Natural Frequency Ratio Research Articles

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

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

Investigation of Strain Gradient Theory for the Analysis of Free Linear Vibration of Nano Truncated Conical Shell

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with partial differentials along with the classical and non-classical boundary conditions. Galerkin’s method and the Generalized Differential Quadrature (GDQ) approach are applied to obtain the linear free vibrations of the carbon nano cone (CNC). The CNC is studied with simply supported boundary condition. The results of the new model are compared with those of the classical and couple stress theories, which point to the conclusion that the classical and couple stress models are special cases of modified strain gradient theory. Results also reveal that rigidity of the nano truncated conical shell in the strain gradient theory is greater than that in the modified couple stress and classical theories respectively, which leads to an increase in dimensionless natural frequency ratio. Moreover, the study investigates the effect of the size parameters on nano shell vibration for different lengths and vertex angles.

Influence of phase difference between kinematic and inertial loads on seismic behaviour of pile foundations in layered soils

A series of dynamic centrifuge experiments was conducted on model pile foundations embedded in a two-layered soil profile consisting of soft-clay layer underlain by dense sand. These experiments were specifically designed to investigate the individual effect of kinematic and inertial loads on a single pile and a 3 × 1 row pile group during model earthquakes. It was observed that the ratio of free-field soil natural frequency to the natural frequency of structure might not govern the phase relationship between the kinematic and inertial loads for pile foundations as reported in some previous research. The phase relationship obtained in this study agrees well with the conventional phase variation between the force and displacement of a viscously damped simple oscillator subjected to a harmonic force. Further, as expected, the pile accelerations and bending moments can be smaller when the kinematic and inertial loads act against each other compared to the case when they act together on the pile foundations. This study also revealed that the peak kinematic pile bending moment will be at the interface of soil layers for both single pile and pile group. However, in the presence of both kinematic and inertial loads, the peak pile bending moment can occur either at the shallower depths or at the interface of soil layers depending on the pile cap rotational constraint.

DIAGNOSTICS OF STRUCTURAL DAMAGE BASED ON THE NATURAL FREQUENCIES RATIO CHANGE

The problems of vibration diagnostics based on the change of natural frequencies of structures are connected with the influence of ambient and operational factors (temperature, humidity, wind, heavy traffic etc.) on the natural frequencies. In some cases, this effect is comparable with the effect of damage itself and reliable diagnostics of damage becomes problematic. To solve this problem, the use of the ratio change between natural frequencies of different mode shapes is proposed as a characteristic of damage. The study has demonstrated that this ratio is unaffected by the environmental and operational factors. Application of the proposed method is illustrated using the example of Z24 reinforced concrete bridge. As the characteristic feature of the reinforced concrete structures damage is the occurrence of multiple cracks, in the analytical model, apart from the size and location of the cracks, the possibility of several locally located cracks was taken into account.The analytical study was performed to calculate the mode shapes and natural frequencies of damaged multi-span beam-like structure. The results reveal that, in order to identify local damage of subcritical size, natural frequency data of at least four modes of vibration are necessary. The eigenfrequencies obtained experimentally in the study of the Z24 bridge were used to confirm that the change in the eigenfrequency ratio can be used to diagnose relatively small local defects in complex structures. At this the reliability of such vibration diagnostics is much higher than based on the change of natural frequencies and mode shapes, since the change in the ratio of natural frequencies does not depend on the environmental conditions and operating conditions of the structure.

Effects of natural frequency ratio on vortex-induced vibration of a circular cylinder in steady flow

This paper investigates the effects of the natural frequency ratio on the vibration response of an elastically mounted circular cylinder in fluid flows at a low Reynolds number of 200 and a mass ratio of 2. The natural frequency ratio (RF) is defined as the ratio of natural frequency in the in-line direction to that in the cross-flow direction. Compared with previous studies, this paper extended the range of natural frequency ratios from 1–2 to 1–4 and found the most complex vibration and wake flow occur at natural frequency ratios of 2.5 and 3. Modes 2S (two single vortices), 2P (two pairs of vortices), and P+S (one pair and a single vortex) are defined as flow modes where two single vortices, two pairs of vortices, and one pair plus and one single vortices are shed from the cylinder in one period of vibration, respectively. The new findings for RF = 2.5 and 3 include a new 2P mode that only exists when RF = 2.5 and 3, a bi-stable wake mode where the wake flow could be either the 2P or the P+S mode, depending upon the initial condition, and, most interestingly, a tri-stable wake mode where the wake flow could be the 2P, P+S, or non-lock-in mode. In bi-stable and tri-stable regimes, once one wake flow mode is set, it does not change to other modes. In addition, the vibrations for a specific flow velocity but different modes may have different amplitudes, but their vibration frequencies are the same. The mode T wake flow is a flow mode where the flow switches between two modes alternately and the vibration has a beating feature. Three types of flow switching in mode T are found: 2S–1S switch, 2S–P+S switch, and 2S–2P switch. Mode 1S is a mode where two single vortices are shed in two vibration periods. It cannot exist itself and must co-exist with mode 2S. A 270°–360° phase between the displacements in the in-line and cross-flow directions suppresses the formation of the mode 2P wake, and a 0°–45° phase stimulates the mode 2P wake.

냉간압연률 및 두께에 따른 STS316L의 감쇠능 및 고유주파수

This study was investigated mechanical properties, damping capacity and natural frequency using STS316L steel with different thickness and cold rolled STS316L steel. The austenite phase was transformed into a martensite phase by cold rolling. Tensile strength increased with an increase of the degree of cold rolling whereas elongation decreased. The damping capacity decreased as the degree of cold rolling increased. The natural frequency showed a tendency to decrease slightly as the degree of cold rolling increased, and increased as the thickness increased. The natural frequency of the FFT analysis was found to be the secondary frequency. The natural frequency ratios showed a constant value, and there was no structure effect.

Analysis of connections and restrictions occurring due to the oscillations of vibrating screen working member and cantilevered screen deck

Research relevance is due to the need of mining companies in a more complete extraction of mineral resources, reduction of crude minerals losses, and extension of deposits’ life. Some enterprises face the problem of complicated high-quality separation of hard-to-screen rock mass. Screen which are common in the industry often become clogged causing decline in the effectiveness of screening. Research aim is to determine the links, build resonant curves and analyze the amplitude oscillations of the working member and cantilevered bars of the screen deck using numerical simulation. Methodology includes the theoretical study of the dual mass oscillatory system with the use of numerical simulation. Results. The motion of the vibrating screen with circular oscillations of the working member, which includes the screen deck of a cascade type with cantilevered bars, is regarded as oscillation of a dual mass system. The amplitudes of oscillations of both masses make in-phase and anti-phase movements relative to the driving force of the drive. The analysis showed that the amplitudes of the working member are practically independent of the screen deck parameters, and bars oscillation amplitudes vary over a wide range. The expressions are given calculating the parameters of cantilevered bars and the values of the initial data of the GIT-51 screen. Resonance curves of amplitude and frequency relations are constructed. The conditions are established under which the oscillation amplitudes of the cantilevered bars take on hyperadmissible values; it is shown that for a particular oscillating system there is a transitional resonance value. Summary. The natural oscillation frequency ratio ranges are established of the entire system with the frequency of forced oscillations in which the oscillation amplitudes of cantilevered bars reach the specified parameters. It is shown that by changing the screen deck parameters at the design stage, it is possible to adjust the inter-frequency range and establish the operating mode of the screen.

2-DOF vortex-induced vibration of two tandem square cylinders with varying natural frequency ratios

In this paper, the two-degree-of-freedom (2-DOF) flow-induced vibrations of two square cylinders in tandem are studied numerically. Both cylinders have a mass ratio of 2 and are placed at a distance of 5D in the inline direction. A characteristics-based split (CBS) finite element algorithm is employed to solve the incompressible flow equations. The Reynolds number (Re) is kept constant at 100, whereas reduced velocity (Ur ) ranges from 3-13. Computations are made for three natural frequency ratios i.e. fr = fnx/fny = 1, 1.5 and 2. Results of the upstream cylinder are similar to that of an isolated square cylinder by other researches; however, the downstream cylinder shows different characteristics due to the effect of wake from the upstream cylinder. All the results for frequency ratios 1 and 1.5 overlapped to each other, indicating that the effect of frequency ratio is inconsiderable, however as fr increases to 2, the effect is observed in both the cylinders. It is to be noted that the effect is sensitive only in the lock-in region. For all fr, fully developed wake patterns at Ur corresponding to the peak vibration amplitudes are of C(2S) type while that for the other higher Ur , are of 2S type. Cylinder motion trajectories are also discussed; except Ur = 7 of fr= 2 at which phase between lift and the lateral displacement is 90°, all the trajectories are appeared to be figure “8” type.

Acoustic-Structure Interaction in an Adaptive Helmholtz Resonator by Compliance and Constraint

Abstract The acoustic energy attenuation capabilities of traditional Helmholtz resonators are enhanced by various methods, including by coupled resonators, absorbing materials, or replacement of rigid walls with flexible structures. Drawing from these concepts to envision a new platform of adaptive Helmholtz resonator, this research studies an adaptive acoustic resonator with an internal compliant structural member. The interaction between the structure and acoustic domain is controlled by compression constraint. By applying uniaxial compression to the resonator, the flexible member may be buckled, which drastically tailors the acoustic-structure interaction mechanisms in the overall system. A phenomenological analytical model is formulated and experimentally validated to scrutinize these characteristics. It is found that the compression constraint may enhance damping capabilities of the resonator by adapting the acoustic-structure interaction between the resonator and the enclosure. The area ratio of the flexible member to the resonator opening and the ratio of the fundamental natural frequency of the flexible member to that of the enclosure are discovered to have a significant influence on the system behavior. These results reveal new avenues for acoustic resonator concepts exploiting compliant internal structures to tailor acoustic energy attenuation properties.

A Novel Bulk-Flow Model for Pocket Damper Seals

Abstract In this paper, a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes (CVs) for each circumferential pocket of the seal. The continuity, circumferential momentum, and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modeled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee–Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth- and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive–negative inlet preswirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behavior of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and preswirl ratio.

Frequency lock-in during nonlinear vibration of an airfoil coupled with van der Pol Oscillator

The frequency lock-in during the nonlinear vibration of a turbomachinery blade is modeled using a spring-mounted airfoil coupled with a van der Pol Oscillator (VDP) oscillator. The proposed reduced-order model uses the nonlinear VDP oscillator to represent the oscillatory nature of wake dynamics caused by the vortex shedding. The damping term in the VDP oscillator is assumed to be nonlinear. The coupled equations governing the pitch and plunge motion of an airfoil are used to approximate the vibration of a turbomachinery blade. Springs having cubic-order nonlinearity for their stiffnesses are used to mount the airfoil. The unsteady lift acting on the blade is modeled using a self-excited nonlinear wake oscillator. The model for wake dynamics takes into account the influence of blade inertia. The nonlinear coupled three degrees of freedom (dof) aeroelastic system is studied for instability resulting in the frequency lock-in phenomenon. The equations are transformed into non-dimensional form, and then the frequencies of the coupled system are plotted to demonstrate the frequency lock-in. Further, the method of multiple scales is used to derive modulation equations which represent the amplitude and phase of the oscillation. The results obtained using the method of multiple scales are compared with direct numerical solutions to verify the present modeling method. The steady-state amplitudes of the response are plotted against the detuning parameter, which represents the frequency response curve. Further, the sensitivity of non-dimensional parameters such as coupling coefficients, mass ratio, reduced velocity, static unbalance, structural damping coefficient and the ratio of uncoupled pitch and plunge natural frequencies on the frequency response is investigated. The study revealed that parameters such as mass ratio, reduced velocity, structural damping coefficient, and coupling coefficients have a stronger influence in suppressing the amplitude of vibration. Meanwhile, parameters such as the frequency ratio, static unbalance, reduced velocity, and mass ratio significantly affect the range of frequency in which the lock-in phenomenon happens. Further, linear perturbation analysis is done to understand the qualitative effect of the system parameters such as coupling coefficients, mass ratio, frequency ratio, and static unbalance on the range of lock-in.

Calculation-and-Experimental Investigation on Natural Frequencies and Oscillation Modes of Pairwise-Shrouded Cooled Turbine Blades

The paper presents the results of simulations and experimental investigations on natural frequencies and oscillation modes of pairwise-shrouded cooled turbine blades and their rings with allowance for a possible frequency mistuning and the assured contact of mating surfaces of the root and shroud platform halves. As the research object, the high-pressure turbine wheel of an aircraft bypass turbojet engine has been selected. 3D finite element models of the turbine wheel blades/ period were developed as a system with structural rotational symmetry. The contact interaction between blades over the mating surfaces was modeled on basis of solving the stationary problem. The calculation-and-experimental investigations were performed for two operating conditions of the engine – the non-running engine and the steady-state maximum take-off condition. Results have been cited for individual, isolated blades. The results show a good agreement between calculated and experimental data. The frequency mistuning of those blades is found to be considerably dependent on oscillation mode number, but the mistuning value is practically not affected by the operating condition of the engine. It is confirmed that two oscillation modes are excited in the blade pair as a regular system in the presence of the mistuning of their frequencies, which are close to the inphase and antiphase frequencies. The ratio of natural frequencies of those oscillation modes is dependent on oscillation mode of isolated blades. It is shown that the frequency mistuning of paired blades due to excitation of two oscillation (inphase and antiphase) modes causes doubling of the number of resonant states of the turbine wheel what must be considered when developing methods to ensure their vibrational reliability.

Influence of Frequency Ratio on the Hydroelastic Response of a Cylinder with Degrees of Freedom under Vortex Induced Vibration

Vortex induced vibration of cylindrical structures is an extensively researched topic. Most of the studies have concentrated on the response of the cylinder in the cross flow (CF) direction. In a realistic ocean environment, structures such as drilling and marine risers are more or less free to vibrate both in CF and in line (IL) directions. It has also been observed that the IL vibrations have significant influence on the CF response. Interaction between the responses in inline and cross flow directions has still been not fully understood. This paper addresses the same through a simplified numerical method for understanding the interaction between these two responses using two dimensional computational fluid dynamics (CFD) simulations. Here analyzes two cases have been considered; where in the cylinder is modeled with two different values of ratio of natural frequency of the cylinder in the IL direction to that in the CF direction. The trends of variation of hydrodynamic and structural parameters have been analyzed to comprehend the effect of directional natural frequency ratio on the cylinder response and hydrodynamic force coefficients. The shedding pattern has also been studied in this paper. An increase by 18% in the value of the lift coefficient and 38 % of that in the drag coefficient has been observed when the frequency ratio is increased from 1 to 2. The results show that the cylinder with frequency ratio 2 is more prone to lock in vibration. This phenomenon may be related to the shifting of shedding pattern from 2S to P + S mode when the frequency ratio is 2.

STUDY OF FLOW-INDUCED MOTION CHARACTERISTICS OF THREE TANDEM CIRCULAR CYLINDERS IN PLANAR SHEAR FLOW

Flow-induced motions of three elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement at $Re =100$ were numerically investigated by using semi-implicit characteristics-based split (CBS) finite element algorithm. Firstly, the results are compared with the existing data in the literature to verify the accurateness of the method. Then, the influence of some key parameters, such as shear ratio ($k$), natural frequency ratio ($r$) and reduced velocity ($U_{\rm r}$) on the characteristics of flow-induced dynamic responses and flow field of three circular cylinders with tandem arrangement was analyzed. The numerical results show that the shear ratio, natural frequency ratio and reduced velocity play an important role in the amplitude and trajectory of motion. The change of maximum amplitude of the upstream cylinder is similar to that of an isolated cylinder case with the increasing of $k$. The maximum amplitudes of the midstream and downstream cylinders increase, and the dual resonance is observed. Meanwhile, the increasing of $k$ causes the extension of the resonance region. With the increasing of $r$, the lock-in region of the upstream cylinder reduces in the in-line direction. However, for the midstream and downstream ones, the dual-lock-in region broadens. On the other hand, the prominent $X-Y$ trajectories of three circular cylinder resemble figure-eight shape and irregular one in the uniform flow. With the change of $k$, the motion orbit transforms from figure-eight to the raindrop shape in the lock-in region. In the larger shear ratio and higher natural frequency ratio case, the dual-raindrop is observed in the $X-Y$ vibrating trajectory of the midstream cylinder. Finally, the flow-induced motion mechanism of three tandem circular cylinders exposed to planar shear flow is revealed according to the analysis of the characteristic of the flow field.

Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface

In the current investigation, the small and large amplitude free vibration characteristics of long cylindrical panels made of FGMs is investigated using the higher order shear deformation shell theory and Donnell kinematic assumptions. The interaction of the panel with a nonlinear hardening/softening foundation in also included into the formulation. The properties of the panel are assumed to be graded across the thickness of the panel and assumed to be temperature dependent. Using the neutral surface concept, the three coupled motion equations of the shell are established and solved for the case of long panels which are immovable simply supported on straight edges. The solution method is based on the two step perturbation technique which results in a closed form expression for the frequencies of the panel as a function of the mid-point deflection. Numerical studies are first validated for the case of long FGM plates. Afterwards novel numerical results are given to show the effect of geometrical parameters, power law index, foundation stiffnesses and temperature elevation. As shown, temperature elevation results in the reduction in natural frequencies and enhancement of the frequency ratio of the panel. Also temperature dependency reduces the natural frequencies and frequency ratios of the panel.

A general comparison the surface layer degree on the out-of-phase and in-phase vibration behavior of a skew double-layer magneto–electro–thermo-elastic nanoplate

The present study investigates and compares the value of the surface layers on the out-of-phase and in-phase vibration behavior of skew double-layer magneto–electro–thermo-elastic (DLMETE) nanoplates. These two nanoplates are coupled by an elastic medium named van der Waals forces; furthermore, the DLMETE nanoplates are surrounded by Winkler and the shear moduli of elastic foundations. The two nanoplates are moving in the same direction in the out-of-phase case; in contrast, in the in-phase mode, those two nanoplates are moving in the opposite direction. Manipulation of the refined plate, surface energy, and nonlocal hypotheses is done to expand the governing equations; furthermore, Hamilton’s principle is utilized to derive the equilibrium equations. Galerkin method is also employed to solve these equations. In addition, for the validation of those equations, the Navier’s method is used. The present research is, therefore, concerned with the effect of the main parameters, namely, external electric potential, external magnetic potential, in-plane mechanical force, elastic foundations, skew angle, and temperature change, on the rate of surface layers of the out-of-phase and in-phase vibration behavior of a skew DLMETE nanoplate. By increasing the skew angles, the in-phase and out-of-phase natural frequency ratios are shown to be converged; following a specific value of skew angle Ψ ≥ 70°, they overlap. By raising the skew angles, the effects of the van der Waals modulus on the vibration behavior are undermined. Therefore, the results of the present work could contribute to designing NEMS/MEMS components which make use of smart composite nanostructures.

Effect of Pendulum Parameters on Performance of Electromagnetic Energy Harvester

This paper presents an analysis of a vibration-based electromagnetic energy harvester with an attached pendulum. The pendulum is used to transform the horizontal harmonic motion of the complete system into the vertical motion of the magnetic oscillator. An electromechanical model of the coupled system is established for numerical simulation. Parametric studies are conducted subsequently on various pendulum mass and length configurations. The results indicate that the system with the natural frequency ratio of 1:2 has higher power outputs and wider frequency bandwidth as compared with other configurations. In the situation of natural frequency ratio of 1:2, higher power outputs can be achieved by an increase in the mass of the pendulum. The results demonstrate the feasibility of using the pendulum as a driver of vertical motion oscillator to harvest vibration energy from the horizontal excitation.

Analyses of fluid-solid coupling dynamics of elastic tubes vibrating in cross flows

Treatments on dynamic interfaces and fluid-solid coupling are critical in systems of tubes vibrating in fluids that are common in tube-strings of deep-water oil drilling systems, marine cluster wells and heat exchangers. This paper proposes a “weakly” coupled algorithm for modeling vortex induced vibrations of elastic tubes submerged in cross flows. In the present algorithm, the elastic tube is discretized with beam elements and the fluid is discretized with volume elements, and the grids for both the tube and fluid is perfectly marched on the interface. Using the shape functions of beam elements, the formula for displacement, velocity, and force approximations are carried out, and convergence criterion analyses are also performed for the fluid-solid coupling interfaces. The present weakly coupling algorithm is developed with a sub-iteration loop to ensure accuracy in handling the dynamic coupling between the elastic tube and fluid. The vortex-induced vibrating characteristics are then analyzed for various elastic tubes at different natural frequencies. Intensive numerical studies are also conducted to examine the effects of the ratio of the elastic tube's natural frequency to the static flow's frequency. It is found that the change of frequency ratio has less effect on the fluid pressure and velocity distributions on the surface of the elastic tube, but more effects on the vibration of the tube. When the frequency ratio is less than 1.009, the vibrating amplitude, period and trajectory of elastic tube decrease with the increase of frequency ratio. While if the frequency ratio is more than 1.009, the vibrating amplitude, period and trajectory are almost unchanged and the elastic tube behaves similarly to a rigid tube. It is also found that there is a critical frequency ratio for a vortex-induced vibration to occur for tubes in cross flows. This finding is important for the prevention of violent vibrations of tubular structures in flows, such as deep-water oil drilling tube-strings, marine cluster wells and heat exchangers.

A Study on Natural Vibration Characteristics of Dome Structure According to Natural Frequency Ratio of Substructure

A Study on Natural Vibration Characteristics of Dome Structure According to Natural Frequency Ratio of Substructure

An oscillator-rotator system: Vibrational maintenance of rotation, stationary synchronous regimes, stability, vibration mitigation

The steady-state dynamics of an oscillator-rotator system excited by a vibrating base is studied with account of reciprocal influence of the rotation on the oscillations. This problem, associated with many engineering applications, in previous works was considered either within framework of 1DoF model neglecting the feedback effect of the rotator on the main body oscillation or by means of rather complicated asymptotic procedures. The proposed straightforward analytical procedure, which sequentially separates the averaged regime and deviations from it without assumption of smallness of inertia forces in the rotator, has been proved to be very exact and efficient. It allows already in the first approximation to reveal previously unnoticed peculiar features of the synchronous stationary regimes. In the second approximation the analytical solution, based on the Fourier series, without introducing small parameters and corresponding asymptotic procedures, results in the approximate analytical description of non-uniform rotation, which is excellently confirmed by the numerical simulation. It has been shown that the synchronous regimes with rotational response of the pendulum may become unstable due to parametric resonances for fluctuations of the angular velocity. These resonances are not associated with a certain ratio of natural frequencies for pendulum swinging and the body oscillation, and can be generated by two different sources. The domain of existence and stability of the stationary synchronous regimes in the parameter space has been determined. As an example of practical application of the analysis, the problem of mitigation of the forced harmonic oscillations by the rotator is considered and some recommendations are given.