Showing papers on "Natural frequency published in 2008"

A vibration energy harvesting device with bidirectional resonance frequency tunability

Abstract: Vibration energy harvesting is an attractive technique for potential powering of wireless sensors and low power devices. While the technique can be employed to harvest energy from vibrations and vibrating structures, a general requirement independent of the energy transfer mechanism is that the vibration energy harvesting device operate in resonance at the excitation frequency. Most energy harvesting devices developed to date are single resonance frequency based, and while recent efforts have been made to broaden the frequency range of energy harvesting devices, what is lacking is a robust tunable energy harvesting technique. In this paper, the design and testing of a resonance frequency tunable energy harvesting device using a magnetic force technique is presented. This technique enabled resonance tuning to ±20% of the untuned resonant frequency. In particular, this magnetic-based approach enables either an increase or decrease in the tuned resonant frequency. A piezoelectric cantilever beam with a natural frequency of 26 Hz is used as the energy harvesting cantilever, which is successfully tuned over a frequency range of 22‐32 Hz to enable a continuous power output 240‐280 μW over the entire frequency range tested. A theoretical model using variable damping is presented, whose results agree closely with the experimental results. The magnetic force applied for resonance frequency tuning and its effect on damping and load resistance have been experimentally determined. (Some figures in this article are in colour only in the electronic version)

Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model

Abstract: Linear models and synchronous response are generally adequate to describe and analyze rotors supported by hydrodynamic bearings. Hence, stiffness and damping coefficients can provide a good model for a wide range of situations. However, in some cases, this approach does not suffice to describe the dynamic behavior of the rotor-bearing system. Moreover, unstable motion occurs due to precessional orbits in the rotor-bearing system. This instability is called “oil whirl” or “oil whip”. The oil whirl phenomenon occurs when the journal bearings are lightly loaded and the shaft is whirling at a frequency close to one-half of rotor angular speed. When the angular speed of the rotor reaches approximately twice the natural frequency (first critical speed), the oil whip phenomenon occurs and remains even if the rotor angular speed increases. Its frequency and vibration mode correspond to the first critical speed. The main purpose of this paper is to validate a complete nonlinear solution to simulate the fluid-induced instability during run-up and run-down. A flexible rotor with a central disk under unbalanced excitation is modeled. A nonlinear hydrodynamic model is considered for short bearing and laminar flow. The effects of unbalance, journal-bearing parameters and rotor arrangement (vertical or horizontal) on the instability threshold are verified. The model simulations are compared with measurements at a real vertical power plant and a horizontal test rig.

Theory of Thermoelastic Damping in Micromechanical Resonators With Two-Dimensional Heat Conduction

Abstract: Analysis of thermoelastic damping (TED) is an important component of the design of low-loss vacuum-operated micro- and nanomechanical resonators used in microelectro- mechanical systems (MEMS). The quasi-1-D theories developed by Zener in 1937, and subsequently improved by Lifshitz and Roukes in 2000, are now widely used in MEMS design. This paper presents an exact theory for TED with 2-D heat conduction that enables a detailed evaluation of the accuracy of the quasi-1-D theories. A Green's function method is used to solve the 2-D heat- conduction equation, and an expression for TED is derived in the form of an infinite series. The effects of beam geometry, length-to- thickness aspect ratio, natural frequency, flexural mode shapes, and structural boundary conditions on TED are investigated for the representative case of single-crystal silicon microbeam resonators. The errors in the exact quasi-1-D theory range from 2% to 80% depending upon the aspect ratio and the mode shape. Implications for the use of the quasi-1-D and 2-D theories in MEMS design are discussed. [2007-0199].

A New Compliant Mechanical Amplifier Based on a Symmetric Five-Bar Topology

Abstract: A mechanical amplifier is an important device, which together with a piezoelectric actuator can achieve motion with high resolution and long range. In this paper, a new topology based on a symmetric five-bar structure for displacement amplification is proposed, and a compliant mechanism is implemented for the amplifier. In short, the new mechanical amplifier is called a compliant mechanical amplifier (CMA). The proposed CMA can achieve large amplification ratio and high natural frequency, as opposed to the existing CMAs, in terms of topology. Detailed analysis with finite element method has further shown that a double symmetric beam five-bar structure using corner-filleted hinges can provide good performances compared with its counterpart, which is based on four-bar topology. Finally, experiments are conducted to give some validation of the theoretical analysis.

Frequency determination from vehicular loading time pulse to predict appropriate complex modulus in MEPDG

Abstract: The complex modulus is used by the Mechanistic-Empirical Pavement Design Guide (MEPDG) for hot-mix asphalt (HMA) time and temperature dependency simulation. The correctness of the design process essentially depends on the accuracy of the conversion from the time domain to the frequency domain since the complex modulus is measured in the frequency domain while vehicular loading is applied in the time domain. That the frequency is calculated as the inverse of the loading time is assumed by the current MEPDG approach. That the frequency can be determined from the angular frequency is suggested by another approach. These two techniques are analyzed in the paper, and it is demonstrated that they only represent approximations for specific cases not encountered in pavement systems. There is presentation of a novel approach for accurate determination of vehicular loading frequency based on a detailed Fourier analysis. A direct and reliable technique to obtain moving load frequency spectrum based on the time pulse data is provided by the proposed Fourier approach. Data from the Virginia Smart Road were used to evaluate and validate this approach. There was analysis of the field loading frequency spectra at different depths and under various vehicle speeds. Analysis results indicated that the MEPDG approach is associated with a 40 to 140% error range in frequency estimation depending on depth of calculation and the vehicle speed. There is estimation of the natural frequency of an HMA layer and investigation of the delayed-response association with HMA viscous properties during the unloading phase based on this method.

Simulated and experimental dynamic response characterization of an electromagnetic microvalve

Abstract: The dynamic response of two electromagnetically actuated microvalves operating in open-air conditions are measured experimentally and simulated using a three-dimensional fluid–structural finite element model. Open-air conditions mean that the fluid inlet and outlet are not pressurized. The dynamic response of the membrane is obtained experimentally by exciting the valve with a step voltage signal of 1 kHz and measuring the membrane vertical displacement using a Polytec Laser Doppler Vibrometer (LDV) system. Vibration analysis of the experimental data provides dynamic parameters such as natural frequency, air damping coefficient, spring constant, and settling time of the membrane. An electromagnetic force model based on the reluctance method is constructed and validated from the experimental data. The validated electromagnetic force model and corrected material properties are then used in a three-dimensional, fluid–structural finite element model to simulate membrane dynamics. Pertinent dynamic parameters such as resonance frequency, spring constant, microvalve closing time, settling time of the membrane, and actuation energy of the microvalve are finally compared with the simulated results. The comparison of experimental and simulation results shows that the finite element model accurately reproduces the dynamics of the membrane in the slip-flow region. A valid simulation method can then be used to simulate microvalve dynamic response in pressurized flow conditions and evaluate new designs. Valve closing time of less than 150 μs is demonstrated in one valve design. The energy required to close the microvalve is in the range of 300–678 μJ.

Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces

Abstract: A method for non-linear modal analysis of mechanical sys- tems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical system's equations of motion. The dissipative aspects of these non- linearities result in complex eigensolutions and the modal pa- rameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The gener- ality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, sta- bility analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dove- tail attachment are proposed. Finally, we propose a study of dy- namical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.

Nonlinear free vibration of tapered mindlin plates with edges elastically restrained against rotation using dqm

Abstract: Large amplitude free vibration analyses of tapered Mindlin rectangular plates with elastically restrained against rotation edges are investigated using different differential quadrature method (DQM). The governing equations are based on the first-order shear deformation plate theory in conjunction with Green's strain and von Karman assumption. The spatial derivatives are discretized using DQM and the harmonic balance method is used to transform the resulting differential equations into frequency domain. A direct iterative method is used to solve the nonlinear eigenvalue system of equations. The convergence of the method is shown and their accuracy is demonstrated by comparing the results with those of the limiting cases, i.e. nonlinear free vibration analysis of plates with classical boundary conditions and also linear free vibration analysis of tapered plates. The effects of the elastic restraint coefficient at the edges and the geometrical parameters on the ratio of the nonlinear natural frequency to linear natural frequency of plates with linearly and bi-linearly varying thickness are studied.

Optimization of clamped circular piezoelectric composite actuators

Abstract: This paper addresses the design of clamped circular piezoceramic composite unimorph and bimorph configurations, specifically the conflicting requirements of maximum volume displacement for a prescribed bandwidth. An optimization problem is formulated that implements analytical solutions for unimorph and bimorph configurations using laminated plate theory, including the use of oppositely polarized piezoceramic patches. A range of actuator geometric parameters are studied, and bounds for volume displacement and natural frequency of optimal designs are determined and presented via design curves. In the selected design space, Pareto optimization results for unimorph and bimorph configurations show that optimal volume displacement is related to the bandwidth by a universal power law such that the product of the square of the natural frequency and the displaced volume, a “gain-bandwidth” product, is a constant. Characteristic trends are also described that are independent of the actuator radius for the Pareto optimal piezoceramic patch thickness and radius versus normalized bandwidth. The results are relevant, for example, in the design of zero-net mass-flux or synthetic jet actuators used in flow control applications.

Modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials

Abstract: Nowadays rotating machines produce or absorb large amounts of power in relatively small physical packages. The fact that those machines work with large density of energy and flows is associated to the high speeds of rotation of the axis, implying high inertia loads, shaft deformations, vibrations and dynamic instabilities. Viscoelastic materials are broadly employed in vibration and noise control of dynamic rotors to increase the area of stability, due to their high capacity of vibratory energy dissipation. A widespread model, used to describe the real dynamic behavior of this class of materials, is the fractional derivative model. Resorting to the finite element method it is possible to carry out the modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials. In general, the stiffness matrix is comprised of the stiffnesses of the shaft and bearings. As considered herein, this matrix is complex and frequency dependent because of the characteristics of the viscoelastic material contained in the bearings. Despite of that, a clear and simple numerical methodology is offered to calculate the modal parameters of a simple rotor mounted on viscoelastic bearings. A procedure for generating the Campbell diagram (natural frequency versus rotation frequency) is presented. It requires the embedded use of an auxiliary (internal) Campbell diagram (natural frequency versus variable frequency), in which the stiffness matrix as a frequency function is dealt with. A simplified version of that procedure, applicable to unbalance excitations, is also presented. A numerical example, for two different bearing models, is produced and discussed.

Experimental Study on Impeller Blade Vibration During Resonance—Part I: Blade Vibration Due to Inlet Flow Distortion

Abstract: Forming the first part of a two-part paper, the experimental approach to acquire resonant vibration data is presented here. Part II deals with the estimation of damping. During the design process of turbomachinery components, mechanical integrity has to be guaranteed with respect to high cycle fatigue of blades subject to forced response or flutter. This requires the determination of stress levels within the blade, which in turn depend on the forcing function and damping. The vast majority of experimental research in this field has been performed on axial configurations for both compressors and turbines. This experimental study aims to gain insight into forced response vibration at resonance for a radial compressor. For this purpose, a research impeller was instrumented with dynamic strain gauges and operated under resonant conditions. Modal properties were analyzed using finite element method and verified using an optical method termed electronic-speckle-pattern-correlation-interferometry. During the experiment, unsteady forces acting on the blades were generated by grid installations upstream of the impeller, which created a distorted inlet flow pattern. The associated flow properties were measured using an aerodynamic probe. The resultant pressure fluctuations on the blade surface and the corresponding frequency content were assessed using unsteady computational fluid dynamics. The response of the blades was measured for three resonant crossings, which could be distinguished by the excitation order and the natural frequency of the blades. Measurements were undertaken for a number of inlet pressure settings starting at near vacuum and then increasing. The overall results showed that the installed distortion screens generated harmonics in addition to the fundamental frequency. The resonant response of the first and the second blade mode showed that the underlying dynamics support a single-degree-of-freedom model.

Effect of shape memory alloy actuation on the dynamic response of polymeric composite plates

Abstract: Dynamic properties such as the natural frequency of a structure have a significant role in the design process. The importance of this consideration is because of resonance. In this case, the amplitude of the vibration is magnified to levels that may lead to a catastrophic event. While the usual design process depends on the collected experiences and statistical data, a developing trend is to implement smart technologies to develop smart structures that are capable of self-monitoring, diagnostics and repair. Smart material components such as shape memory alloys (SMAs) and piezoelectric ceramics are increasingly being used by vibration control practitioners. In this paper, the alteration of the natural frequency of composite structures using nitinol-based shape memory alloy wires will be presented using the analyses of strain energy perturbations on a plate. These governing strain equations will be solved analytically and numerically to show the effect of point forces acting in a distributive manner and the subsequent effect it has on the plate's stiffness and hence it's natural frequency. Different SMA configurations placement will be studied and compared to computational and experimental findings in order to optimize the control strategy.

Fault Current Waveform Analysis of a Flux-Lock Type SFCL According to LC Resonance Condition of Third Winding

Abstract: The flux-lock type superconducting fault current limiter (SFCL) can apply the magnetic field into the high-T c superconducting (HTSC) element by adopting the magnetic field coil in its third winding. To apply the magnetic field into the HTSC element effectively, the capacitor for LC resonance is connected in series with the magnetic field coil. However, the current waveform of third winding for the application of the magnetic field is affected by the LC resonance condition for the frequency of the source voltage and can affect the waveform of the limited fault current. In this paper, the current waveform of the third winding in the flux-lock type SFCL according to LC resonance condition during a fault period was analyzed. From the differential equation for its electrical circuit, the current equation of the third winding was derived and described with the natural frequency and the damping ratio as design parameters. Through the analysis according to the design parameters of the third winding, the waveform of the limited fault current was confirmed to be influenced by the current waveform of the third winding and the design condition for the stable fault current limiting operation of this SFCL was obtained.

Topology optimization of compressor bracket

Abstract: Topology optimization is very useful engineering technique especially at the concept design stage. It is common habit to design depending on the designer’s experience at the early stage of product development. Structural analysis methodology of compressor bracket was verified on the static and dynamic loading condition with 2 bracket samples for the topology optimization base model. Topology optimization is able to produce reliable and satisfactory results with the verified structural model. Base bracket model for the topology optimization was modeled considering the interference with the adjacent vehicle parts. Objective function was to minimize combined compliance and the constraint was the first natural frequency over 250 Hz. Multiple load cases such as normal mode calculation and gravity load conditions with 3-axis direction were also applied for the optimization, expecting an even stress distribution and vibration durability performance. Commercial structural optimization code such as optistruct of Altair Engineering was used for the structural topology optimization. Optimization was converged after 14 iterations with the satisfaction of natural frequency constraint. New bracket shape was produced with the CATIA based on the topology optimization result. The new bracket from topology optimization result was compared with the traditional concept model and topology optimization base model under 4 load cases. 14 % 1’st natural frequency of new bracket with only 4 % mass increment increased compared to the concept model. 31 % mass decreased compared to the base model without the increment of stress under gravity load cases. It was analyzed thata new bracket would not fail during a vibration durability test, and these results were verified with a fabricated real sample under the durability condition.