• Smart Structures and Systems
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• v.16 no.4
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• pp.623-640
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• 2015

This paper presents techniques to harvest higher voltage from piezoelectric cantilever energy harvester by structural alteration. Three different energy harvesting structures are considered namely, stepped cantilever beam, stepped cantilever beam with rectangular and trapezoidal cavity. The analytical model of three energy harvesting structures are developed using Euler-Bernoulli beam theory. The thickness, position of the rectangular cavity and the taper angle of the trapezoidal cavity is found to shift the neutral axis away from the surface of the piezoelectric element which in turn increases the generated voltage. The performance of the energy harvesters is evaluated experimentally and is compared with regular piezoelectric cantilever energy harvester. The analytical and experimental investigations reveal that, the proposed energy harvesting structures generate higher output voltage as compared to the regular piezoelectric cantilever energy harvesting structure. This work suggests that through simple structural modifications higher energy can be harvested from the widely reported piezoelectric cantilever energy harvester.

• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.445-462
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• 1995

Previous studies of a stepped cantilever with two straight segments under a suddenly applied constant force (a step load) applied at its tip have shown that the validity of deformation mechanisms is governed by certain geometrical restrictions. Single and double-hinge mechanisms have been proposed and it is shown in this paper that for a stepped cantilever with a stronger tip segment, i.e. $M_{0.1}$ > $M_{0.2}$, where $M_{0.1}$ and $M_{0.2}$ are the dynamic fully plastic bending moments of the tip and root segments, respectively, the family of possible yield mechanisms is expanded by introducing new double and triple-hinge mechanisms. With the aid of these mechanisms, it is shown that all initial deformations can be derived for a stepped cantilever regardless of its geometry and the magnitude of the dynamic force applied.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.401-410
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• 2008

The natural frequency of a beam plays an important role in not only vibration analysis but also understanding its dynamic characteristics. It is complicated to analyse the natural frequency of a stepped beam with discontinuously varying section. Approximate analysis methods such as Rayleigh-Ritz method, FEM, etc. are frequently used for the vibration analysis of stepped beams. In such a case, accuracy of these methods depends upon the number of partitioned elements, the number of the iterations in calculation and the assumed mode shape. This study presents an approximate analysis method for the fundamental natural frequency analysis of stepped cantilever beam, using equivalent beam transformation technique. Validity and usefulness are verified by comparing the proposed method with FEM for several example problems.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.3
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• pp.17-23
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• 2006

The strength estimation is carried out for injection molded plastic stepped gear. The stepped gear is considered as a plate model which is fixed by two edges and freed on the other sides. The stress of common normal gear is calculated by Lewis formula which can be derived quite simply from the equation fur the stress at the root of a cantilever beam. Stress ratio(step factor) between the common normal gear and stepped gear is proposed for the ratio of the bending stress of normal gear and that of stepped gear. This study proposes the step factor added in Dupont equation which is used for strength estimation of injection molded plastic stepped gear.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.92-97
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• 2004

The aim of this study is to estimate the strength of injection molded plastic stepped gear. We considered stepped gear as plate model which are fixed by two edges. While, on the other sides are free. Normal gear is calculated by Lewis formula which can be derived quite simply from the equation for the stress at the root of a cantilever beam. Stress ratio(step factor) is represented for the ratio of the bending stress of normal and the bending stress of stepped gear, and it is plotted by face width factor. This study is propose the step factor added in Dupont equation which are strength estimation of step gear

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.801-804
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• 2006

The purpose of this paper is to investigate the stability of stepped cantilever columns with a tip mass of rotatory inertia and a translational spring at one end. The column model is based on the Bernoulli-Euler theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibration of columns with stepwise variable cross-section and subjected to a subtangential follower force is solved numerically using the corresponding boundary conditions. And the bisection method is used to calculate the critical divergence/flutter load. The frequency and critical divergence/flutter load for the stepped column with a single step are presented as functions of various non-dimensional system parameters: the segmental length parameter, the section ratio, the subtangential parameter, the mass, the moment of inertia of the mass, and the spring parameter.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.4
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• pp.80-88
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• 1997

An experimental investigation of the fatigue through crack growth behavior under simple stepped variable loading condition has been performed using Al7075-T651. Experiments were carried out by using cantilever bending type specimens, with chevron notches on a small electro-magnetic test machine. Tensile overloads have a retarding effect on the fatigue crack growth rates, therefore tensile overloads were used for the beneficial effect on the fatigue life. While in most cases compressive overloads have only a vanishing effect on crack growth rates, some experiments with single edge crack tension specimens reveal a marked growth retardation. The stress ratios used in this investigations varies from R=0.32 to 0.81, from R=0.04 to 0.76, from R=-0.15 to 0.73, and from R=-0.33 to 0.68 and the peak load for each case was not varied. The crack growth and crack closure were measured by Kikukawa's compliance method with a strain gauge mounted on the backside of each specimens. The results obtained are as follows. When the stepped variable load was applied, the smaller the stress ration was, the larger the delayed retardation of the crack growth rate was. The fatigue crack growh rate data obtained for through cracks were plotted well against the effective stress intensity factor range from 4.0 to 20.0MP{a^{SQRT}m}. It was found that the effective stress intensity factor range ratio was related well to the opening stress intensity factor, the maximum stress intensity factor, and crack length.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.3
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• pp.82-88
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• 1997

This paper derives the generalized stiffness to find dynamic characteristics and its derivatives of a continuous system. And a new sensitivity analysis method is presented by using the amount of change of generalized stiffness and vibrational mode caused by the variation of stiffness. In this paper, to get or detect appropriate results, cantilever beam and stepped beam and stepped beam are used. Deviations of sensitivity coefficient, natural frequency, and vibrational mode are calculated as result, and compared with the theoretical exact values.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.4 s.142
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• pp.341-349
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• 2005

With increasing demands of high speed transportation, recently a lot of high speed marine vehicles, such as SWATH, semi-planing craft, planing craft, hydrofoil craft, SES and so on, have been paid attention especially in high speed region over the Froude number 0.5. The resistance characteristics of the vehicles should be experimentally evaluated in the towing tank. At the Seoul National University, a light-weight cantilever type towing carriage was devised and installed in the towing tank. Wireless measurement devices were also provided for appropriate data acquisition during high-speed towing tests. With the new carriage system, a series of model tests were performed to investigate the hydrodynamic characteristics of a stepped planning hull in the towing tank and the resistance performances of the hull are introduced in this report.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2812-2818
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• 1996

A cantilever beam with a mass and a spring at the end can be use to model a miniature flexible arm. It is necessary to know the natural frequencies and mode shapes to discuss its free vibration, especially when modal analysis is employed. A beam is clamped-free. In this paper we look at the lateral vibration of beams that have step changes in the properties of their cross sections. The frequency equation is derived by Bernoulli-Euler formulation and is sloved by the separation of variable. The parameters of the beam, 'mass and spring stiffness' are defined as nondimensionalized parameters for wide application of the results. According to the change of eigenvalues and mode shape are presented for this beam. The results presented are the eigenvalues and the natural frequencies for the first three modes of vibration. Results show that the parameters have a significant effect on the natural frequency.