scholarly journals Effect of Potential Energy Variation on the Natural Frequency of an Euler–Bernoulli Cantilever Beam Under Lateral Force and Compression

2017 ◽  
Vol 84 (5) ◽  
Author(s):  
B. Béri ◽  
G. Stépán ◽  
S. J. Hogan
Keyword(s):  
Potential Energy ◽  
Theoretical Result ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Vibration Frequency ◽  
Lateral Force ◽  
Bending Vibration ◽  
Energy Variation ◽  
Frequency Calculation

A cantilever beam is subjected to both lateral force and compression under gravity. By taking into account the potential energy variation of the system, we develop a theoretical result that greatly simplifies the bending vibration frequency calculation in agreement with the experiments.

scholarly journals The Static and Dynamic Sensitivity of Magnetostrictive Bioinspired Whisker Sensor

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Ran Zhao ◽  
Qingjie Yuan ◽  
Jianwu Yan ◽  
Qanguo Lu
Keyword(s):  
Natural Frequency ◽  
Cantilever Beam ◽  
Vibration Frequency ◽  
Experimental System ◽  
High Sensitivity ◽  
First Order ◽  
Dynamic Sensitivity ◽  
Flow Sensing ◽  
Technical Indicator ◽  
Static Sensitivity

Magnetostrictive bioinspired whisker is a new kind of sensor that can realize tactile and flow sensing by utilizing magnetoelastic effect. The sensitivity is a key technical indicator of whisker sensor. The paper presented a new magnetostrictive whisker based on Galfenol cantilever beam, as well as its operation principle. Then, the static and dynamic sensitivity of the whisker sensor was investigated by using a self-made experimental system. The results illustrated that the proposed sensor has a high sensitivity. Its static sensitivity is 2.2 mV/mN. However, its dynamic sensitivity depends on the vibration frequency. When working at the natural frequency of the cantilever beam, the dynamic sensitivity performs an obvious increase—1.3 mV/mN at 3.5 Hz (the first-order natural frequency) and 2.1 mV/mN at 40 Hz (the second-order natural frequency), respectively.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

Hybrid-Bistable Vibration Energy Harvester With Adaptive Potential Well

2018 ◽  
Author(s):  
Jinki Kim ◽  
Patrick Dorin ◽  
K. W. Wang
Keyword(s):  
Energy Harvesting ◽  
Potential Energy ◽  
Cantilever Beam ◽  
Potential Barrier ◽  
Energy Barrier ◽  
Electrical Power ◽  
Vibration Energy ◽  
Frequency Spectra ◽  
Potential Energy Barrier ◽  
Piezoelectric Energy

Many common environmental vibration sources exhibit low and broad frequency spectra. In order to exploit such excitations, energy harvesting architectures utilizing nonlinearity, especially bistability, have been widely studied since the energetic interwell oscillations between their stable equilibria can provide enhanced power harvesting capability over a wider bandwidth compared to the linear counterpart. However, one of the limitations of these nonlinear architectures is that the interwell oscillation regime may not be activated for a low excitation level that is not strong enough to overcome the potential energy barrier, thus resulting in low amplitude intrawell response which provides poor energy harvesting performance. While the strategic integration of bistability and additional dynamic elements has shown potential to improve broadband energy harvesting performance by lowering the potential barrier, there is a clear opportunity to further improve the energy harvesting performance by extracting electrical power from the kinetic energy in the additional element that is induced when the potential barrier is lowered. To explore this opportunity and advance the state of the art, this research develops a novel hybrid bistable vibration energy harvesting system with a passive mechanism that not only adaptively lowers the potential energy barrier level to improve broadband performance but also exploits additional means to capture more usable electrical power. The proposed harvester is comprised of a cantilever beam with repulsive magnets, one attached at the free end and the other attached to a linear spring that is axially aligned with the cantilever (a spring-loaded magnet oscillator). This new approach capitalizes on the adaptive bistable potential that is passively realized by the spring-loaded magnet oscillator, which lowers the double-well potential energy barrier thereby facilitating the interwell oscillations of the cantilever across a broad range of excitation conditions, especially for low excitation amplitudes and frequencies. The interwell oscillation of the cantilever beam enhances not only the piezoelectric energy harvesting from the beam but also the electromagnetic energy harvesting from the spring-loaded magnet oscillator by inducing large amplitude vibrations of the magnet oscillator. Numerical investigations found that the proposed architecture yields significantly enhanced energy harvesting performance compared to the conventional bistable harvester with fixed magnet.

scholarly journals Research on the Approximate Calculation Method of the Fundamental Frequency and Its Characteristics on a Tensioned String Bridge

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 126
Author(s):  
Guangwei Zhou ◽  
Changzhao Qian ◽  
Changping Chen
Keyword(s):  
Finite Element ◽  
Fundamental Frequency ◽  
Vibration Frequency ◽  
Structural Characteristics ◽  
Physical Characteristics ◽  
Parameter Analysis ◽  
Lateral Bending ◽  
Bending Vibration ◽  
Main Cable ◽  
Symmetrical Vibration

As a new type of composite bridge, the dynamic structural characteristics of a tensioned string bridge need to be deeply studied. In this paper, based on the structural characteristics of a tensioned string bridge, the Rayleigh method is used to derive formulas for calculating the frequencies of vertical, antisymmetric and lateral bending vibrations. The characteristics of the vertical and lateral bending vibration frequencies are summarized. The fundamental frequencies of the antisymmetric vertical bending and lateral bending of the tensioned string bridge are the same as that of the single-span beam under the corresponding constraint conditions. The shape and physical characteristics of the main cable have no effect on the frequency. The vertical bending symmetrical vibration frequency of the tensioned string bridge is greater than the corresponding symmetrical vibration frequency of the simply supported beam. The shape and physical characteristics of the main cable have a greater impact on the vertical bending symmetrical vibration frequency than the lateral bending frequency, and the vertical bending symmetrical vibration frequency increases with an increasing rise-to-span ratio. The tension force of the main cable has no influence on the frequency of tensioned string bridges. The first-order frequency of the tensioned string bridge is generally the vertical bending symmetrical vibration frequency. By adopting a tensioned string bridge structure, the fundamental frequency of a structure can be greatly increased, thereby increasing the overall rigidity of the structure. Finally, an engineering example is applied with the finite element parameter analysis method to study the vibration frequency characteristics of the tensioned string bridge, which verifies the correctness of the formula derived in this paper. The finite element analysis results show that the errors between the derived formula in this paper and the finite element calculation results are less than 2%, indicating that the formula derived in this paper has high calculation accuracy and can meet the calculation accuracy requirements of engineering applications.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

Analysis of Coupled Bending-Axial Vibration of a Rotor

2013 ◽  
Vol 662 ◽  
pp. 608-611 ◽  
Author(s):  
Jian Feng Ye ◽  
Chun Long Zheng ◽  
Xue Shi Yao
Keyword(s):  
Axial Force ◽  
Vibration Frequency ◽  
Torsional Vibration ◽  
Stiffness Matrix ◽  
Tensile Force ◽  
Vibration Frequencies ◽  
Axial Vibration ◽  
Bending Vibration ◽  
Centrifugal Load ◽  
Rotor Model

Aiming at a rotor model, the coupled bending-axial vibration is being analyzed.Calculation results show that the prestress relative to rotational centrifugal load may influence bending vibration frequencies of a rotor.The bending vibration frequencies will increase when the prestress increases.The axial vibration frequency has not an influence because the direction of the spinning prestress is perpendicular to axis.When a rotor is applies axial force, a compressional force will tend to increase the axial vibration frequencies while a tensile force will decrease the axial vibration frequencies.The effects of the prestress(centrifugal load )of the spinning rotor and the axial prestress can be accounted by an adjustment of the stiffness matrix for analysis.By use of the stiffness matrix,the changed axial and bending vibration frequencies can be explained.The coupled bending-axial vibration may take place when the bending vibration frequencies have increased in the state of the changed prestress.In the end, the coupled bending-axial vibration frequency can be calculated.On the basis of prestress, the coupled lateral-torsional vibration and the coupled torsional-axial vibration frequency can be analysed,similarly.

Thermal Performance Improvement of a Heat Sink With Piezoelectric Vibrating Fins

2010 ◽  
Author(s):  
Hee Seung Park ◽  
Sung Jin Kim
Keyword(s):  
Natural Frequency ◽  
Performance Improvement ◽  
Thermal Performance ◽  
Vibration Frequency ◽  
Heat Sink ◽  
Vibration Amplitude ◽  
Piezoelectric Actuators ◽  
Convection Heat ◽  
Heat Transfer Characteristics ◽  
Heat Sink Temperature

A heat sink with piezoelectric vibrating fins is developed through attaching piezoelectric actuators to the fins of a heat sink, and the heat transfer characteristics of the heat sink are experimentally investigated. Thermal performance improvement of the heat sink by the vibration of the fins is observed compared to the thermal performance of a natural convection heat sink with static fins under a fixed heat sink geometry condition. The thermal performance of the heat sink changes as the vibration amplitude of the fins or the vibration frequency of the fins changes. Particularly, if the vibration frequency of the fins matches up to the natural frequency of the fins, the vibration amplitude is significantly increased by resonance and the thermal performance also increases. The natural frequency of the fins changes with the heat sink temperature because the geometry of the fins changes and the properties of the fins change due to the temperature change.

Effects of Ceramsite Concrete Strength on Natural Frequency Based on ANSYS

2012 ◽  
Vol 204-208 ◽  
pp. 4124-4127
Author(s):  
Hao Qing Wang ◽  
Qiu Kong ◽  
Zhou Ping Yu ◽  
Wei Jun Yang
Keyword(s):  
Natural Frequency ◽  
Seismic Design ◽  
Vibration Frequency ◽  
Concrete Strength ◽  
Reinforcing Steel ◽  
Material Parameters ◽  
Modeling Analysis ◽  
Steel Bar ◽  
Environmental Vibration

By separate modeling analysis based upon ANSYS, SOLID65 unit of the entity is selected to simulate ceramsite concrete, and reinforcing performance is selected to simulate the effect of reinforcing steel bar. The strength on natural frequency’s effects was studied through changing the ansys model’s material parameters of ceramsite concrete. The strength of ceramsite concrete can be determined and applied to the anti-seismic design according to the size of the environmental vibration frequency.

Shunt Tuning of a Piezoelectric Cantilever Beam Resonator

2003 ◽  
Author(s):  
Muturi G. Muriuki ◽  
William W. Clark
Keyword(s):  
Stainless Steel ◽  
Piezoelectric Material ◽  
Analytical Model ◽  
Cantilever Beam ◽  
Lead Zirconate Titanate ◽  
Vibration Frequency ◽  
Experimental Testing ◽  
Lead Zirconate ◽  
Beam Resonator ◽  
Piezoelectric Cantilever

This paper presents the design and analysis of a cantilever beam resonator that is driven by a piezoelectric material. The beam is a bimorph structure with Lead Zirconate Titanate (PZT) and stainless steel or aluminum layers. The PZT layer is electroded in segments to form a sensor and actuator pair for feedback to drive the resonator. An additional PZT segment is used, in conjunction with a capacitive shunt circuit, to change the vibration frequency of the resonator. The study is based on an analytical model of the beam and experimental testing.

Parameter Identification of a Cantilever Beam Immersed in Viscous Fluids With Potential Applications to the Probe Calibration of Atomic Force Microscopes

2009 ◽  
Author(s):  
Wenlung Li ◽  
S. P. Tseng
Keyword(s):  
Parameter Identification ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Present Method ◽  
Present Report ◽  
Excitation Frequency ◽  
Spring Constant ◽  
Target System ◽  
Phase Lag ◽  
Identification Method

The main objective of the report is to present a new identification method has been derived for single-degree, base-excited systems. The system is actually to mimic a probe of cantilever type of AFMs. In fact, the idea of the present report was initiated by needs for in situ spring constant calibration for such probe systems. Calibration processes can be treated as parameter identification for the stiffness of the probe before it is used. However, sine a real probe is too small to be seen by bare eyes and too costly to verify, a cantilever beam was adopted to replace it during the study. The present method starts with giving a chirp excitation to the target system, and to lock the damped natural frequency. Once the damped natural frequency is obtained, it is possible to locate the frequency at which the phase lag is equal to π/2. From which, the excitation frequency is then purposely changed to that frequency and the corresponding steady-state responses are measured. In the meantime, the system dissipative energy or power may also need to be stored. In fact, the present identification formulation is to express the spring constant of the target systems in terms of two measurable parameters: the phase angle and the system damping. The former can be computed from the damped natural frequency while the latter can be identified along with measuring the input power. The novel formulation is then numerically simulated using the Simulink toolbox of MATLAB. The simulation results clearly showed the current identification method can work with good accuracy. Following the numerical simulation, experimental measurements were also carried out by a cantilever beam that its free end was immersed to viscid fluids. The fluids of different viscosity were used to mimic the environments of a probe in use. The experimental results again substantiated the correctness of the present method. Thus it is accordingly concluded that the new recognition algorithm can be applied with confidence.

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