• Smart Structures and Systems
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• v.16 no.5
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• pp.891-918
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• 2015

In many of microdevices a part of a microbeam is covered by a piezoelectric layer. Depend on the application a DC or AC voltage is applied between upper and lower side of the piezoelectric layer. A common method in many of previous works for evaluating the response of these structures is discretizing by Galerkin method. In these works often single mode shape of a uniform microbeam i.e. the microbeam without piezoelectric layer has been used as comparison function, and so the convergence of the solution has not been verified. In this paper the Galerkin method is used for discretization, and a comprehensive analysis on the convergence of solution of equation that is discretized using this comparison function is studied for both clamped-clamped and clamped-free microbeams. The static and dynamic solution resulted from Galerkin method is compared to the modal expansion solution. In addition the static solution is compared to an exact solution. It is denoted that the required numbers of uniform microbeam mode shapes for convergence of static solution due to DC voltage depends on the position and thickness of deposited piezoelectric layer. It is shown that when the clamped-clamped microbeam is coated symmetrically by piezoelectric layer, then the convergence for static solution may be obtained using only first mode. This result is valid for clamped-free case when it is covered by piezoelectric layer from left clamped side to the right. It is shown that when voltage is AC then the number of required uniform microbeam shape mode for convergence is much more than the number of required mode in modal expansion due to the dynamic effect of piezoelectric layer. This difference increases by increasing the piezoelectric thickness, the closeness of the excitation frequency to natural frequency and decreasing the damping coefficient. This condition is often indefeasible in microresonator system. It is concluded that discreitizing the equation of motion using one mode shape of uniform microbeam as comparison function in many of previous works causes considerable errors.

• Smart Structures and Systems
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• v.14 no.3
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• pp.397-418
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• 2014

In this paper, a simple two-step method for structural vibration-based health monitoring for beam-like structures have been extended to plate-like structures with though-thickness cracks. Crack locations and severities of plate-like structures are detected using a hybrid approach. The interval wavelet transform is employed to extract crack singularity locations from mode shape and support vector regression (SVR) is applied to predict crack serviettes form crack severity detection database (the relationship of natural frequencies and crack serviettes) using several natural frequencies as inputs. Of particular interest is the natural frequencies estimation for cracked plate-like structures using Rayleigh quotient. Only the natural frequencies and mode shapes of intact structures are needed to calculate the natural frequencies of cracked plate-like structures using a simple formula. The crack severity detection database can be easily obtained with this formula. The hybrid method is investigated using numerical simulation and its validity of the usage of interval wavelet transform and SVR are addressed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.10a
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• pp.305-306
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• 2012

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.06a
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• pp.185-186
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• 2008

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.10a
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• pp.395-396
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• 2009

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.223-233
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.971-976
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• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in rectangular coordinates rather than in polar coordinates, in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Rectangular coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters: the rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.117-126
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• 2016

In this paper, a numerical procedure for the natural vibration analysis of plates with openings and carlings based on the assumed mode method is extended to assess their forced response. Firstly, natural response of plates with openings and carlings is calculated from the eigenvalue equation derived by using Lagrange's equation of motion. Secondly, the mode superposition method is applied to determine frequency response. Mindlin theory is adopted for plate modelling and the effect of openings is taken into account by subtracting their potential and kinetic energies from the corresponding plate energies. Natural and frequency response of plates with openings and carlings subjected to point excitation force and enforced acceleration at boundaries, respectively, is analysed by using developed in-house code. For the validation of the developed method and the code, extensive numerical results, related to plates with different opening shape, carlings and boundary conditions, are compared with numerical data from the relevant literature and with finite element solutions obtained by general finite element tool.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.7
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• pp.667-675
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• 2012

A damage estimation method for support structure of offshore wind turbine using modal parameters is presented for effective structural health monitoring. Natural frequencies and mode shapes for a support structure with monopile of an offshore wind turbine were calculated considering soil condition and added mass. A neural network was learned based on training patterns generated by the changes of natural frequency and mode shape due to various damages. Natural frequencies and mode shapes for 10 prospective damage cases were input to the trained neural network for damage estimation. The identified damage locations and severities agreed reasonably well with the accurate damages. Multi-damage cases could also be successfully estimated. Enhancement of estimation result using another parameters as input to neural network will be carried out by further study. Proposed method could be applied to other type of support structure of offshore wind turbine for structural health monitoring.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.659-676
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• 2008

The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.