Optimal Natural Frequency Research Articles

Investigation to resonant frequency control of high power ultrasonic transducer based on the beating model

The response time of the resonant frequency tracking is a critical parameter to evaluate the performance of a high power ultrasonic system. In this investigation, we present a novel approach of frequency tracking based on the beating vibration model, which demonstrates improvement result compared with the conventional PLL method. We explore and enclose quantitatively the static and dynamic characteristics of the transducer at conditions of different temperatures, driving voltages and frequencies. It is found that the beating vibration occurs if the driving frequency is deviated from the optimal natural frequency. To reveal the mechanism of the beating vibration, an equivalent model is established. We propose a novel calculation algorithm of trust domain method to search accurately the resonant frequency in the response time, ensuring the resonant vibration of the ultrasonic transducer. The verification experiment is conducted in a PFGA and DSP controller, which verifies that the resonant frequency is determined within 30 ms. Our proposed approach can quickly decrease the beating time and fast achieving the resonant vibration, compared with the other frequency tracking methods.

Multi-objective optimization for maximum fundamental frequency and minimum cost of hybrid graphene/fibre-reinforced nanocomposite laminates

The present article proposes a multi-objective optimization study aiming at the optimal cost-effective design of nano-reinforced laminates. To maximize the fundamental frequency and minimize the cost, a hybrid laminate is studied, introducing both conventional fibres and graphene nanoplatelets reinforcement. A multi-objective genetic algorithm optimization is adopted to provide the optimal natural frequency and cost for the laminate. Optimization is implemented using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which converges to near-optimal solutions for all scenarios tested. The vibration problem is solved using the finite element method and the first-order shear deformation theory. Effective material properties are derived using micromechanical equations. Different optimization problems are solved using one to four types of design variables, including graphene and fibre distribution along the thickness, layer thickness, and fibre angles. Results indicate that increasing the graphene nanoplatelets content and keeping the minimum fibre content leads to cost-effective design. A drastic increase in the fundamental frequency and decrease in the cost is obtained for the hybrid graphene/fibre-reinforced laminate compared to conventional fibre-reinforced composites.

Determination of the first natural frequency of an elastic rod of a discrete-continuous vibratory system

A continuous rod-shaped member (a body with distributed inertia and rigidity parameters), which is the object of the investigations, is considered. To ensure the optimal natural frequency concerning the oscillations of the reactive (exciting) mass of the three-mass discrete vibratory system, with the use of the Krylov-Duncan functions, the mathematical model describing forced oscillations of the continuous member considered as a disturbing body of the three-mass discrete-continuous vibratory system is established, and the corresponding frequency equation is analytically derived. The obtained theoretical results are verified using the Finite Element Method in SolidWorks software. The novelty of the present paper consists in substantiation of the possibilities of implementing the continuous rod-shaped members with distributed inertia and rigidity parameters for exciting the oscillations of the three-mass discrete-continuous inter-resonance vibratory systems.

Optimal Design of Maxwell-Viscous Coulomb Air Damper With a Modified Fixed Point Theory

Abstract Air damper dynamic vibration absorber (DVA) is modeled using Maxwell transformed element and coulomb element. This damper serves to minimize vibration at resonant and operation of constant speed machine. Its stiffness and damping factor are transformed from Maxwell to Voigt arrangement. Meanwhile, viscous equivalent Coulomb damping is expressed by absolute relative motion. System transmissibility contours are plotted by min–max approach. Its optimal parameters are determined using this approach. Contour operation minimization is obtained from minimum system transmissibility. Moreover, exact solution of fixed points and optimal natural frequency ratio are obtained by a modified fixed point theory. Optimal design curve is derived by Coulomb damping derivative and maximum condition. Operational vibration level is minimized by 7% at the operation minimization using minimum condition. On the experimental side, test platform of the air damper is constructed using linear slide block system. Computational model of the air damper is established by its physical details and experimental data. Linear relationship is obtained between viscous and Coulomb damping angles. Modified fixed points are validated by frequency response function resonant peaks. Experimental vibration level is minimized by 5%, which being close to the minimization result. The model is validated within 5% accuracy by its optimal experimental curve.

Study on modal analysis and chip breaking mechanism of Inconel 718 by ultrasonic vibration-assisted drilling

In this study, both theoretical and experimental research was conducted to investigate the role played by a difficult-to-machine material, Inconel 718, in improving the surface finish quality in drilling holes. Ultrasonic vibration technology was applied to assist with the drilling process. An axial ultrasonic vibration-assisted drilling (UAD) system was designed to determine the structural relationships between different component parts, based on which an axial UAD model was established. Abaqus finite element software was applied to perform model simulation and an analysis was conducted of the structure to find its optimal natural frequency and vibration mode. The conditions for complete geometric chip breaking based on the mechanisms of UAD and chip breaking, as well as pre-set parameters, were inferred and the theoretical domain of complete geometric chip breaking was mapped. Subsequently, a range of different parameters was applied to conduct experiments on the drilling process, from which it was established that the characteristics of chipping satisfy the conditions required for complete geometric chip breaking. Finally, under the circumstances where the parameters for the drilling process are identical and chip breaking conditions are met, UAD was found to be advantageous over conventional drilling (CD) as the former produces a more apparent chip breaking effect. Additionally, UAD can reduce the Ra value and abrasion of cutting tools, thus improving the quality of the hole drilling process.

Natural Frequency Optimization of Wireless Power Systems on Power Transmission Lines

Optimizing the natural frequency is crucial for dc-to-load efficient wireless power transfer (WPT) applications on high voltage (HV) power transmission lines. However, a comprehensive optimization approach with the coupling factor and the losses on power electronics both taken into consideration is still in absence. By modeling losses dissipated on various parts, including the class-D inverter, the rectifier, and the resonant loops, a numerical approach is proposed in this paper to evaluate the optimal natural frequency for maximum dc-to-end efficiency. As the system efficiency is also affected by the operating frequency, which is resilient for practical operation, practical operating strategies are applied to determine the working parameters. Furthermore, considering that the HV WPT systems may work with various coupling factors, optimal natural frequencies for various coupling factors are analyzed and compared. Several groups of experiments are conducted to verify the effectiveness of the proposed numerical approach. Experimental results show that the approach can effectively predict the optimal natural frequency. When compared with the cases where the natural frequency is 100 or 600 kHz, an efficiency enhancement of about 20% can be achieved using the optimized natural frequency. When compared with the cases where the natural frequency is optimal for maximum $Q$ value, an efficiency of 9% can still be achieved for loosely coupled occasions.

Improvement on sound transmission loss through a double-plate structure by connected with a mass–spring–damper system

It is well-known that the acoustic performance of double-plate structures deteriorates rapidly around the mass–air–mass resonance frequency. In this study, a mass–spring–damper system connected between incident and radiating plates is used to improve the sound transmission loss at low-frequency ranges. First, a full structural-acoustic modal coupling model is developed to analyze the vibration and acoustical behaviour of the double-plate structures with mass–spring–damper system. Because there are in-phase or out-of-phase vibrations between double plates, tuning the natural frequency of the mass–spring–damper system exactly to the mass–air–mass resonance frequency cannot guarantee the maximum improvement on transmission loss. Optimal natural frequency and mass of the mass–spring–damper system were found as a solution of optimization problem with a global cost function defined as frequency-averaged sound transmission loss in the desired frequency range (around mass–air–mass resonance frequency). Finally, some numerical calculation results are presented. The calculated results show that the sound transmission loss of a double-plate structure can be improved significantly using optimally tuned mass–spring–damper system. The results indicate that an overall improvement of 12 dB below 1000 Hz can be achieved when the mass of the mass–spring–damper system equals to 10% weight of the double-plate structure.

J1010506 床衝撃用制振装置の開発([J101-5]制振(1))

The present paper describes damping effect of the impact damper having two vibrators on a floor. Response of the damper is investigated and the optimal natural frequency rates of the vibrators are calculated based on numerical simulations. And the vibrator of the damper and the floor due to floor impact is observed by a high speed camera. Some important results of the study are as follows: 1) Optimum value of natural frequency rates is combination that vibrators collide head-on and collide many times. 2) Effect of the damper for impulse force is clearly observed. And damping effect is in proportion to impact force. 3) Effect of the damper for step force is limited by an additional mass corresponding to the step force on the floor. The natural frequency rates do not become optimal and the number of collisions between two vibrator decreases when the added mass is heavy.

J1810101 釣合いおもりの上下振動を利用したエレベータ・ロープの横振動抑制([J181]昇降機システムの安全とダイナミクス)

An elevator rope for high-rise building is forcibly excited by the displacement of the building caused by earthquakes and wind forces. In high-rise building, the elevator rope may resonate with the natural frequency of the building; hence, effective solution to reduce the rope displacement is demanded. In this paper, it is confirmed to suppress of the transverse vibration of elevator rope using vertical vibration of counterweight. Rope lateral vibration is controlled by fluctuating rope tension using up-and-down motion of this counterweight. Finite difference analyses of rope vibration with counterweight are performed to verify of this method. Experiments involving forced vibration of a rope whose length is constant are performed. The optimal natural frequency of vertical vibration is about 2 times of the natural frequency of the rope.

Countermeasure against chatter in end milling operations using multiple dynamic absorbers

The present study investigates the effect of multiple dynamic absorbers on chatter generated in the end milling operations by performing stability analysis and a cutting test. The dynamic absorbers proposed in the present paper are attached to a collet chuck in order to suppress tool chatter caused by the bending vibration of the tool and spindle system. The dynamic milling model is considered to have two orthogonal degrees of freedom. The dynamic absorbers, which have identical mass, damping ratio, and natural frequency, are assumed to have a single degree of freedom that rotates with a tool and spindle system. In the present paper, stability analyses are performed by means of complex eigenvalue analysis for each angular immersion of the cutting edge in order to investigate the effect of the dynamic absorbers on the stability of the dynamic milling model. The optimal natural frequency and damping ratio of the dynamic absorbers to maximize the chatter-free axial depth of cut are shown to vary with spindle speed. Furthermore, the effect of the dynamic absorbers on chatter is validated by a cutting test, and the experimental results are confirmed to agree qualitatively with the analytical results.

J181011 動吸振器を用いたエレベーターロープの横振動抑制

An elevator rope for high-rise building is forcibly excited by the displacement of the building caused by earthquakes and wind forces In high-rise building, the elevator rope may resonate with the natural frequency of the building, hence, effective solution to reduce the rope displacement is demanded In this paper, a method to suppress the rope displacement by using dynamic damper is presented Finite difference analyses of rope vibration with dynamic damper are performed to verify the validity of this method The optimal natural frequency of dynamic damper is about 2 times of the natural frequency of the rope The rope sway can be reduced to about 1/2, when the cage is stopped

Topology optimization of periodic Mindlin plates

Periodic structures exhibit unique dynamic characteristics that make them act as tunable mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the ‘pass bands’ and wave propagation is completely blocked within other frequency bands called the ‘stop bands’ or ‘band gaps’. The spectral width of these bands can be optimized using topology optimization. In this paper, topology optimization is used to maximize the fundamental natural frequency of Mindlin plates while enforcing periodicity. A finite element model for Mindlin plates is presented and used along with an optimization algorithm that accounts for the periodicity constraint in order to determine the optimal topologies of plates with various periodic configurations. The obtained results demonstrate the effectiveness of the proposed design optimization approach in generating periodic plates with optimal natural frequency and wide stop bands. The presented approach can be invaluable design tool for many structures in order to control the wave propagation in an attempt to stop/confine the propagation of undesirable disturbances.

자동차용 사판식 압축기의 흡, 토출밸브 설계

This paper was studied to design process considered flexibility and reliability of suction and discharge valves. Flexibility and reliability of valves are main important factors in compressor valves design. And they are incompatible with efficiency of compressor. In this study, we have performed the optimal design of CO2 compressor valves to consider these factors. At first, we analyzed performance simulation of compressor to obtain optimal flexibility level of valves. From this simulation, we could get some important data at valve design like the optimal natural frequency and the height of retainer. After that we studied to reliability of valves corresponding to optimal flexibility level by finite element method. For each case bending stress and natural frequency were obtained by it. Also we investigated the fatigue stability to obtain optimal valve shape that ensured to reliability.

Elastic-Dynamic Rotor Blade Design with Multiobjective Optimization

An efficient multidisciplinary design optimization methodology is applied in the design of a rotor blade to meet minimum weight, minimum vibration, and maximum material strength requirements. The design study is a high-aspect-ratio articulated flexible blade with a thin-walled multicell cross section at high tip Mach numbers. The rotor blade analysis consists of two subsets to increase efficiency in numerical methods used in each discipline. The first subset is an elastic analysis using an idealized model by chordwise segments and spanwise elements, which can provide efficient material reassignment for minimum weight design. The second subset is a dynamic analysis for optimal natural frequency placement and vibratory vertical hub shear reduction. A high-order finite element from the gradient adaptive transfinite element family formulated by the second author is used to reduce computational requirements and to improve results without increasing the number of elements. The optimization procedure is decomposed into two levels for efficient handling of the design variables and objective functions and their correlation

Carrier synchronization for homodyne and heterodyne detection of optical quadriphase-shift keying

Through analysis and simulation, the authors investigated the performance of four carrier-synchronization techniques suitable for both homodyne and heterodyne detection of optical quadriphase-shift keying: the discrete-time decision-directed loop, the analog decision-directed loop, the Costas quadriphase loop, and the fourth-power phase-locked loop. Accounting for shot noise, laser phase noise, and feedback delay, they optimize the loop natural frequency and specify laser-linewidth requirements. The performance discrepancy between the best and worst of these loops is found to be small; accounting for inherent loop delays only, the linewidth requirements range from Delta vT<2.5*10/sup -5/ to Delta vT<5.2*10/sup -5/, where Delta v is the beat laser linewidth and T is the baud interval. Hence other considerations, such as ease of implementation, will govern the design choice for most practical systems. For the case when propagation delays in the feedback loop are significant, a simple and accurate method for estimating the laser-linewidth requirement and corresponding optimal natural frequency is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system

The frequency locus method is summarized and then applied to the optimization of the spring and damper rates for a dynamic vibration absorber. The primary system to which the vibration absorber is attached consists of a force-excited sprung mass with associated viscous damping. The construction of the frequency loci for the overall system leads to the determination of graphical criteria for the optimization, and thence to the discovery of a tuning function which enables the optimal natural frequency for the absorber to be determined. The tuning function can be minimized by numerical methods and the solutions, which depend only on the mass ratio (μ) and primary relative damping rate (ζ1) are presented in the form of a computed family of curves. The optimum relative damping rate (ζ20) for the vibration absorber may be found directly once the optimum tuning frequency has been obtained.

Influence of the sign of rib eccentricity on the optimal natural-frequency vibrations of a cylindrical shell design

Influence of the sign of rib eccentricity on the optimal natural-frequency vibrations of a cylindrical shell design