Inertial Elements Research Articles

Research on adaptive control strategies for grid-friendly photovoltaic storage network systems

Abstract To address the critical issue of frequency stability in grid-connected photovoltaic energy storage systems, a control strategy based on grid-friendly technologies is proposed. This strategy integrates the principles and topology of traditional Virtual Synchronous Generator (VSG) with adaptive VSG control and pre-synchronization techniques. Firstly, based on the traditional VSG control strategy, the frequency operation curve of the VSG is divided into three intervals corresponding to different control modes: islanding mode, PV-storage frequency stabilization mode, and adaptive regulation mode. Each mode is analysed to understand the impact of different inertia and damping coefficients on system output characteristics. A control strategy that allows for adaptive adjustment of inertia and damping coefficients is designed, referencing the power angle characteristic curve and frequency oscillation curve of a synchronous generator (SG). By introducing inertia elements, the robustness of the system against disturbances is enhanced. Utilizing the operational characteristics of energy storage, the combined PV and energy storage system can better interact with and support the grid. Finally, simulation experiments are conducted by using MATLAB/Simulink. The proposed strategy is compared with traditional adaptive control and VSG control strategies. The results demonstrate that the proposed grid-friendly VSG control strategy offers superior frequency stability, robustness, and response speed.

A Compensator Microelectromechanical Acceleration Transducer with a Piezoelectric Sensing Element and Optical Reading

Introduction.Modern mobile control objects require the use of highly sensitive transducers of motion parameters, e.g., acceleration, with a wide measurement range. Increased sensitivity to measured parameters can be achieved by using precision optics, e.g., based on the tunneling effect. However, operating ranges of induced movements are less than a micrometer, which creates difficulties in positioning the sensing element. In order to improve manufacturability, to extend the measurement range and to reduce errors of acceleration transducers with optical tunneling, compensation circuits with a piezoelectric actuator as an active sensor can be used.Aim.To extend the measurement range of microelectromechanical acceleration transducers through the use of an integrated approach, including the introduction of a compensation circuit for sensor movements based on the inverse piezoelectric effect and detection of these movements by optical means.Materials and methods.An approach to compensating sensor movements is proposed. This approach consists in using a bimorph piezoelectric plate as an inertial element. The use of optical reading of sensor sub-micrometer displacements is considered.Results.A block scheme and a functional scheme of a compensator micro-opto-electromechanical acceleration transducer with a bimorph piezoelectric sensing element are developed. Deformations in the sensing element under the influence of accelerations (up to 100 m/s2) and compensation voltages, whose amplitude does not exceed several volts, are investigated to ensure the possibility of using the optical tunneling effect in the proposed transducer.Conclusion.A mathematical model of the transducer was developed and studied. A 2.5-fold increase in the measurement range was achieved. It was shown that the introduction of compensation feedback does not decrease the permissible frequency range of measured accelerations.

Longitudinal wave attenuation and bandgap analysis of a novel type hybrid tunable resonator metamaterial

Achieving vibration suppression or wave attenuation of tunable local resonance metamaterials without physical modification of the resonator has received a lot of attention recently. In this paper, a hybrid tunable metamaterial with a resonator containing a lever mechanism, an electromagnetic device, and a feedback system is proposed to achieve tunable bandgap and longitudinal wave attenuation. Unlike ordinary metamaterials, inertial amplification mechanisms and negative stiffness elements are involved in our proposed metamaterials. The function of the electromagnetic device and the feedback control are considered to theoretically derive the dispersion relation. The effective mass, the effective stiffness, the displacement transmission rate, and the band structure of the proposed metamaterial are analyzed, and the contributions of some key parameters on the bandgap are investigated. The accuracy of the analytical band structure is verified by the wave transmittance curves obtained by numerical simulation and the transient displacement response of a single oscillator. The results show that the proposed metamaterial yields broadband tunable bandgap in the low-frequency range, which enables the isolation of low-frequency longitudinal vibrations. This study provides a novel option for constructing integrated metamaterials to achieve vibration suppression and wave attenuation.

An improved algorithm for solving inverse problems of the dynamics of robotic devices at SCAS KIDYM

The paper presents the results of studies of an analytical algorithm for constructing a resolving system of linear equations to determine the driving forces and moments in the links of robotic devices of arbitrary structure during movement. This algorithm is implemented as an analytical algorithm in a special computer algebra system (SCAS) KiDyM, on the basis of which numerical calculations of the specified forces and moments are generated in the process of performing work processes, positioning mechanisms in the required positions, parking movements, etc. The KiDyM software package is used to solve mechanics problems of a wide class of discrete mechanical systems of arbitrary structure and type of motion for engineering and scientific calculations. A theoretical justification for the developed new approach, analytical and numerical proof of its effectiveness from the point of view of the process of automatically obtaining resolving equations, computational efficiency and accuracy of results are presented. The proposed algorithm is the result of the development of an algorithm that was previously implemented in SCAS KiDyM and was similar in purpose. Unlike the previously implemented algorithm, which generates a resolving system of equations after constructing the dynamic equations, the new algorithm is built into the process of generating dynamic equations - it sorts the model elements - inertial, dissipative, elastic and force elements of known forces and moments form the right side, and force elements with unknown forces and moments, they form a matrix of the left side of equations that solve the inverse problem of dynamics. The article gives a comparative analytical conclusion of one and another algorithm and shows the coincidence of the resulting equations. Also, using examples of calculations of the inverse problem of the dynamics of a portal crane and two 6-degree manipulators, the advantages of the new approach are shown.

Modal Analysis of 15 MW Semi-Submersible Floating Wind Turbine: Investigation on the Main Influences in Natural Vibration

One of the sources of sustainable energy with great, still untapped potential is wind power. One way to harness such potential is to develop technology for offshore use, more specifically at high depths with floating turbines. It is always critical that their structural designs guarantee that their natural frequencies of vibration do not match the frequencies of the most important oscillatory loads to which they will be subjected. This avoids resonance and its excessive undesired oscillatory responses. Based on that, a 3D finite element model of a 15 MW semi-submersible floating offshore wind turbine was developed in the commercial software ANSYS Mechanical ® to study its dynamic behavior and contribute to the in-depth analysis of structural modeling of FOWTs. A tower and floating platform were individually modeled and coupled together. The natural frequencies and modes of vibration of the coupled system and of its components were obtained by modal analysis, not only to verify the resonance, but also to investigate the determinant factors affecting such behaviors, which are not extensively discussed in literature. It was found that there is strong coupling between the components and that the tower affects the system as a result of its stiffness, and the floater as a result of its rotational inertia. The platform’s inertia comes mainly from the ballast and the effects of added mass, which was considered to be a literal increase in mass and was modeled in two manners: first, it was approximately calculated and distributed along the submerged flexible platform members and then as a nodal inertial element with the floater being considered as a rigid body. The second approach allowed an iterative analysis for non-zero frequencies of vibration, which showed that a first approximation with an infinite period is sufficiently accurate. Furthermore, the effects of the mooring lines was studied based on a linear model, which showed that they do not affect the boundary conditions at the bottom of the tower in a significant way.

Study of the phase characteristics of vibration sensors and conditions of orthogonalization of their measuring basis for the systems of vibration control and vibration testing of materials

To identify the most vibration-sensitive structures of the materials during vibration tests, it is necessary to determine the vibration vector in an orthogonal basis The effectiveness of the tests depends on the accuracy of the vector measurement. The transverse sensitivity of tri-axial vibration transducers, which have found vast application in various vibration measuring and material testing systems, leads to increased measurement errors and limits the frequency range of measurements. The errors can be reduced to almost zero using the proposed method of electronic orthogonalization, which involves rotation of the sensitivity vectors until they coincide with the orthogonal basis, resulting in zero transverse sensitivity. This approach has been successfully developed and works rather well in the low frequency band of the vibration transducer frequency response, wherein the amplitude-characteristics are linear and there is no phase shift in the channels. An emphasis is made on the influence of the phase characteristics of vibration sensors on the formation of orthogonalizing matrices that determine the requirements for an orthogonalizer. The structure of the installation for automated recording amplitude-frequency and phase-frequency responses of the vibration transducer, methodology and results of experimental study of a tri-axial piezoelectric accelerometer (TPA) with one inertia element and oblique-angle measuring basis are presented. The results obtained under vibration activated in three mutually perpendicular directions along the measuring axes show that the transducer measuring system is properly designed to provide for effective broadband orthogonalization of the measuring basis. The results obtained can be used to develop orthogonalizing transducers that eliminate transverse sensitivity in a wide frequency range, as well as to improve the design of sensors and their metrological characteristics.

Reliability-based design optimization of tuned mass-damper-inerter for mitigating structural vibration

The tuned mass-damper-inerter (TMDI), comprising mass blocks, springs, dampers, and two-terminal inertial elements, has garnered significant attention as an advanced iteration of the tuned mass damper (TMD) in recent years. However, previous studies of TMDI's design are primarily conducted according to the theoretical formulas based on deterministic analysis assuming harmonic excitations or stochastic analysis assuming Gaussian white noise type excitations. This treatment falls short of capturing the non-stationary and non-Gaussian characteristics exhibited by engineering excitations and thus cannot ensure the safety of controlled structure. A few studies considering non-stationary excitations and based on reliability metrics, in conjunction with stochastic simulation methods, often confront excessive computational overhead. Aiming at such a challenge, the reliability-based design optimization (RBDO) of TMDI system, combining the probability density evolution method (PDEM) and genetic algorithm (GA), for mitigating structural vibration under non-stationary excitations is performed in this study. For the purposes of illustration, a single-degree-of-freedom system attached the TMDI and subjected to stochastic ground motions is studied. Considering the cases of different levels of inertance-to-mass ratios, the RBDO of the TMDI is carried out. The solutions by the theoretical formulas and by the variance-based design optimization are compared to verify the superiority of the proposed method. For assessing the seismic mitigation performance of the optimized TMDI system, probability density evolution analysis of structure-TMDI system with three levels of inertance-to-mass ratios is performed. Comparison between the RBDO of TMDI and that of TMD under consistent mass ratio is further addressed. Numerical results reveal the technical advantages of TMDI in a probabilistic sense, i.e., high vibration mitigation performance, considerable mass reduction, and less stroke demand.

Discrete Acoustics: ARMA-modeling of Time Processes, Theory

In physics, in particular, acoustics, time is traditionally considered as a continuous coordinate. Some exception is signal processing, where sampling is necessary for calculations on computers. But all acoustic problems are formulated and solved using time-continuous models described by differential equations and their solutions in the form of continuous time functions. Meanwhile, these problems can be formulated and solved in an equivalent way using discrete-time models described by finite-difference equations and their solutions in the form of time series. As the experience of some other fields of science, for example, control theory, shows, the discrete approach has a number of advantages over the continuous approach, the useof which greatly facilitates the solution of many problems. This paper aims to partially fill the gap in acoustics that exists here and is aimed at creating the theoretical foundations of a discrete-time approach to solving acoustic problems. The paper is limited to the consideration of one oscillatory system widely used in acoustics— a linear structure with N degrees of freedom consisting of lumped inertial, elastic and dissipative elements, to which, in particular, the finite element method leads. For several continuous models of this system, equivalentdiscrete-time models are constructed in the paper, finite-difference equations are derived and their solutions are obtained. The criterion of equivalence of continuous and discrete models in the paper is the mathematically exact equality of the corresponding solutions at all discrete points in time. Based on this criterion, analytical relations have been established between the parameters of continuous and discrete models and their equations, which make it possible to build its discrete-time model based on a continuous model of the systemand, conversely, to build its continuous model based on a known discrete model. Special attention is paid in the paper to the forced vibrations of the system under the action of kinematic excitation, which is important in many acoustic problems, whereas in the literature only force excitation is considered. The paper also discussesone of the most useful properties of discrete modeling—the simplicity of constructing discrete models based on experimentally measured signals. A corresponding example is given. Note that the term “ARMAmodel” is an abbreviation for “autoregressive and moving average model”, generally accepted in control theory, systems theory and other fields of science.

Transient scattering of a Rayleigh wave by a cluster of subwavelength resonators—Towards asymptotic modeling of seismic surface metabarriers

A seismic metabarrier (intended for surface waves mitigation effect) is modeled as a cluster of single-degree-of-freedom resonator units deposited on the surface of an isotropic homogeneous elastic half-space. It is assumed that each resonator has a frictionless flat rigid base of diameter much smaller than the wavelength of an incoming surface wave. The slow-motions asymptotic method is applied for constructing the first-order asymptotic model of multiple time-dependent scattering of a pulsed Rayleigh wave with respect to the vertical displacements of the resonators (including their rigid bases and inertial elements) and the normal contact forces (time-dependent integral characteristics of the contact reactions beneath the resonator bases). Both the stationary and transient multiple scattering scenarios are considered. The variation of the amplitude reduction factor due to the model parameters variation is studied in detail.

Damping of an Oscillatory System with Incomplete Sealing of the Air Cavity by a Magnetic Fluid

Purpose. Investigate the damping of an oscillatory system with incomplete sealing of the air cavity with a magnetic fluid.Methods. The study was carried out on an experimental setup developed on the basis of known methods and equipment for magnetic measurements and manufactured independently. A ring neodymium magnet (NdFeB alloy) 60x24x10 mm in size was used as a magnetic field source. The magnetic field strength at the center of the magnet, measured with a TPU-01 milliteslamer, is 220 kA/m. An inductor, a GVT-427B amplifier, and a GwInstek GDS-72072 digital oscilloscope were used to display oscillograms. Samples of magnetic fluid based on Fe3O4 magnetite stabilized with oleic acid were studied. Kerosene was used as the carrier liquid.Results. The results of an experimental study of the elasticity and damping of an oscillatory system with incomplete sealing of the air cavity by a magnetic fluid bridge are presented. The level of sealing of the air cavity varies due to the process of pumping gas through capillaries of various radii. To explain the regularities obtained, a model theory is proposed in the approximation of a viscous gas flow according to the Poiseuille law, and the conclusions of the wellknown theory of sound propagation in molecular acoustics and the theory of sound ducts are also drawn. The relaxation mechanism imposes a restriction on the type of vibrational gas flow through the capillaries, which takes into account the "throughput" capacity of the capillaries. The proposed model explains the presence of a maximum in the dependence of the attenuation coefficient on the capillary radius and its decrease with an increase in the volume (height) of the gas cavity.Conclusion. The proposed relaxation theory of vibrational gas flow through capillaries predicts anomalously large damping coefficients and almost complete damping of an oscillatory system with a magnetic fluid inertial element. The use of the data obtained is advisable in the design of new shock absorbers, since a magnetic fluid damper with capillaries is capable of damping low-frequency oscillations.

Impact of bioclimatism and passive solutions on thermal performance: Feedback from an experimental wood-concrete house in a Mediterranean climate

This article is based on the analysis of the thermal behavior of an experimental house in a Mediterranean climate. This well insulated house presents 3 specificities: inertial elements mainly in the heart of the house with a wood frame envelope, large bay windows, and an interior patio facilitating the safe opening at night. The work focuses on the contribution of passive solutions: the valorization and management of solar gain, natural ventilation at night, thermal inertia and thermal insulation. Dynamic thermal simulations complete the analysis of the measurements. The concept has demonstrated its interest in the summer period with a comfort that can be maintained provided that the available passive solutions are used adequately. The thermal inertia coupled with the natural night ventilation allows to maintain a stable maximum daily indoor temperature lower than the outdoor temperature with a daily thermal amplitude up to 13 °C. The concrete slab of the ground floor exchanges with the indoor air up to 10 W/m2 during the day and up to 25 W/m2 with the natural night ventilation. The flow rate of the latter is estimated at 3.5 to 5.5 vol/h. In winter, the thermal inertia of the slab allows to make better use of solar gains, with for example a thermal flux penetrating the slab that can reach up to 60 W/m2, and represents, cumulated over the day, an energy transferred to the slab up to 300 Wh/m2. This energy is diffused throughout the night with an intensity of about 10 W/m2.

An Improving Model on Contact Time of The Inertial Impact Switch

Inertial impact switch is a widely used inertial force recognition element in electromechanical trigger fuze of missiles, rockets and artillery shells. In this paper, the impact responses of inertial switch are investigated with abundant acceleration loads through the dynamics analysis. Based on the Machete hammer experiment, the accuracy of the dynamics model is verified with a very small error. The systematic dynamic analysis shows that the contact time of impact proceeding keeps continuously increasing with greater pulse width and acceleration load. On the other hand, the threshold of switch decreases alone with the pulse time. To improve the performance index of the inertial impact switch, a spherical structure model is proposed. Surprisingly, a significant improvement of the contact time is discovered comparing with the cylindrical structural model. The proposed new structure will provide important technical reference for the practical application of devices in fuze technology field.

Simulation of dynamic characteristics of suspension hydraulic bushing

The hydraulic bushing is a common vibration isolator, and its dynamic characteristics influence the ride comfort of the vehicle. Aiming at a suspension hydraulic bushing with inertia components, a one-dimensional model of the hydraulic bushing is established based on Amesim. Secondly, a parameter identification method is proposed, and the equivalent piston area of the hydraulic bushing and the diaphragm strain stiffness are identified by this method. Finally, the identified parameters are input into the Amesim model, and the data results are compared with the experimental results after processing with MatLab. The results show that the dynamic characteristic curve of the hydraulic bushing calculated by this method is consistent with the test curve and can well predict the dynamic characteristics of the hydraulic bushing with inertia elements.

Low cost inertial sensor attitude fixation algorithm and accuracy analysis

Aiming at the problems of angle oscillation, slow convergence speed, and low accuracy of traditional algorithms in low cost inertial element attitude determination, this study proposes an improved attitude algorithm based on geomagnetic correction robust model assisted adaptive step gradient descent. Firstly, a robust ellipsoid fitting algorithm is proposed to correct the geomagnetic anomaly data. Then, an adaptive step size model is established based on the momentum gradient descent method, and the iterative optimization parameters are automatically adjusted according to the error function. At the same time, the dynamic limiting mean filter is used to constrain the attitude angle, to calculate the optimal attitude information of the sensor. Finally, the algorithm is verified by static and dynamic experimental data. The results show that the improved algorithm can effectively suppress the angle oscillation, optimize the attitude convergence effect, and improve the accuracy of low cost inertial sensor attitude calculation.

Measuring device for systems of technical vibro-diagnosis of power equipment

RELEVANCE. Among the various methods for assessing the technical condition of power equipment, vibration diagnostics occupies an important place. Therefore, improving the quality of hardware for vibration diagnostics is currently extremely important. THE PURPOSE. To develop a vibration sensor with a new principle of operation for systems of technical vibration diagnostics of power equipment, as well as to theoretically substantiate the performance of the proposed sensor. METHODS. When solving the set goal, the main provisions of the theory of vibration diagnostics were applied. RESULTS. A design of the vibration acceleration sensor has been developed, the peculiarity of which is that it is excited by means of constructive coupling capacitors, the first electrode of which is made in the form of a thin-walled metal split cylinder, the role of the second electrodes is performed by the lower row of the winding of each measuring coil, and the function of the inertial element is performed by a screen made in the form of a metal ring fixed on a suspension in the form of a membrane. Based on the electrical equivalent circuit of the sensor, a theoretical substantiation of its operability and efficiency was made. Variants of circuit solutions for the primary and secondary measuring transducers of the measuring device for vibration diagnostics systems have been developed. The primary measuring transducer contains directly a vibration displacement sensor, a sinusoidal voltage source, an input differential measuring amplifier and an analog filter containing a narrow-band filter, a broadband amplifier and a buffer amplifier. The secondary measuring transducer contains a quadrature detector of information signals, an output buffer amplifier and a quadrature reference voltage driver. A block diagram of the hardware solution for the vibration acceleration registration system is also proposed. CONCLUSION. The developed sensor has improved output characteristics and can be used not only for vibration control of power equipment, but also for measuring mechanical vibrations in technical diagnostic systems of various other machines and mechanisms, as well as for tasks of spectral seismic exploration.

DYNAMIC AND MATHEMATICAL MODELS OF THE HYDROIMPULSIVE VIBRO-CUTTING DEVICE WITH A PRESSURE PULSE GENERATOR BULT INTO THE RING SPRING

Structural calculation scheme of the hydropulse device for vibration cutting with built-in ring with pressure pulse generator (PPG) is considered. On the basis of the structural scheme and cyclogram of the working cycle of the device, its dynamic and mathematical models were developed, in which the hydraulic link is represented by a visco-elastic model of the working fluid (energy carrier) composed of the inertial elastic and dissipative elements (Kelvin-Foyga's body).

ALGORITHM OF ELECTRIC CIRCUIT STATE MATRIX TRANSFORMATION USING THE MODIFIED NODAL ANALYSIS

The article proposes the algorithm of electric circuit state matrix transformation obtained by the modified nodal analysis. The algorithm is aimed at reducing the system of electrical circuit differential equations to Cauchy problem form for the purpose of subsequent solution. Application of the modified nodal analysis to an electric circuit with energy inertial elements leads to a system of ordinary differential equations, which contains a singular matrix before the derivatives vector in matrix form if there are ungrounded capacitors in a circuit. For this reason, direct reduction of this equations system to Cauchy problem form is impossible. The idea of solving such systems is to pass from equations with potentials to equations with voltages and subsequent division of the equations system into two pieces: containing derivatives and without them. An important step in the transformation to equations with voltages is the elimination of linearly dependent rows of the singular matrix. The algorithm of that transformation is based on the analysis of the adjacency matrix compiled for the capacitors of the electrical circuit, and is the subject of this work. The algorithm can be used for topologically arbitrary connection of an unlimited number of capacitors. For the purpose of demonstration, an example of using the algorithm is given in the article.

ОЦЕНКА РЕЗОНАНСНЫХ РЕЖИМОВ ПРИВОДА ГЛАВНОГО ДВИЖЕНИЯ ТОКАРНОГО СТАНКА С БЕССТУПЕНЧАТЫМ РЕГУЛИРОВАНИЕМ

The study objective is to define and evaluate the resonant drive modes of the lathe primary motion continuously rated. The problem to which the paper is devoted is to draw up a design scheme of a dynamic torsional drive system for the lathe primary motion with the spindle speed continuously rated and to make a calculation that allows finding out the lowest natural torsional vibration frequencies of the drive. Research methods: analysis of a multi-mass analytical model of the lathe drive primary motion, followed by its reduction to models with a smaller number of masses (inertial elements). The novelty of the work is in the development of software that allows simplifying linear dynamic systems and finding out natural frequencies. Study results: the dynamic quality of the drive is analyzed, which gives the opportunity to find non-resonant zones of the drive by the rotational and toothed frequencies of forced vibrations with the help of the frequency ranges of shafts. Conclusions: the developed software makes it possible at the design stage to simplify the dynamic system, find the lowest natural frequencies of torsional vibrations and take measures to exclude resonant phenomena.

Multi-Sensor Fusion for Lateral Vehicle Localization in Tunnels

The satellite navigation signal in the tunnel is weak, and it is difficult to achieve accurate lateral positioning in complex conditions such as low-speed congestion by relying solely on inertial navigation or line image recognition, which is one of the problems of automatic driving at present. In this paper, a lane-level location method based on multi-sensor fusion is proposed. Using the machine vision method, detecting lane lines with the monocular camera, and fitting the lane lines to determine the driving status of the vehicle based on the lane line information. The top view of the lane line is taken by the binocular camera, and the distance of the vehicle from the lane line and the width of the lane are calculated from the pictures taken by the binocular camera. Obtaining the heading angle information of the vehicle using the gyroscope in inertial navigation and the distance information of the vehicle using the odometer. When a car changes lanes or overtakes, the new lane the vehicle is in is calculated by calculating the difference in heading angle and combining it with the lane width and odometer information so as to complete the lateral positioning of the vehicle. The simulation results show that the algorithm has high lateral positioning accuracy. The positioning accuracy is less affected by the drift of inertial elements, and the error will not accumulate.

Exact Augmented Perpetual Manifolds Define Specifications for the Steady States of Similar Rigid Body Modes, a Corollary for Nonautonomous Systems

Recently, the perpetual points in mathematics have been defined. In mechanical systems, the perpetual points for linear and some nonlinear systems are associated with rigid body motions and they form the perpetual manifolds. The mechanical systems that admit perpetual manifolds of rigid body motions are called perpetual mechanical systems, and these systems are not limited to linear (with a zero natural frequency) only but also nonlinear systems are considered. The concept of perpetual manifold is extended to the augmented perpetual manifold that is defined in externally forced mechanical systems when all the accelerations are equal but not necessarily zero. A proved theorem defines the external forcing conditions that a mechanical, and also a structural system can have solutions described by the exact augmented perpetual manifolds, which are the rigid body motions. Herein a corollary is proved defining the conditions that the steady states of a mechanical and also a structural system are associated with rigid body motions. The internal forces corresponding to the structural elements of the original system are separated to these forces that are associated with a perpetual mechanical (structural) system and the rest forces, which are associated with boundary structural elements, as external forces are considered. The developed theory is applied in a nonlinear perpetual structural system for the design of four types of boundaries, linear, nonlinear smooth, nonsmooth, and nonlinear generalized forces boundaries, and the numerical results verified the developed theory. This design can be considered as a passive control method for vibration mitigation of mechanical and structural systems, since in the exact augmented perpetual manifolds all the inertia elements move without oscillations and the sum of their internal forces is zero. This work is rather significant in engineering since it can be used for the structural design of systems.