula has been presented for solving an n-th, n = 2, 3, ${\ldots}$, order ordinary differential equation with strong linear damping forces. Like the solution of the unified Krylov-Bogoliubov-Mitropolskii (KBM) method or the general Struble's method, the new solution covers the un-damped, under-damped and over-damped cases. The solutions are identical to those obtained by the unified KBM method and the general Struble's method. The technique is a new form of the classical MTS method. The formulation as well as the determination of the solution from the derived formula is very simple. The method is illustrated by several examples. The general MTS solution reduces to its classical form when the real parts of eigen-values of the unperturbed equation vanish.

• Earthquakes and Structures
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• v.4 no.4
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• pp.341-363
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• 2013

Earthquake response calculation, parametric analysis and seismic parameter optimization of base-isolated structures are some critical issues for seismic design of base-isolated structures. To calculate the earthquake responses for such non-symmetric and non-classical damping linear systems and to implement the earthquake resistant design codes, a modified complex mode superposition design response spectrum method is put forward. Furthermore, to do parameter optimization for base-isolation structures, a graphical approach is proposed by analyzing the relationship between the base shear ratio of a seismic base-isolation floor to non-seismic base-isolation one and frequency ratio-damping ratio, as well as the relationship between the seismic base-isolation floor displacement and frequency ratio-damping ratio. In addition, the influences of mode number and site classification on the seismic base-isolation structure and corresponding optimum parameters are investigated. It is demonstrated that the modified complex mode superposition design response spectrum method is more precise and more convenient to engineering applications for utilizing the damping reduction factors and the design response spectrum, and the proposed graphical approach for parameter optimization of seismic base-isolation structures is compendious and feasible.

• Smart Structures and Systems
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• v.21 no.2
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• pp.195-205
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• 2018

Research on Lamb wave-based damage identification in plate-like structures depends on precise knowledge of dispersive wave velocity. However, boundary reflections with the same frequency of interest and greater amplitude contaminate direct waves and thus compromise measurement of Lamb wave dispersion in different materials. In this study, non-reflecting boundaries were proposed in both numerical and experimental cases to facilitate time-frequency characterization of Lamb wave dispersion. First, the Lamb wave equations in isotropic and laminated materials were analytically solved. Second, the non-reflecting boundaries were used as a series of frames with gradually increased damping coefficients in finite element models to absorb waves at boundaries while avoiding wave reflections due to abrupt property changes of each frame. Third, damping clay was sealed at plate edges to reduce the boundary reflection in experimental test. Finally, the direct waves were subjected to the slant-stack and short-time Fourier transformations to calculate the dispersion curves of phase and group velocities, respectively. Both the numerical and experimental results suggest that the boundary reflections are effectively alleviated, and the dispersion curves generated by the time-frequency analysis are consistent with the analytical solutions, demonstrating that the combination of non-reflecting boundary and time-frequency analysis is a feasible and reliable scheme for characterizing Lamb wave dispersion in plate-like structures.

• Journal of Mechanical Science and Technology
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• v.20 no.8
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• pp.1139-1148
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• 2006

This paper addresses the analytical modeling and dynamic response of the advanced composite rotating blade modeled as thin-walled beams and incorporating viscoelastic material. The blade model incorporates non-classical features such as anisotropy, transverse shear, rotary inertia and includes the centrifugal and coriolis force fields. The dual technology including structural tailoring and passive damping technology is implemented in order to enhance the vibrational characteristics of the blade. Whereas structural tailoring methodology uses the directionality properties of advanced composite materials, the passive material technology exploits the damping capabilities of viscoelastic material (VEM) embedded into the host structure. The VEM layer damping treatment is modeled by using the Golla-Hughes-McTavish (GHM) method, which is employed to account for the frequency-dependent characteristics of the VEM. The case of VEM spread over the entire span of the structure is considered. The displayed numerical results provide a comprehensive picture of the synergistic implications of both techniques, namely, the tailoring and damping technology on the dynamic response of a rotating thin-walled b ε am exposed to external time-dependent excitations.

• Smart Structures and Systems
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• v.18 no.6
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• pp.1125-1143
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• 2016

Forced vibration analysis of a simple supported viscoelastic nanobeam is studied based on modified couple stress theory (MCST). The nanobeam is excited by a transverse triangular force impulse modulated by a harmonic motion. The elastic medium is considered as Winkler-Pasternak elastic foundation.The damping effect is considered by using the Kelvin-Voigt viscoelastic model. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Timoshenko beam theory by using finite element method. The effects of the transverse shear deformation and rotary inertia are included according to the Timoshenko beam theory. The obtained system of differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. Numerical results are presented to investigate the influences the material length scale parameter, the parameter of the elastic medium and aspect ratio on the dynamic response of the nanobeam. Also, the difference between the classical beam theory (CBT) and modified couple stress theory is investigated for forced vibration responses of nanobeams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.6
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• pp.486-494
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• 2004

This paper addresses the dynamic modeling and closed-loop eigenvibration analysis of composite rotating pretwisted fan blade modeled as non-uniform thin-walled beam with bi-convex cross-section fixed at the certain presetting angle and incorporating piezoelectric induced damping capabilities. The blade model incorporates non-classical features such as transverse shear, rotary inertia and includes the centrifugal and Coriolis force field. A velocity feedback control law relating the piezoelectiriccally induced transversal bending moment at the beam tip with the appropriately selected kinematical response quantity is used and the beneficial effects upon the closed loop eigenvibration of the blade are highlighted.

• Steel and Composite Structures
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• v.32 no.2
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• pp.253-264
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• 2019

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-$K{\acute{a}}rm{\acute{a}}n$ 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.