Parametric Excitation Research Articles

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

With global electricity requirements due to increase in the coming years and growing pressure to reduce dependence on fossil fuels, universal demand for renewable energy is projected to grow. Marine energy, including wave energy, is an active research area, with potential to meet future energy demands, due to its high energy density. With a view to using a pendulum system in a floating object to extract energy from ocean waves, this paper analyses the effects of pendulum orientation and excitation type on the system’s dynamics. Three excitation scenarios, surge, heave and dynamic tilt of the floating object, with various pendulum orientations, were analysed and simulated. Both linearised and nonlinear systems were investigated with the former providing insight into the nonlinear system’s behaviour. Effects of pendulum orientation on power output potential differs significantly with excitation type and pendulum properties. While expected peak power output is observed at the resonant frequency and twice the resonant frequency under direct and parametric excitations respectively for both systems, the linearised system also exhibits regions of instability. These instability regions under parametric excitations were investigated with consideration for energy harvesting applications. Theoretical and experimental findings revealed that dynamic tilt excitations can be utilised for broadband energy harvesting at the expense of the peak power output. While peak average power output for these excitations for the considered system parameters is relatively low, 1 W versus 12.5 W for heave excitation, the bandwidth is very broad and starts from 0 rad/s frequency if tilt excitation amplitude is above 1.1 rad.

Mode-resolved micromagnetics study of parametric spin wave excitation in thin-film disks

Mode-resolved micromagnetics study of parametric spin wave excitation in thin-film disks

Study of vibration patterns and response transfer relationships in walnut tree trunks

Fruit tree trunk is the support structure of the whole tree, carrying the task of vibration transmission to all levels of branches, fruit tree trunk vibration response to the design and optimization of the vibration harvesting device to provide guiding value. In this paper, the vibration response and harvesting test was carried out for four walnut fruit trees with different morphology and size, and the vibration transmission relationship between the excitation device and the fruit tree as well as inside the fruit tree was analyzed and studied according to the acceleration response curves at each position point under different frequencies. At the same time, the theoretical vibration pattern of the fruit tree and the measured spatial three-dimensional vibration pattern were constructed, and the response transfer law between each point of the fruit tree was further analyzed in terms of the vibration pattern and direction of each position point on the tree. The results show that the excitation response acceleration is basically no attenuation inside the device, but there is some attenuation in the clamping part due to the presence of damping pads. The vibration response in the fruit tree trunk is greater in amplitude farther from the excitation point. The phase relationship between each position point is basically the same in the theoretical vibration mode and the measured vibration mode, but there is damping in the actual fruit tree, which leads to the accumulation of phase hysteresis in the transmission of excitation parameters. The actual response trajectory is a narrow ellipse, and the different position points show different rotational relationships along the ellipse trajectory due to the growth of the fruit tree.

Kinematic Stability Analysis of Anchor Cable Structures in Submerged Floating Tunnel under Combined Parametric–Vortex Excitation

The submerged floating tunnel is a marine transportation infrastructure that links two shorelines. The tunnel tube body’s buoyancy exceeds gravity, with anchoring ensuring equilibrium. Anchoring reliability is crucial. This study presents a three-way coupled kinematic model for the mooring structure, formulated on Hamilton’s principle and Kirchhoff’s assumption. It explores the impact of the tube body’s buoyancy-to-weight ratio and the sea current’s angle of incidence on mooring motion response. By solving the motion analysis model, Hill’s equation system is derived to assess the parameter instability of the anchor cable structure. The coefficient of excitation instability intervals for the submerged floating tunnel is determined and validated. The findings indicate the following: (1) Increasing the float-weight ratio reduces displacement response amplitudes in all directions, bringing downstream and transverse currents closer to their initial positions; (2) Changes in current direction angles result in decreased downstream excitation strength and increased transverse displacement response with the same excitation direction; (3) The instability interval visualization effectively predicts anchor cable structure instability under parametric excitation. Structures within the instability region are deemed unstable, while those outside are considered stable.

Nonlinear Vibrations of the Piezoelectric-Laminated Composite Cantilever Rectangular Plate Subjected to the Transverse and Parametric Excitation

The intelligent structure will be the key to the industrial manufacturing field in the future, piezoelectric materials are the most commonly used active materials in many mechatronic and vibration control systems. In this paper, we illustrated the nonlinear vibration behaviors of the piezoelectric-laminated composite cantilever rectangular plate subjected to transverse and parametric excitation. Two piezoelectric layers are attached to the upper and lower surfaces of graphite/epoxy composite laminated plate. The nonlinear dynamic equations are derived via the classical laminated plate theory, von Karman large deformation theory, the constitutive equation of the piezoelectric materials, and the Hamilton principle. Considering the Galerkin method, the nonlinear ordinary differential equations for the two-order vibration mode of the piezoelectric laminated composite cantilever rectangular plate are achieved. The multiple scale method is applied to obtain the average equations to study the nonlinear vibration characteristic of the stable motion. The primary resonance and the 1:1 internal resonance of the piezoelectric laminated composite cantilever rectangular plate are investigated. The amplitude-frequency response curves, force-amplitude response curves, time histories, phase curves, and bifurcation diagrams are given to investigate the nonlinear dynamic characteristic of the piezoelectric laminated composite cantilever rectangular plate. The detailed parametric analyses show that bubble response curves are separated from the amplitude-frequency response curves with the continuous increase of the external excitation due to the internal resonance. In addition, the results reveal the energy transform between the various order vibration modes of the system. This work is expected to provide theoretical guidance for the nonlinear vibration of the smart piezoelectric laminated composite structure.

Effect of stability state transition of variable potential well in tri-hybridized energy harvesters

Energy harvesting is a crucial technology for self-powering wireless sensor nodes and mobile terminals. In addressing this, we utilized a variable potential well to create a tri-hybrid energy harvester that integrates piezoelectric effect, electromagnetic induction, and triboelectric effect. The compression and stretching of a compressible magnet-spring oscillator alter the system’s potential well, thereby promoting the operation of the piezoelectric unit (PU), electromagnetic unit (EU), and triboelectric unit (TU). A coupled electromechanical model using Hamilton’s principle was established. By calculating the static potential energy and restoring force, we discussed the stability state transition, revealing that when the magnet distance is less than 38 mm, the system transitions from a mono-stable to a bi-stable state. The experimental study investigated the impact of excitation and structural parameters on voltage and power. A high excitation level enhances all three units. The TU demonstrates excellent electrical performance under high potential energy in the bi-stable state, while the PU performs best in mono- and bi-stable switching structure. The EU shows relatively balanced electrical performance across various conditions. These findings offer new insights into enhancing energy harvesting capabilities for external circuits.

A tunable pendulum-like piezoelectric energy harvester for multidirectional vibration

Harvesting energy from vibrations using piezoelectric mechanism has attracted much attention for powering wireless sensors over the past decade. This paper proposes a tunable pendulum-like piezoelectric energy harvester for multidirectional vibration (TP-PVEH) to enhance the power generation characteristic, durability, and environmental adaptability of energy harvester. Unlike traditional cantilevered piezoelectric vibration energy harvesters (PVEHs), which typically lowered working frequencies by adding the weight of proof mass at the end of beam or reshaping beam, TP-PVEH employed a pendulum to harness low-frequency vibrations. Moreover, in contrast to typical pendulum-like PVEHs, the pendulum in this design was not mounted at the end of beam but was attached to a radial spherical plain bearing (RSPB) structure, which avoided the irreversible beam damage caused by gravitational force. TP-PVEH utilized simple-pendulum-induced RSPB motion to smoothly pluck piezoelectric beams, subjecting the piezoelectric beams to unidirectional compressive stress only. Meanwhile, the RSPB structure's capability to facilitate multidirectional rotation enabled TP-PVEH to efficiently capture energy from various directions. Theoretical analysis, numerical analysis and experiment tests were conducted to validate the design and examine how excitation and structural parameters influenced on the output performance of TP-PVEH. The results demonstrated that the excitation amplitude, excitation angle, proof mass, and mass distance brought significant effects on the output characteristic of TP-PVEH. The working frequency, output voltage and power could be efficiently tuned by the abovementioned parameters. With an excitation amplitude of 3 mm, TP-PVEH achieved an optimal output power of 9.81 mW and an output power density of 11.37 μW/mm3, operating with a load resistance of 200 kΩ at a frequency of 12.5 Hz.TP-PVEH could power 100 blue LEDs and a calculator. Additionally, the ability of TP-PVEH to charge capacitors further demonstrated its practical power supply capabilities.

Dynamic reliability and seismic fragility analysis for high concrete-faced rockfill dam slopes subjected to stochastic earthquake and parameter excitation via PDEM

The randomness of material parameters and earthquake excitation greatly impacts the seismic stability of high concrete-faced rockfill dam (CFRD) slopes. However, no research has comprehensively analyzed the impacts of stochastic earthquake excitations, random parameters and their coupled effects on seismic stability of CFRD slopes and selected a multi-indicator evaluation criterion to carry out performance-based safety assessment. This paper develops a novel and comprehensive framework for evaluating the seismic stability of CFRD slopes based on the generalized probability density evolution method (GPDEM) with high efficiency and accuracy. The effects of three kinds of randomness on seismic stability of CFRD slopes were comprehensively compared and analyzed on the basis of multi-indices (safety factor (FS), cumulative slip displacement and cumulative time with FS < 1.0). Firstly, the nonlinear shear strength parameters of 40 high CFRDs were statistically collected to obtain the statistical characteristics of rockfill material strength parameters of actual CFRD projects. Secondly, three kinds of random samples were generated using generalized F-discrepancy (GF-discrepancy) method and Spectral expression-Random function (SERF) method. Then, the GPDEM was introduced to combine with three indices to perform the stochastic analysis and reliability evaluation. Finally, the fragility analysis of the CFRD slope was conducted. The results reveal that FS is more sensitive to the ground motions randomness, while cumulative slip displacement and cumulative time with FS < 1.0 are more sensitive to the material parameters randomness. The seismic safety evaluation of CFRD slopes based on multiple indices with full consideration of coupled randomness effects is necessary.

Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model

Articulated swimming robots have a promising potential for various marine applications. A common theoretical model assumes ideal fluid, where the viscosity is negligible and the swimmer–fluid interaction is induced by reactive forces originating from added mass effect. Some previous works used this model to study planar multi-link swimmers under kinematic input prescribing all joint angles. Inspired by biological swimmers in nature that utilize body flexibility, in this work we consider an underactuated three-link swimmer where one joint is periodically actuated while the other joint is passive and viscoelastic. Analysis of the swimmer’s nonlinear dynamics reveals that its motion depends significantly on the amplitude and frequency of the actuated joint angle. Optimal frequency is found where the swimmer’s net displacement per cycle is maximized, under symmetric periodic oscillations of the passive joint. In addition, upon crossing critical values of amplitude or frequency, the system undergoes a bifurcation where the symmetric periodic solution loses stability and asymmetric solutions evolve, for which the swimmer moves along an arc. We analyze these phenomena using numerical simulations and analytical methods of perturbation expansion, harmonic balance, Floquet theory, and Hill’s determinant. The results demonstrate the important role of parametric excitation in stability and bifurcations of motion for flexible underactuated locomotion.

Impact of the Exciter and Governor Parameters on Forced Oscillations

In recent years, the frequency of forced oscillation events due to control system malfunctions or improper parameter settings has increased. Tuning the parameters of exciters and governor models is crucial for maintaining power system stability. Traditional simulation studies typically involve small transient disturbances or step changes to find optimal parameter sets, but existing optimization algorithms often fall short in fine-tuning for forced oscillations. Identifying the sensitive parameters within these control models is essential for ensuring stability during large, sustained disturbances. This study focuses on identifying these critical exciter and governor model parameters by analyzing their influence on sustained forced oscillations. Using Kundur’s two-area system, we analyze common exciter models such as SCRX, ESST1A, and AC7B, along with governor models like GAST, HYGOV, and GGOV1, utilizing PSS®E software version 34. Sustained forced oscillations are injected at generator-1 of area-1, with individual parameter changes dynamically simulated. By considering a local oscillation frequency of 1.4 Hz and an inter-area oscillation mode of 0.25 Hz, we analyze the impact of each parameter change on the magnitude and frequency of forced oscillations as well as on active and reactive power outputs. This novel approach highlights the most influential parameters of each tested model—such as exciter, governor, and turbine gains, as well as time constant parameters—on the impact of forced oscillations. Based on our findings, the sensitive parameters of each tested model are ranked. These would provide valuable insights for industry operators to fine-tune control settings during oscillation events, ultimately enhancing system stability.

Effects of excitation parameters on fretting wear and corrosion of 316L stainless steel under random impact-sliding condition

In heat exchanger applications, the random vibration due to fluid excitation can cause mechanical wear between tubes and supports. In corrosive environments, the synergy between wear and corrosion can make wear more severe. Therefore, this paper focused on the effects of excitation amplitude and excitation force ratio (drag force/lift force) on fretting wear and corrosion of 316L stainless steel under random impact-sliding conditions. The results showed that as the excitation parameters increased, the friction coefficient and total wear amount would increase, the open circuit potential (OCP) decreased and the polarization curve self-corrosion potential shifted negatively. All synergistic coefficients in this paper were greater than 1, indicating that there was an obvious positive synergy between wear and corrosion. In the fretting wear and corrosion process, pure wear always played a dominant role. Under impact-sliding conditions, as the excitation force increased, the rate of wear-promoted corrosion increased from 3.0 × 10−7 to 2.0 × 10−6 g/h, an increase of 6.67 times. However, the rate of corrosion-promoted wear decreased from 1.1 × 10−6 to 2.0 × 10−7 g/h, a decrease of 5.5 times, showing a certain self-limiting property. The total synergy rose slowly with the increase of excitation parameters. The wear mechanism of materials under impact is characterized by adhesive wear, while under impact-sliding conditions, the wear mechanism involves abrasive wear and corrosion wear.

Preparing pure 43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{43}$$\\end{document}Ca+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} samples in an ion trap with photoionization and parametric excitations

We present a practical scheme for the efficient preparation of laser–cooled 43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{43}$$\\end{document}Ca+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} ions in an ion trap. Our approach integrates two well-established methods: isotope-selective photoionization and isotope-specific parametric excitation. Drawing inspiration from the individual merits of each method, we have successfully integrated these techniques to prepare extended chains of 43\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{43}$$\\end{document}Ca+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} ions, overcoming the challenge posed by their low natural abundance of 0.135% in a natural source. Furthermore, we explore the subtleties of our scheme, focusing on the influence of different factors on the purification process. Our investigation contributes to a broader understanding of the technique and highlights the adaptability of established methods in addressing specific isotopic challenges.

On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

A new four-dimensional chaotic system with rich transitional characteristics between dissipative and conservative.

The general form of the Hamiltonian function serves as the foundation for the creation of a new four-dimensional chaotic system in this study. We discover that the external excitation parameter d, the internal parameter a, and all initial values have a transforming influence on the system property. Additionally, the corresponding fractional-order chaotic system in accordance with the constructed four-dimensional chaotic system is proposed. It is found that as the order q rises, the system transforms gradually from a dissipative system to a conservative system. Multiple coexisting attraction flows based on the Hamiltonian energy magnitude are present in this dual-property chaotic system. The complexity analysis shows that the system has a high level of complexity. NIST test indicates that the chaotic sequences produced by this dual-property chaotic system exhibit good pseudo-randomness. Finally, a Digital Signal Processing-based hardware platform confirms the physical realizability of the system.

Periodic response and stability analysis of a bistable viscoelastic von Mises truss

This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.

Nonlinear vibrations of variable speed rotating graphene platelets reinforced blades subjected to combined parametric and forced excitation

It is generally acknowledged that the disturbance of rotating speed will cause parametric resonance for blades, and the presence of rotor displacement also can make the blade vibrate transversely. However, the coupled resonance mechanism of blades under the combined action of rotating speed disturbance and rotor displacement is not yet clear. To answer this question, this article investigates the nonlinear coupled resonance behavior of rotating blades in two cases: typical tuned (the frequency ratio of parametric and forced excitations equals 2:1) and frequency ratio detuned. A nonlinear vibration equation for rotating blades is established based on Euler beam theory in conjunction with geometric nonlinearity. The mixing rule and modified Halpin-Tsai model are used to calculate the effective properties of GPLRMF materials. Subsequently, using the method of varying amplitudes (MVA), an approximate analytical solution of the coupled resonance response is derived, the Jacobian matrix is used to determine the stability of non-trivial solutions, and the accuracy of the analytical results is verified with the aid of numerical solutions. Finally, the steady-state response of typical tuned and detuned coupled resonance is analyzed, and the influence mechanism of factors such as excitation amplitude, excitation phase angle and other parameters on coupled resonance is studied in detail. The results indicate that the supercritical coupled resonance curve exhibits double resonance peaks and jumps. Meanwhile, the steady-state response of coupled resonance highly depends on the excitation phase angle.

Optimized ultrasound neuromodulation for non-invasive control of behavior and physiology

Focused ultrasound can non-invasively modulate neural activity, but whether effective stimulation parameters generalize across brain regions and cell types remains unknown. We used focused ultrasound coupled with fiber photometry to identify optimal neuromodulation parameters for four differentarousal centers of the brain in an effort to yield overt changes in behavior. Applying coordinate descent, we found that optimal parameters for excitation or inhibition are highly distinct, the effects of which are generally conserved across brain regions and cell types. Optimized stimulations induced clear,target-specific behavioral effects, whereas non-optimized protocols of equivalent energy resulted in substantially less or no change in behavior. These outcomes were independent of auditory confounds and, contrary to expectation, accompanied by a cyclooxygenase-dependent and prolonged reduction inlocal blood flow and temperature with brain-region-specific scaling. These findings demonstrate that carefully tuned and targeted ultrasound can exhibit powerful effects on complex behavior and physiology.

Dynamic Analysis and PD Control in a 12-Pole Active Magnetic Bearing System

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton’s second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system’s amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system’s spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor’s motion, but it also increases the system’s instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion.

Performance Improvement of Three-Spring Quasi-Zero-Stiffness Isolator by Shape Memory Alloy Damper

Quasi-zero stiffness vibration isolators (QZSI) can effectively resolve the contradiction between the load bearing and the vibration isolation for low-frequency vibration systems. The three-spring QZSI is a classical QZSI. However, constrained by its geometrical relationship, the working stroke of the QZSI is limited, and the isolation performance will deteriorate when the displacement response is significant. To solve this question, the shape memory alloy (SMA) damper, characterized by lower secondary stiffness, partially replaces the positive-stiffness spring of the three-spring QZS isolator to widen its effective working stroke, which forms a novel SMA-QZSI. Based on a piecewise linear constitutive model of SMA, a theoretical model of the force–displacement relationship of SMA-QZSI is established. Subsequently, the approximate analytic amplitude–frequency response equation of the non-smooth nonlinear SMA-QZSI system under harmonic excitation is obtained by the average method and verified numerically. In addition, the effects of mechanical parameters of SMA springs and external excitation parameters on mechanical behaviors and low-frequency isolation performance of the SMA-QZSI isolator are discussed. Finally, the static and dynamic experiments of SMA-QZSI are conducted to verify its force–displacement relationship and isolation performance. The results show that the proposed SMA-QZSI has remarkable low-frequency vibration isolation performance.

Square Parametric Excitation: A Digital Resonant Method for the Quadrupole Ion Trap.

Digital ion trap technology is an alternate method for driving quadrupole ion traps and mass filters using variable frequency, fixed amplitude RF square waves in place of variable amplitude, fixed frequency RF sine waves. This technique offers some advantages such as an increase in the high mass analysis range by varying frequency and lower overall voltage requirements. Here, we present a complex square waveform developed for resonant parametric excitation in a quadrupole linear ion trap. Unlike traditional resonance methods, the driving RF square wave and auxiliary square wave are coupled using the same digital circuitry without the need for transformer coupling. In this work, we use this complex waveform to selectively excite the first order parametric resonances of ion motion. The square parametric excitation method presented here employs a simple and repetitive circuit design consisting of a low-voltage waveform generator followed by a series of high-voltage MOSFET switches. This design allows for resonance methods to be easily implemented in the all-digital quadrupole. The complex square waveform can perform the same useful functions as sine wave auxiliary signals, such as selective mass elimination and mass isolation. We also demonstrate that the mass resolution performance and S/N of our digital mass spectrometer is improved by applying the complex square waveform during ion ejection.