Vibration suppression of atomic-force microscopy cantilevers covered by a piezoelectric layer with tensile force

M. H. Korayem,A. Alipour,D. Younesian 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.9

In this paper, vibration suppression of a micro-beam covered by a piezoelectric layer is studied. The micro-beam is modeled with the specific attention to its application in AFM. The AFM micro-beam is a cantilever one which is stimulated close to its natural frequency by applying a harmonic voltage to the piezoelectric layer. The beam is an Euler-Bernoulli beam which abbeys Kelvin-Voigt model. Using such model supplies the comparison between elastic and viscoelastic beams; and one of the most important properties of viscoelastic materials, damping effect can readily be investigated. The pump provides an axial load with the result that it suppresses the vibrations. First, the vibration equations are extracted using Lagrangian and extended Hamiltonian method in vertical, longitudinal, as well as torsional directions and are discretized by exploiting the Galerkin mode summation approach. The discretized time-domain equations are solved by the aid of the Runge-Kutta method. The viscoelastic beam is compared with the elastic one, and the effects of damping ratio on vibration responses are presented. Additionally, the effects of micro-pump load, excitation voltage, and initial twist angle are investigated on the amplitude of vibration and natural frequency of system. It is observed that viscoelasticity of beam and axial load of the pump reduce vibrations and provide uniform time-domain responses without beatings.

크랙과 집중질량을 가진 회전 외팔보의 진동 해석

김경호(Kyung - Ho Kim),엄승만(Seung - Man Eom),유홍희(Hong Hee Yoo) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

In this paper the vibration analysis of rotating cantilever beams having a crack and a concentrated mass are performed. The influences of a concentrated mass, the crack depth, and the crack position on the natural frequencies of the rotating cantilever beam are investigated by a numerical method. The cracked cantilever beam is modeled based on the Euler-Bernoulli beam theory. The flexibility due to crack is calculated using a fracture mechanics theory. The crack is assumed to be opened during the vibrations. As inspected, as the crack depth and the concentrated mass increase, the natural frequencies of the beam decrease. In general, the natural frequencies of the rotating cantilever beam are more sensitive to the rotating angular velocity than the depth of the crack and the position of the crack.

Analytical and Experimental Investigation of Partially Covered Piezoelectric Cantilever Energy Harvester

Rouhollah Hosseini,Mohsen Hamedi,임종범,김재환,Jedol Dayou 한국정밀공학회 2017 International Journal of Precision Engineering and Vol.18 No.3

Electrical energy is normally generated through different sources such as hydroelectric, wind, heat, nuclear transformation, chemical reactions or vibrations. Nowadays, harvesting power from mechanical vibration is one of the novel technologies that usually can be done by systems based on electromagnetic, electrostatic, piezoelectric and combination of them. Piezoelectric systems can convert motion from the vibrating structures into electrical power. Cellulose Electro-active paper (EAPap) has been recognized as a novel smart piezoelectric material that can be used for energy harvesting purposes. One of the most prevalent method for vibration energy harvesting is using unimorph piezoelectric cantilever beams. In this paper, an analytical solution based on distributed parameter model is presented to calculate the generated energy from vibration of cantilever substrate that is partially covered by EAPap material. In the studied structure, piezoelectric layer thickness in comparison to the length of the beam and thickness of substrate material can be considered very thin. Thus its effect on the vibration behavior of structure is negligible. The results are validated by experimental values. The analytical data was found to be very close to experimental results and finite element simulation values. Findings from this study provide guidelines on system parameters that can be manipulated for more efficient performance in different ambient source conditions.

Cantilever형 바이몰프 압전소자의 출력특성에 관한 연구

김용혁(Yong-Hyuk Kim) 대한전기학회 2010 전기학회논문지 Vol.59 No.3

Using piezoelectric elements to harvest energy from ambient vibrations has been of great interest over the past few years. Due to the relatively low power output of piezoelectric materials, there are many study to improve the energy harvesting efficiencies. This paper is study the efficiencies of the output energy considering the cantilever piezoelectric bimorph using aluminum vibration beam. when the length of vibration beam and the piezoelectric body becomes same and the maximum output power comes out. DC voltage was increased as the beam thickness and vibration frequency was increased. The vibration beam was able to achieve very large energy value.

Experimental analysis of electromagnetic vibration damping of a cantilever beam

M. R. Siddiqui,I. Ahmad,M. Khan,S.M. Ahmad 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10

Vibration attenuation is necessary in many electro-mechanical systems. In this paper electromagnetic damping is applied on a flexible cantilever beam (FCB) made of ferromagnetic material. The lateral vibration is controlled by employing two electromagnetic poles mounted in the same axis as that of a vibrating cantilever beam. A power amplifier is developed to provide desired current to the electromagnet. Comparison of damping achieved at different electromagnetic forces is presented. The study employs a new method of applying a constant DC power to one of the electromagnets while other is connected to a variable current source. Experimental results are presented that show the effectiveness of the presented approach.

The effect of internal axial forces of a cantilever beam with a lumped mass at its free end

Zhang, Jinfu Techno-Press 2018 Coupled systems mechanics Vol.7 No.3

When a cantilever beam with a lumped mass at its free end undergoes free transverse vibration, internal axial forces are produced in the beam. Such internal axial forces have an effect on free transverse vibration of the beam. This effect is studied in this paper. The equations of motion for the beam in terms of the generalized coordinates including the effect are derived. The method for determining free transverse vibration of the beam including the effect is presented. In numerical simulations, the results of free transverse vibration of the free end of the beam including and not including the effect are obtained. Based on comparison between the results obtained, the conclusions concerning the effect are given.

테이퍼진 단면을 가진 회전 외팔보의 진동해석

이준희(Lee, Jun-Hee),유홍희(Yoo, Hong-Hee) 한국소음진동공학회 2009 한국소음진동공학회 논문집 Vol.19 No.4

A vibration analysis for a rotating cantilever beam with the tapered cross section is presented in this study. The stiffness changes due to the stretching caused by centrifugal inertia forces when a tapered cantilever beam rotates about the axis perpendicular to its longitudinal axis. When the cross section of cantilever beam are assumed to decrease constantly, the mass and stiffness also change according to the variation of the thickness and width ratio of a tapered cantilever beam. Such phenomena result in variations of natural frequencies and mode shapes. Therefore it is important to the equations of motion in order to be obtained accurate predictions of these variations. The equations of motion of a rotating tapered cantilever beam are derived by using hybrid deformation variable modeling method and numerical results are obtained along with the angular velocity and the thickness and width ratio.

Eigen-Frequency of a Cantilever Beam Restrained with Added Mass and Spring at Free End or a Node Point

Woo-Gun Sim(심우건) 한국산학기술학회 2018 한국산학기술학회논문지 Vol.19 No.12

열 교환기/원자로의 과도한 진동을 방지 하려면 진동해석을 설계 단계에서 수행해야 한다. 진동 문제에서 고유 진동수의 정보는 열 교환기/원자로의 안전성을 평가하기 위하여 요구된다. 본 논문은 일단 지지보에 발생되는 고유치 문제를 해석하기 위하여 수치해석 방법인 Galerkin의 방법을 기술하였다. 일단 지지보는 자유단 끝점 또는 모드의 노드 포인트에 부가질량과 스프링에 의하여 구속되어 있다. 수치해석으로 구한 고유진동수는 간단한 해석 방법과 간단한 테스트에 의하여 각각 구한 결과와 비교 되었다. Galerkin의 방법을 사용하여 논의된 일단 지지보의 고유 진동수를 구할 수 있음을 보였다. 부가질량 증가함에 따라 고유 주파수는 감소하며 스프링 힘의 증가에 따라 고유 주파수는 상승함을 보였다. 무거운 부가 질량은 가연성 배관의 지지대 역할을 함을 보였다. 일단 지지보의 끝단에 설치된 부가 질량의 경우에 개발된 기존의 어림적 해석방법으로도 일차 모두의 고유 진동수를 비교적 정확하게 구할 수 있음을 알 수 있었다. In order to avoid excessive vibration, it is required to carry out a vibration analysis of heat-exchanger/nuclear- reactor at the design stage. Information of eigen-frequency in the vibration problem is required to evaluate safety of heat-exchange/nuclear reactor. This paper describes a numerical method, Galerkin’s method, to solve the eigenvalue problem occurred in a cantilever beam. The beam is restrained with added mass and spring at the free end or a node point of a mode shape. The numerical results of eigen-frequency were compared with simple analytical and experimental results given by simple approach and simple test, respectively. It is found that Galerkin’s method is applicable to estimate the eigen-frequency of the cantilever beam. The frequencies become lower with increasing the added mass and the frequencies increase with the spring force. It is shown the heavy added mass has a role of support on the flexible tube. The eigen-frequency of the first mode, for the system with the added mass mounted at the free end, can be calculated by the approximate analytical method existing with more or less accuracy.

Sensitivity Analysis of Dynamic Response by Change in Excitation Force and Cross-sectional Shape for Damped Vibration of Cantilever Beam

Seong-Ho Yun(윤성호) 한국기계가공학회 2021 한국기계가공학회지 Vol.20 No.8

This paper describes the time rate of change of dynamic response of a cantilever beam inserted with a damping element, such as bonding, which is excited under a general force at various locations. A sensitivity analysis was performed in a finite element model to show that two types of second-order algebraic governing equations were used to predict the rate of change of dynamic displacement: one is related to the modal coordinate linked to a physical coordinate, and the other to the design parameter of the time rate of change of displacement. The sensitivity differential equation formulation includes more complicated terms compared with that of the undamped cantilever beam. The sensitivities of the dynamic response were observed by changing the location of the excitation force, displacement extraction, and cross-sectional area of the beam. The analytical results obtained by this suggested theory showed a relatively good agreement when compared with those obtained using the commercial finite element program. The suggested analysis procedure enables the prediction of the response sensitivity for any finite element model of the dynamic system.

An experimental method to determine glass elastic modulus based on the fundamental frequency of the elastic support-free end beam

Kun Jiang,Danguang Pan 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.88 No.2

Silicate glass is usually a brittle and plate-like material, and it is difficult to measure the elastic modulus by the traditional method. This paper develops a test method for the glass elastic modulus based on the fundamental frequency of the cantilever beam with an elastic support and a free end. The method installs the beam-type specimen on a semi-rigid support to form an elastic support-free end beam. The analytic solution of the stiffness coefficients of the elastic support is developed by the fundamental frequency of the two specimens with known elastic modulus. Then, the glass elastic modulus is measured by the fundamental frequency of the specimens. The method significantly improves the measurement accuracy and is suitable for the elastic modulus with the beam-type specimen whether the glass is homogeneous or not. Several tests on the elastic modulus measurement are conducted to demonstrate the reliability and validity of the test method.