Oscillation Method Research Articles

Bounded controls for discrete-time linear systems subject to input time delay

This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches.

Enhanced CO2 sequestration based on hydrate technology with pressure oscillation in porous medium using NMR

Carbon dioxide (CO2) is a dominant greenhouse gas in the atmosphere that contributes to global warming. A promising approach to mitigate CO2 emissions is CO2 capture and storage (CCS) through clathrate hydrate crystallization under the seafloor; however, numerous issues regarding the mechanisms of concentration, efficiency, and stability of CO2 hydrate sequestration in seafloor sediments remain under dispute. This study employed low-field nuclear magnetic resonance (NMR) measurements to observe the in-situ formation of CO2 hydrate using the pressure oscillation method in porous media and evaluate the carbon sequestration efficiency. Our results indicate that CO2 hydrates are preferentially formed in large pore spaces, further hindering the subsequent gas contact with water in isolated pores. Additionally, a high initial water saturation is more conducive to high-quantity CO2 hydrate capture and sequestration in a pressure variation environment with a higher driving force. The proposed pressure oscillation method could effectively break the mass transfer barriers in the later stage of hydrate formation with the help of CO2 solubility fluctuations, significantly increase the rate of later hydrate formation, and shorten the period of hydrate sequestration.

Efficiency improvement by a beam filtering ring in a relativistic backward wave oscillator at low magnetic field

This paper presents a design method of the relativistic backward wave oscillator at low magnetic field, which can improve the efficiency by 29% in the particle in cell simulation. The core of this method is to introduce a beam filtering ring. The beam filtering ring takes the characteristic of the radial position change as the electron oscillates. The structure manipulates the axial current, so that a large proportion of the electrons expected to be in the accelerated phase in the slow-wave structure is absorbed by the structure. It greatly enhances the bunching of the beam in the RF field and improves the beam-wave conversion efficiency significantly. The particle in cell simulation results reveal that at a permanent magnet with a magnetic induction intensity of 0.68 T, the output microwave power of the relativistic backward wave oscillator with a beam filtering ring is 5.9 GW, and the conversion efficiency can be up to 54% when the diode voltage is 890 kV and the beam current is 12.2 kA.

Evaluation of Tumor Resection Effect of Color Doppler Ultrasound Positioning Guided Breast-Conserving Surgery Using Nano-Contrast Agent.

This study aimed to explore the clinical value of Fe3O4-based magnetic lipid nano-contrast agent in breast-conserving surgery for breast cancer using color doppler ultrasound positioning and to analyze the tumor resection effect of breast-conserving surgery. On account of Fe3O4 magnetic nanoparticles prepared by the chemical co-precipitation method, magnetic lipid ultrasonic microbubbles (MLU-MBs) were prepared by mechanical oscillation method after surface modification using polyethylene terephthalate (PET). Characterization and analysis of the prepared MLU-MBs were performed using scanning electron microscopy (SEM), energy spectrometer, transmission electron microscopy (TEM), and Fourier infrared spectroscopy (FIRS). A high-frequency alternating magnetic field was used to detect the heating of MLU-MBs and the color ultrasound machine was applied to observe the enhancement effect of the MLU-MBs on rabbit liver images. 92 patients undergoing breast-conserving surgery for breast cancer were taken as the research objects and were divided into a nano group (MLU-MB as contrast agent) and a control group (conventional contrast agent) according to the differences of intraoperative contrast agents, with 46 cases in each group. Before the surgery, both groups of patients were positioned and marked the tumor boundary under ultrasound. The differences in tumor volume (TV), amount of tissue removed, resection rate, and positive rate (PR) of resection margins were compared between the two groups. The results showed that the Fe3O4 magnetic nanoparticles were particles with an average particle size of about 15nm, and their iron and oxygen percentages were consistent with the content of Fe3O4. The MLU-MBs were spherical particles of about 1120nm, containing phosphorus (P), oxygen(O), and Ferrum (Fe). Under 30A and 220kHz of output current and frequency, the temperature rise of the MLU-MBs suspension with different concentrations was 10 ~ 60°C, and the temperature was constant after heating for 45 minutes. Compared with the rabbit liver parenchyma, the image was greatly enhanced. TV, the amount of tissue removed, the resection rate, and the PR of resection margins in the nano group were obviously lower than those in the control group (P<0.05). It showed that MLU-MBs with good image enhancement effect on account of Fe3O4 magnetic nanoparticles were successfully prepared and it could effectively reduce the PR of normal tissues and the positive margin of two-fold resection during breast-conserving surgery for breast cancer and showed good accuracy and stability.

Rheological and Thermal Conductivity Study of Two-Dimensional Molybdenum Disulfide-Based Ethylene Glycol Nanofluids for Heat Transfer Applications

The rheological behavior of two-dimensional (2D) MoS2-based ethylene glycol (EG) nanofluids (NFs) was investigated at low volume concentrations (0.005%, 0.0075%, and 0.01%) in a wide temperature range of 0–70 °C and at atmospheric pressure. A conventional two-step method was followed to prepare NFs at desired volume concentrations. Based on the control rotational (0.1–1000 s−1 shear rate) and oscillation (0.01–1000% strain) methods, the viscoelastic flow curves and thixotropic (3ITT (three interval thixotropic) and hysteresis loop) characteristics of NFs were examined. Shear flow behavior revealed a remarkable reduction (1.3~14.7%) in apparent dynamic viscosity, which showed concentration and temperature dependency. Such remarkable viscosity results were assigned to the change in activation energy of the ethylene glycol with the addition of MoS2. However, the nanofluids exhibited Newtonian behavior at all temperatures for concentrations below 0.01% between 10 and 1000 s−1. On the other hand, strain sweep (@1Hz) indicated the viscoelastic nature of NFs with yielding, which varied with concentration and temperature. Besides, 3ITT and hysteresis loop analysis was evident of non-thixotropic behavior of NFs. Among all tested concentrations, 0.005% outperformed at almost all targeted temperatures. At the same time, ~11% improvement in thermal conductivity can be considered advantageous on top of the improved rheological properties. In addition, viscosity enhancement and reduction mechanisms were also discussed.

Using a Combination of PID Control and Kalman Filter to Design of IoT-based Telepresence Self-balancing Robots during COVID-19 Pandemic

COVID-19 is a very dangerous respiratory disease that can spread quickly through the air. Doctors, nurses, and medical personnel need protective clothing and are very careful in treating COVID-19 patients to avoid getting infected with the COVID-19 virus. Hence, a medical telepresence robot, which resembles a humanoid robot, is necessary to treat COVID-19 patients. The proposed self-balancing COVID-19 medical telepresence robot is a medical robot that handles COVID-19 patients, which resembles a stand-alone humanoid soccer robot with two wheels that can maneuver freely in hospital hallways. The proposed robot design has some control problems; it requires steady body positioning and is subjected to disturbance. A control method that functions to find the stability value such that the system response can reach the set-point is required to control the robot's stability and repel disturbances; this is known as disturbance rejection control. This study aimed to control the robot using a combination of Proportional-Integral-Derivative (PID) control and a Kalman filter. Mathematical equations were required to obtain a model of the robot's characteristics. The state-space model was derived from the self-balancing robot's mathematical equation. Since a PID control technique was used to keep the robot balanced, this state-space model was converted into a transfer function model. The second Ziegler-Nichols's rule oscillation method was used to tune the PID parameters. The values of the amplifier constants obtained were Kp=31.002, Ki=5.167, and Kd=125.992128. The robot was designed to be able to maintain its balance for more than one hour by using constant tuning, even when an external disturbance is applied to it. Doi: 10.28991/esj-2021-SP1-016 Full Text: PDF

Along-Wind Aerodynamic Damping of Wind Turbine Towers: Determination by Wind Tunnel Tests and Impact on Tower Lifetime

As wind turbines become larger and their towers more slender, aeroelastic effects play a bigger role in the wind turbine’s dynamic behavior. This study focuses on the along-wind aerodynamic damping of wind turbine towers, which has been determined by wind tunnel experiments using the forced oscillation method according to Steckley’s approach. Reynolds number scale effects have been considered through surface roughness modifications using sand paper and a dimple pattern, which have been described in detail. The wind tunnel measurements are performed in sub-critical, critical and trans-critical flow regimes, as well as in low- and high-turbulence conditions, which allows for an accurate description of the required relative roughness and Reynolds numbers for achieving trans-critical conditions. The resulting along-wind aerodynamic damping values according to Steckley’s and Holmes’ approaches are compared, and an analytical relation between them is established. Both approaches are then used in aeroelastic multi-body-simulations of an onshore 6 MW reference wind turbine and their impact on the wind turbine lifetime is evaluated through fatigue proofs at the tower base section. Holmes’ approach seems more appropriate for the application in aeroelastic multi-body simulations. A lifetime extension for the wind turbine tower of approximately 0.4% is achieved for the reference wind turbine tower, which roughly corresponds to 1 to 2 months for 20 years of operation. An analytical expression is given for the estimation of the tower’s aerodynamic damping in parked and operating conditions.

High-Resistance Connection Diagnosis in Five-Phase PMSMs Based on the Method of Magnetic Field Pendulous Oscillation and Symmetrical Components

An online approach for diagnosing high-resistance connection (HRC) faults in five-phase permanent magnet synchronous motor drives is presented in this article. The development of this approach is based on a so-called “magnetic field pendulous oscillation (MFPO)” technique and symmetrical components method. Under HRC fault condition, a “swing-like” MFPO phenomenon is observed compared to the healthy condition. Furthermore, with the extracted current features in symmetrical components domain, different HRC fault types are successfully identified and distinguished. These fault types include single-phase faults, e.g., HRC fault in phase-A; two-phase nonadjacent faults, e.g., HRC fault in phase-A&C; and two-phase adjacent faults, e.g., HRC fault in phase-A&B. Meanwhile, the localization of the faulty phase/phases is also accomplished, and the fault severity is estimated. In this approach, only sensing of the phase currents is needed. Hence, the implementation cost is very low since the sensory data of the currents are typically already available in the closed-loop vector-controlled drives for control purpose and no additional sensors or related signal conditioning circuits are required. The effectiveness of the presented diagnostic approach is verified by simulations and experimental results.

Improved Glass Bead-Vortex Oscillation Method for DNA Extraction from Diatom.

To examine the effect of improving diatom DNA extraction by glass bead - vortex oscillation method. The DNeasy PowerSoil Pro kit was used as control, two plant DNA extraction kits with different principles (New Plant genomic DNA extraction kit and Plant DNA Isolation kit) and one whole blood DNA extraction kit (whole blood genomic DNA extraction kit) were selected to extract diatom DNA from lung tissue and water sample of the same drowning case. The combination of mass ratio of glass beads with different sizes and vortex oscillation time was designed, and the optimal DNA extraction conditions were selected with the addition of glass beads oscillation. The extracted products of the conventional group and the modified group were directly electrophoretic and detected by diatom specific PCR. Finally, all the extracts were quantified by qPCR, and the Ct values of different groups were statistically analyzed. When the frequency of vortex oscillation was 3 000 r/min, the optimal combination of DNA extraction was vortex oscillation for 4 min, and the mass ratio of large glass beads to small glass beads was 1∶1. The DNeasy PowerSoil Pro kit was used as a reference, and the Ct value of 10 mL water sample was greater than that of 0.5 g tissue. The Ct values of the other three kits used for plant DNA extraction decreased after the glass beads-vortex oscillation method was used, and the Ct values of the tissues before and after the improvement were statistically significant (P<0.05). The whole blood genomic DNA extraction kit used in this study could successfully extract diatom DNA, the extraction of water samples was close to DNeasy PowerSoil Pro kit, after the modified method was applied to tissue samples, the difference in Ct value was statistically significant (P<0.05). However, when the three kits were used to extract diatom DNA from water samples, Ct values before and after the improvement were only statistically significant in New Plant genomic DNA extraction kit group (P<0.05). The improved glass bead-vortex oscillation method can improve the extraction efficiency of diatom DNA from forensic materials, especially from tissue samples, by plant and blood DNA extraction kits.

MyotonPro Is a Valid Device for Assessing Wrist Biomechanical Stiffness in Healthy Young Adults.

BackgroundThe MyotonPro is a portable device for measuring biomechanical and viscoelastic properties in superficial soft tissues. The aims of this study are firstly to validate the MyotonPro compared to a reliable gold-standard frame and secondly to observe the influence of MyotonPro measurement on the total wrist viscoelasticity.MethodsThree silicone polymers with different elastic properties were assessed with the MyotonPro and with a reference rheometer (Universal Tribometer Mod). Then, a free oscillations method was used to measure the passive elastic and viscous stiffness of the wrist and compared to MyotonPro forearm measurements.ResultsA one-way ANOVA demonstrated the validity of the MyotonPro's stiffness (p = 0.001), decrement (p < 0.001), and relaxation (p = 0.008) parameters for measuring the elastic stiffness (k) of the three polymers. The MyotonPro parameters demonstrated excellent reliability on the forearm. Proximal and distal anterior myofascial measurements of the MyotonPro were moderately correlated to the elastic stiffness (p = 0.0027–0.0275, absolute r = from 0.270 to 0.375) of the wrist while the postero-distal myofascial tissues of the forearm demonstrated a moderate correlation with the viscous stiffness of the wrist (p = 0.0096–0.0433, absolute r = from 0.257 to 0.326).DiscussionThe MyotonPro is a valid device for measuring elastic stiffness as well as a portable, affordable, and easy-to-use tool for quantifying the biomechanical properties and viscoelasticity of myofascial tissue in healthy subjects.

Oscillation-Induced Mixing Advances the Functionality of Liquid Marble Microreactors.

Droplet-based microreactors often uncover fascinating phenomena and exhibit diverse functionality, which make them applicable in various fields. Liquid marbles (LMs) are non-wetting droplets coated with particles, and these features highlight their potential as microreactors. However, sophisticated experimental designs are typically hindered because it is difficult to obtain sufficient substance mixing in these miniature, damage-prone, self-supporting liquid containers. Here, we demonstrate that subjecting LMs to vertical oscillations by audio signals represents a controllable approach that allows sufficient mixing with variable dynamic modes. The characteristics and key issues in LM oscillation are systematically explored. The effects of oscillation on application potential are examined. Under oscillation conditions, homogeneous mixing can be achieved within a few seconds in LMs consisting of either water or viscous liquids. Importantly, the structures of materials synthesized in LMs can be regulated by modulating the oscillation modes. The variable modes, flexible adjustability, high efficiency, and wide applicability of this oscillation method make it a verified manipulation strategy for advancing the functionality of LM microreactors.

The effects of compression ratio and combustion initiation location on knock emergence by using multiple pressure sensing devices

Knock research is an essential study because knock limits spark-ignition (SI) engine power output, durability, noise, fuel consumption, and emission performance. The thermal efficiency of an engine can be improved by increasing the compression ratio, but at the same time it leads to the possibility of end gas autoignition inside the chamber. The objective of this work was to show the effect of three different compression ratios (CRs) 8.5, 9.5, and 10.5 on the mechanism of knock. In order to achieve this four equispaced spark plugs were fitted around the circumference of a special metal liner to initiate flame fronts from those plugs by firing with different spark approaches (e.g. spark timing, number, and location). In addition, six pressure sensors were installed at various locations to precisely record the autoignition event by monitoring pressure oscillations, combustion characteristics, and knock intensity. In-cylinder pressure and heat release rate (HRR) analyses were applied to distinguish the knocking combustion for the three different CRs. The results showed that a greater number of spark plugs produced more stable combustion even for a delayed spark timing (ST) than a single spark plug, but also increased pressure oscillations, HRR and knock propensity with higher CRs due to an increase in pressure and temperature inside the cylinder. The maximum amplitude of pressure oscillation (MAPO) method was used to determine the knock intensity, and it was observed that at the lowest CR of 8.5 three spark plugs gave higher MAPO values compared to four spark plugs for the same operating conditions. However, four spark plugs instigated higher MAPO values than three spark plugs for the higher CRs of 9.5 and 10.5 because, with the increase of CR and spark plug numbers, the pressure and temperature were increased during the combustion event, which was coupled with the compression effect on the unburned end gas mixture. Additionally, Fast Fourier transform (FFT) and wavelet methods were implemented to observe the frequencies induced during knock. It was found that sparking four plugs provoked various vibration modes in different amplitude ranges with the different CRs.

Study on synthesis of LiGa0.3In0.7Se2 polycrystal by vapor transporting temperature oscillation method

LiGaxIn1−xSe2 is one of promising semiconductor nonlinear optical crystals for laser frequency conversion in the mid-IR spectral range. Single-phase LiGa0.3In0.7Se2 polycrystal were synthesized directly from the constituent elements by vapor transporting and temperature oscillations method. According to this method, explosions of quartz ampoule that result from selenium vapor pressure at high temperature were solved. After synthesis, structure and composition of the obtained ingot were measured. And the results manifest that high purity LiGa0.3In0.7Se2 polycrystal were successfully synthesized and intermediate impurities have not been found on the compound.

The Application of Electrochemical Oscillation Methods for Identification of Traditional Chinese Medicine Materials

Electrochemical oscillation reflects the overall characteristics of the system under test in terms of redox activity. It has proven to be advantageous in analyzing and processing complex components of herbal systems, such as polysaccharides and proteins. Therefore, it is widely used in the quantitative or qualitative tests of traditional Chinese medicines (TCMs) for identification and quality control. Electrochemical oscillation has several advantages such as high sensitivity, stability and micro sample requirement. Compared with other traditional methods, the interaction of multi-component in the TCMs was taken into account, which provides new ideas for the search of TCMs. Here, we presented a brief introduction on the progress on the topic, which promoted the development of electrochemical oscillation and the standardization of TCMs in the last twenty years. Electrochemical oscillation method is cheap, sensitive, fast, stable and convenient for the identification and quality control of TCMs. Reaction systems and the visualization of the fingerprints can be improved in the future.

Застосування методу головних компонент в задачі аналізу спектрів вільних коливань

This article addresses the main methods used for analysis, distribution, and classification of input data space. The main aspects of applying these methods are analyzed and determined. In this study it is found that the method of the principal components analysis (PCA) is the most suitable. Possible principal components analysis algorithms are described. A combination of these algorithms is used to distribute the input data in the analysis of signals and their spectra obtained by non-destructive testing after applying a free oscillations method. The article aims to study the possibility of reducing the vector of informative features after applying principal components analysis without losing the quality of recognition of the state of objects. The objects of study may be components of electric motors (shunt magnetic conductor), parts of aircraft made of composite materials and other structures that require analysis by non-destructive testing methods. Spectra taken during non-destructive testing by the method of free oscillations of samples of carbon fiber panels from defective and defect-free zones were studied. The analysis of three, five and ten harmonics was conducted and the maximum number of the principal components and the values of maximum dispersions of these components for the input values set of amplitudes were determined. The Mahalanobis distance was used to analyze the quality of the distribution of the input data space into classes (defect-free and defect zones of the sample). The quality of the separation of values from the damaged and undamaged zones of the sample into two classes was improved. Therefore, the use of principal component analysis, in this study, can increase the reliability of the recognition of the state of objects.

Gnielinski’s correlation and a modern temperature-oscillation method for measuring heat transfer coefficients

The heat transfer coeffcient is one of the most important parameters in the design of apparatuses in which convective heat transport takes place. Classical direct methods based on determining basic thermal quantities can be used for measuring heat transfer coeffcients. Another option is to measure concentrations, electric current or other quantities that can be transformed to thermal quantities using the analogy between heat and mass transport. The temperature-oscillation method is less frequently used, although the theoretical basis of the method dates back to 1997, and although the method has the major advantage that the heat transfer coeffcients can be measured without making any contact with the heat transfer surface. In the temperatureoscillation method, the heat transfer surface is exposed to an oscillating heat flux, and the temperature response on this surface can be measured by a contactless method (e.g. infra-red thermography). The heat transfercoeffcients can be determined on the basis of mathematical relations between the oscillating heat flux and the temperature response. However, the method depends on an appropriate method for processing the measured data when it is necessary to correct some conditions that are not included in the mathematical model. This paper evaluates the impact of processing the experimental data on the resulting heat transfer coeffcients in one of the basic geometrical configurations – the flow of a liquid in a pipe with a circular cross section. In this paper, we present the results of a comparison of real experiments based on the temperature oscillation method and numerical modeling of the heat transfer in this geometry, using the ANSYS CFD commercial system.

Prospective theoretical investigations of optical, dielectric, mechanical and third-order NLO property in potassium tri-hydrogen di-succinate single crystal

A propitious third-order nonlinear optical crystal potassium tri-hydrogen di-succinate (PTHS) (C8H11O8K) is grown by conventional slow evaporation technique maintained at 303 K. Single crystal XRD analysis (SXRD) evidences the grown crystal pertain to centrosymmetric space group P21/c with monoclinic crystal system and powder X-ray diffraction (PXRD) confirms the purity of the grown crystal. The existence of various functional groups was assessed by Fourier transform infrared (FTIR) spectral analysis and the optical absorption study authenticates to the transparency in the visible region. ICP-OES study substantiates the prevalence of alkali metal potassium. Interestingly, the Urbach energy of the grown crystal is explored to be minimum proving the good crystalline nature of the yielded crystal. The various optical constants were calculated in detail. The optical band gap was used to determine the position of the valence band (Ev) and conduction band (Ec) and the Wemple-Di-Domenico single oscillator method was used to find the different dispersive parameters. In dielectric, the various solid state parameters including electronic polarizability were calculated with different formulas and the value was proved to be higher than that of KDP. To determine the mechanical stability, Vickers microhardness test was carried out and their indentation size effect was elucidated by using different models. The crystal exhibits negative photoconductivity. By using photo acoustic study, the thermal diffusivity value is 1.25 times greater than standard KDP, signifying that the harvested crystal is remarkable material for nonlinear optical applications. In brief, the real and imaginary parts are reviewed by Z-scan technique and the susceptibility was compared with other single crystals.

A heuristic review on the homotopy perturbation method for non-conservative oscillators

The homotopy perturbation method (HPM) was proposed by Ji-Huan. He was a rising star in analytical methods, and all traditional analytical methods had abdicated their crowns. It is straightforward and effective for many nonlinear problems; it deforms a complex problem into a linear system; however, it is still developing quickly. The method is difficult to deal with non-conservative oscillators, though many modifications have appeared. This review article features its last achievement in the nonlinear vibration theory with an emphasis on coupled damping nonlinear oscillators and includes the following categories: (1) Some fallacies in the study of non-conservative issues; (2) non-conservative Duffing oscillator with three expansions; (3)the non-conservative oscillators through the modified homotopy expansion; (4) the HPM for fractional non-conservative oscillators; (5) the homotopy perturbation method for delay non-conservative oscillators; and (6) quasi-exact solution based on He’s frequency formula. Each category is heuristically explained by examples, which can be used as paradigms for other applications. The emphasis of this article is put mainly on Ji-Huan He’s ideas and the present authors’ previous work on the HPM, so the citation might not be exhaustive.

Performance and mechanism of polyacrylamide stabilizers in coal water slurry

The stability of coal water slurry (CWS) is a significant factor affecting its storage and transportation. However, the understanding of the mechanism of high-molecular-weight polymer used as stabilizers in CWS is still limited. We experimentally studied the rheological behaviors and stability performance of coal water slurry prepared with anionic (APAM), cationic (CPAM) and nonionic (NPAM) polyacrylamide. Apparent viscosity and rheology were measured using a viscometer. The rod penetration method incorporating with the oscillation method was applied to evaluate the stability performance of CWS. The zeta potential measurement and interaction energy calculations were also conducted. The results showed that the apparent viscosity of CWS increased with the addition of all the three PAMs. CWS by adding either APAM or CPAM behaved as a pseudoplastic fluid while the CWS with the addition of NPAM behaved as a dilatant fluid. The CWS with 0.1 wt% (on the dry coal basis) APAM exhibited the best stability performance. The settling rate for this slurry was the lowest (6.67%), and the zeta potential was the highest (−22.33 mV). The CWS by adding APAM had the highest total interaction energy between coal particles among four samples. The mechanism that controls the stability of CWS may be relevant to the increased electrostatic repulsive energy between coal particles by adding APAM, which depends on the surface potential of coal particles.

A Simple Frequency Formulation for the Tangent Oscillator

The frequency of a nonlinear vibration system is nonlinearly related to its amplitude, and this relationship is critical in the design of a packaging system and a microelectromechanical system (MEMS). This paper proposes a straightforward frequency prediction method for nonlinear oscillators with arbitrary initial conditions. The tangent oscillator, the hyperbolic tangent oscillator, a singular oscillator, and a MEMS oscillator are chosen to elucidate the simple solving process. The results, when compared with those obtained by the homotopy perturbation method, exhibit a good agreement. This paper introduces a very convenient procedure for attaining quick and accurate insight into the vibration property of a nonlinear vibration system.