Experimental and numerical studies on partial similitude of rotor system considering the vibration consistency

Zhang X., Luo Z., He F., Yu B.

A similarity method for rotating composite blades in thermal environment is developed for the problems of difficulty, time consumption, high cost, and risk in the dynamic test under a high-temperature environment. Within this study, a set of scaling laws are derived for thin-walled composite plates based on their dynamic models and the applicability of the scaling laws is demonstrated in the similitude design of composite blades. The present dynamic model takes into account thermal stress and centrifugal stiffening effect. Analytical calculations show that the scaled models at relatively low temperatures can well reproduce the dynamic characteristics of their corresponding prototypes at high temperatures when taking into account the scaling of temperature change and rotational speed. • Thermal stress and centrifugal stiffening effect are considered in the dynamic model. • The scaling laws for temperature change, rotational speed, natural frequency, and acceleration response are deduced. • Models at low temperatures are used to predict prototypes in high-temperature operating environments. • The scaling laws for thin-walled composite plates are applicable to the prediction of composite blades.

Liu P., Wang X., Wang Y., Mao F.

Complete similitude and distorted similitude are widely used in the experimental verification of large equipment structures. However, the existing similitude studies have only a single distorted factor and insufficient prediction accuracy. And the coupled shells cannot be scaled down for experimental verification due to the limitation of wall thickness. Aiming at solving the above problems, a new method of distorted similitude for coupling scaling laws is proposed. The coupling distorted scaling laws and the complete scaling laws of coupled cylindrical–conical shells are established to study the bending mode natural frequency. The predictive performance of different distorted factors on prototype characteristics is investigated. The simulation results show that the prediction errors of the coupling distorted scaling laws established by this method for the prototype natural frequency are less than 0.32%. Experimental results show the proposed method can predict the bending mode natural frequency of the prototype, and its error is within ± 1 % . The method proposed in this paper has less simulation calculation and high precision, and can be extended to more complex thin-walled structures. • A new method for establishing the coupling scaling laws is proposed. • The coupling distorted scaling laws and the complete scaling laws of coupled cylindrical–conical shells are established for the first time. • The proposed method has very high prediction accuracy and less simulation calculation, compared with the existing method. • The predicted performance of different distorted factors is studied for the first time.

Zhang J., Davey K., Darvizeh R., Sadeghi H.

The use of scaled experiments and physical models to investigate the complex responses of large-scale structures under high-rate loading is well-established. The approach however is recognised to suffer from deficiencies when substitute materials are involved as sought material-property combinations are not always available in readily accessible materials. This practical issue is one of scale effects where the behaviour of a scaled-physical model can depart sometimes markedly from the full-scale response. This was certainly the situation prior to the recent arrival of a new scaling theory called finite similitude with the establishment of new similitude rules but at the cost of additional scaled experiments at different scales. This paper examines the benefits of two scaled experiments in physical modelling to examine whether the existing problems posed by the paucity of material behaviours can be remedied by combining the results of two experimental trials at different scales. The focus here is on pressure-vessel response when exposed to projectiles and blast loading to provide non-trivial behaviours that are typically not easily captured with a single scaled experiment. The investigation is performed with the aid of a commercial finite element analysis software and the Conwep blast-loading analysis to reveal that the flexibility provided by two scaled models is significant. Although perfect replication of full-scale behaviour is not always achievable the ability to design scaled experiments with combinations of standard materials is shown to provide good levels of accuracy. • A new two-experiment approach to physical modelling. • A procedure for material selection founded on a standard impact test. • A demonstration of how two scaled experiments can capture high-rate responses. • Failure analysis for pressure vessels made of dissimilar materials and loaded at rate.

Davey K., Sadeghi H., Adams C., Darvizeh R.

• Two new forms of the finite similitude scaling theory for vibration analysis. • A new high-order anisotropic space scaling approach is trialed. • The two-experiment anisotropic theory can replicate full-scale responses. • The new scaling theories can account for plate thickness change with scale. • Perfect replication for hollow sections with thickness change is shown possible. • The breaking of geometric similarity locally and globally is shown possible. A calculus for scaled experimentation has recently appeared in the open literature founded on the continuous (metaphysical) concept of space scaling . The new theory for isotropic scaling (termed finite similitude ) is a single-parameter theory that provides similitude rules that link unlimited numbers of scaled experiments to predict the behavior of any full-scale system. A facet of the theory is that it relates scalar, vectorial and tensorial coefficients and is therefore indirectly influenced by the choice of inertial-coordinate frames characterizing the full and scaled experiments. This feature is explored in this paper to relate objects that are skewed with a particular focus on thin-walled vibrating structures, which find widespread industrial usage but also benefit from anisotropic scaling in their thickness direction. The focus here is on the recently developed first-order finite similitude theory involving two scaled-down experiments for scaled vibrational analysis. The efficacy of the proposed scaling method is examined by means of analytical and numerical simulations. Case studies involving thin-walled plates and hollow beams, subject to free and forced vibration, confirm that titanium prototypes can be represented with high accuracy (∼0% error) by scaled models of identical and different materials (viz., steel and aluminum).

Zhao R., Jiao Y., Qu X.

• The proposed scaling strategy ensures dynamic similarity by optimizing structural parameters of rotor systems . • The distance between disk and bearing has significant influence on the first-order critical speed in optimization process. • Increasing the weighing coefficient of a certain order of critical speed effectively reduces the deviation in optimization. • The optimized GDSM rotor predicts the prototype more accurately than the SSM rotor. • Such scaling strategy practically guides the design and manufacturing of experimental rotor systems. It is difficult to perform practical experiments on working gas turbine rotors due to the factors of safety and implementability etc. Therefore, it is of great importance to design a well-scaled test rig that can accurately predict the dynamic characteristics of a prototype rotor. In this paper, a design method for scaled rotor systems considering dynamic similarity and restricted support stiffness is proposed. The structural similarity coefficients of the strictly scaled model (SSM) in a rotor system are obtained based on the similarity theory and scaling law. Key optimization parameters and ranges are determined through sensitivity analysis. By genetic algorithm, the geometrically distorted scaled model (GDSM) in rotor system with dynamic similarity is established to modify the SSM rotor. Moreover, modal experiments are carried out to verify the validity of the proposed scaling design method. Results show that the type, number and accuracy of optimized parameters are important in optimization design. The critical speed of the first three orders of the GDSM rotor are very close to ones in the prototype, and the maximum percentage deviation is 1.18%. Experimental results show that the rotor developed by the geometrically distorted scaling method is able to reflect the dynamic properties of prototype accurately despite the slightly distorted partial structural parameters. Such proposed design method can provide a highlight in the design and manufacturing of the key components of gas turbine rotors for laboratory.

Zhang C., Wei J., Peng B., Cao M., Hou S., Lim T.C.

• The dynamic similarity relationship of gear transmission system is derived. • The similarity ratio of peak-to-peak value of vibration response is proposed. • Two modification methods of machining error distortion are proposed. • The modification methods are verified by numerical analysis and experiments. Accurate setting of the gear machining error to a certain expected value is a difficult task. A non-ideal value may cause the system to not meet the complete similarity condition and reduce the prediction accuracy of the scale model (SM). In this study, the similarity relationship of a gear transmission system, considering the machining error, was derived using the equation analysis method. To address the problem of machining error distortion, a similarity ratio of the peak-to-peak value of the vibration response, and two modification methods for SM prediction are proposed herein. In the first method, the load is modified, whereas in the second method, the similarity ratio is modified. A node finite-element model and transmission error experiment were used to verify the accuracy of the two methods. The results indicate that the prediction of the changing trend and amplitude of the vibration response was accurate. The modified load method should be used in the design stage for the working conditions, and the modified similarity ratio method should be used in the experimental data processing stage. Graphical Abstract .

Dewi D.K., Abidin Z., Budiwantoro B., Malta J.

This paper deals with scale-fullscale models of rotor-bearing systems on rotating condition. The investigation is focused on the gyroscopic effect, which causes forward and backward whirl frequencies. When the rotor-bearing system is scaled proportionally in its dimension (height, length, and width), the scaling factor of whirl frequencies can be derived. It depends on the ratio between a transverse and polar moment of inertia on its rotating axis called the gyroscopic factor. The experimental study is conducted to validate it on three scaled rotor-bearing systems, which shifts its disc from the middle of the shaft on the scale of 1:1, 2:1, and 3:1 to clearly show the gyroscopic effect on first bending natural frequency. The scaling factor is then validated using the Campbell diagram by finding its critical speed. From this critical speed, the whirl frequencies along the range of the full-scale model speed can be obtained. The result also shows that the scaling factor remains the same whether it is at rotation or rest condition. Consideration must be made on the effect of the structural design, that is, blade and support, because of its unsymmetric stiffness that can cause backward whirl frequencies. The bearing stiffness must be ensured to be scaled proportionally, especially on journal bearing cases. This finding can be used by engineers to deal with scaling method implementation on rotating machinery design.

Zhou L.

• The similitude of free vibration of functionally graded material cylinders under thermal environment is studied for the first time. • A novel similitude method named energy similitude correction method is proposed. • The similitude distortion problem caused by FGM and thermal environment is solved. • The distorted similitude relationship of FGM cylinders under thermal environment is established. • Through numerical verification, the method proposed reaches high accuracy. In order to obtain the thermal modal characteristics of FGM (Functionally graded material) cylinders, scaled model test is an efficient experimental approach, and its theoretical core is to establish the similitude relationship. However, under the influence of non-scalability of FGM and thermal environment, the traditional similitude method will lead to serious dynamic distortion. In this article, the similitude of free vibration of FGM cylinders under thermal environment is studied for the first time, and a novel similitude method is proposed to solve the complex similitude distortion problem. Firstly, the similitude distortion problem caused by FGM and thermal environment is analyzed in details. Secondly, the mechanical analyses of FGM cylinders are carried out. Then, a novel similitude method named energy similitude correction method is proposed, and the distorted similitude relationship of FGM cylinders under thermal environment is derived. Finally, this method is verified through various numerical examples. The results show that, for FGM cylinders under thermal environment, the proposed method can solve the similitude distortion and establish the distorted similitude relationship with high accuracy. Moreover, the method can be applied to various FGM cylinders with different thicknesses, gradient coefficients and temperature conditions.

Wang S., Xu F., Zhang X., Dai Z., Liu X., Bai C.

• The directional framework of similarity laws for structural impact is proposed, especially for geometric distortion . • Spatial directions and structural geometric characteristics are explicitly expressed in dimensionless numbers . • Correction methods of the velocity, the density and the geometry are used to address various distortion problems at scaling. • Various dimensionless response equations can be clearly, concisely and perfectly expressed. • Refined scaling analyses under the proposed framework are given numerically. A directional framework of similarity laws, termed oriented-density-length-velocity (ODLV) system, is suggested for the geometrically distorted structures subjected to impact loads. The distinct feature of the framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for all basic physical quantities are explicitly expressed by three characteristic lengths of spatial directions, which overcomes the inherent defects only with one scalar length in the traditional dimensional analysis. Meanwhile, similarity laws of the directional stresses, strains and displacements are expressed by different power law relationships of the ratios of undistorted characteristic lengths to distorted characteristic lengths. Therefore, the ability of similarity theory to express structural geometric characteristics are effectively developed. Based on the newly proposed framework, the non-scalabilities of geometric and material distortion (including strain hardening and strain rate effects) and the gravity effects could be compensated by correction methods of velocity, density and geometry. The analytical models of beams subjected to impact mass and impulsive velocity are verified. The results show that the proposed framework has excellent performance for expressing various dimensionless response equations and geometrically distorted scaling. A numerical model of circular plate subjected to dynamic pressure pulse is further carried out to verify the geometrically distorted scaling of the directional components of displacement, strain and stress. The refined analysis results show that, structural dimensionless responses in different directions can behave good consistency between the scaled model and the prototype in both the spatial and the temporal fields, with the correction of the directional physical quantities using different powers of the ratios of characteristic lengths.

Li L., Luo Z., He F., Sun K., Yan X.

• This paper proposes a method to obtain scaling laws for rotor systems. • The power in scaling laws is represented by a function related to scaling factor. • The proposed method can predict the dynamic characteristic in partial similitude. • Testing for both prototype and model is carried out to verify the proposed method. • The proposed method can improve prediction accuracy compared with existing methods. Similitude theory is widely used to predict the structural responses of the full-size prototype through scaled models and is categorized into complete and partial similitude according to the way of scaling parameters. Partial similitude is more flexible in practical design engineering, but its accuracy still needs to be improved. This study presents an improved partial similitude approach, which can be used to establish the scaling laws and understand the scaling behaviors of rotor systems. The aim is to overcome the insufficient accuracy of the existing methods in predicting the dynamic characteristic of rotor systems. The power in scaling laws is represented by a function, which is related to the scaling factor of the prototype to be predicted. In this work, the power function is developed by incorporating the Levenberg–Marquardt method and sensitivity analysis. The accuracy and effectiveness of the proposed partial similitude method are validated through numerical and experimental case studies, where the distortion in geometrical dimension is considered. The dynamic characteristic of prototypes is predicted through the scaled model. Furthermore, the accuracy of the proposed method is evaluated by using the existing methods. Both the numerical and experimental case studies indicate that the proposed method achieves higher accuracy than the existing methods in predicting the dynamic characteristic of rotor systems.

Ochoa-Cabrero R., Alonso-Rasgado T., Davey K.

Abstract A new approach to scaled experimentation has recently appeared in the open literature where hitherto unknown similitude rules have been discovered. The impact of this discovery on biomechanics is the focus of this paper, where rules for one and two scaled experiments are assessed. Biomechanical experimentation is beset by problems that can hinder its successful implementation. Availability of resources, repeatability and variability of specimens, ethical compliance and cost are the most prominent. Physical modeling involving synthetic composite materials can be used to advantage and circumvent ethical concerns but is presently impeded by cost and the limited scope of standardized geometries. The increased flexibility of the new approach, combined with the application of substantially cheaper three-dimensional printed materials, is investigated here for bone biomechanical experiments consisting of mechanical tests for the validation of finite element models by means of digital image correlation. The microstructure of the scaled materials is analyzed using a laser confocal microscope followed by the construction and validation of numerical models by means of a Bland–Altman statistical analysis. Good agreement is obtained demonstrated with means under 18 microstrains (μϵ) and limits of agreement below 83 μϵ. Consequently, numerical results for the new similitude approach shows an average percentage error of 3.1% and 4.8% for the optimized results across all values. The two-scaled experiment approach results in a sevenfold improvement for the average difference values of strain when compared to the single-scaled experiment, so demonstrating the potential of the new approach.

Adams C., Bös J., Melz T.

Engineers often use similitude analyses to design small scale models for experimental tests or to design size ranges of mechanical structures such as drive technology systems. This paper is concerned with similitude analysis methods for vibration analyses of rectangular plates. If their geometry is scaled by different factors (distorted similitude), the scaling laws approximate the actual vibration responses with a certain accuracy only. This paper introduces a performance measure that reliably assesses how well the scaling laws approximate the actual vibration responses of rectangular plates. This measure, the so-called Mahalanobis distance, applies in a-posteriori analyses, where the vibration responses obtained from the scaling laws are compared to the actual ones. Numerical and experimental investigations on vibrating rectangular plates validate that the Mahalanobis distance is suitable to assess the performance of similitude analyses. The Mahalanobis distance can be linked to the geometrical properties of the rectangular plates in order to define a maximum permissible distortion of the geometry. Scaling laws approximate the vibration responses of the rectangular plates sufficiently well up to this maximum permissible distortion. Furthermore, the performance of two different state-of-the-art similitude analysis methods is compared. Both similitude analysis methods are found to perform well up to the maximum permissible amount of geometrical distortion. • Similitude analysis is applied to plates with geometrical distortion. • A performance measure for similitude methods is defined. • The performance measure is validated in numerical and experimental investigations. • Permissible limits for the geometrical distortion are determined.

Lu S., Wang P., Ni W., Yan K., Zhao S., Yang C., Xu P.

To improve the passive safety protection of crash energy management (CEM) passenger train, this paper presents the energy absorption design study for CEM passenger trains based on a 1/8th-scale model. By analysing the similarity of thin-walled structures for CEM trains, the similitude ratios of physical parameters were obtained and used to design the scaled train model. The dynamic responses of scaled train were analysed through finite element simulation and collision test. Compared to the test results, the errors of dynamic responses in simulation were within 1.79%, indicating that the finite element model of scaled train was accurate and can be used to study the energy absorption characteristics of CEM passenger trains. To improve the crashworthiness of CEM passenger trains, selecting six key parameters affecting energy absorption of head car and middle car as design variables, and taking the maximum energy absorption of head car and the minimum standard deviation of energy absorption for middle cars as targets, a multi-objective optimization was carried out to gain the optimal solution of key energy absorption parameters. Optimization results indicated that the energy absorption of head car has been increased by 195.20%, and the standard deviation of the energy absorption of middle cars has been decreased by 81.06%.

Li Y., Luo Z., Liu J., Ma H., Yang D.

• A unified approach for modeling of the rotor with a bolted-disk joint is proposed. • Effect of tangential stiffness and transition point of bending stiffness are evaluated. • The dynamic model of the bolted-disk joint is presented with two-nodes. • Nonlinear properties of the rotor-bearing system with bolted-disk joint are investigated. • Present work provided a method to detect the change of bolted-joint performance. In large rotating machines, the rotor system involves multistage disks, where bolted joints are the basic form to connect the adjacent disks. Those bolted joints, subjected to unbalanced forces and moments during normal operation, influencing the rotor dynamics and giving rise to different motion states, which are of interest for investigations focusing on vibration signatures and dynamic stability. However, little research has been done on the rotor vibration characteristics considering dynamic parameters of bolted-disk joints. Thus, the bolted-disk joint element with two nodes is proposed by characterizing the mechanical relationship between the adjacent disks in this paper. Then, in terms of the proposed joint element and lumped mass modeling method, the dynamic model for the rotor system with a bolted-disk joint is established. After that, the responses of the system are solved numerically using the Newmark-β method, and bifurcation diagram, three-dimensional spectral plots, Poincare maps as well as spectral plots are used to analyze the dynamic behaviors under different tangential stiffness and transition point of bending stiffness of the bolted joint. Additionally, the influences of the bending stiffness of bolted-disk joint on system response are also examined. Finally, utilizing the rotor dynamic responses experiment performed at a bolted-joint rotor-bearing test rig with an electric tightening wrench, some of the results from the simulation study are verified. The present work provides a theoretical basis for detecting the performance of the bolted joint of the rotor-bearing system, and prevent failure caused by changes in the stiffness of the bolted joint.

Adetoro O.B., Cardoso R.P.

• A unified scaling model for the exact dynamic similitude of solid continuum. • New set of dimensionless scaling number for scaling dynamic solid structures. • Geometrical and temporal scaling of dynamical systems using different materials. • The proposed model is demonstrated using different and complex dynamical problems. Dynamic similitude has proven to be a valuable tool, which is widely adopted in fluid mechanics. However, even with the ever-growing interest in dynamic similitude in solid mechanics, there is still no unified scaling law applicable to any given solid structure or system, and this has prevented the broad adoption of similitude in the field. Here we develop a unified similitude model for solid mechanics using the momentum and the energy conservation. The model allows for the use of different materials in both elastic and plastic regimes. Never reported dimensionless numbers are derived for the first time in this article, and this set of numbers is sufficient for strictly accurate dynamic similitude of any solid structure. Very different case studies are considered, and the perfect agreement seen in compared results confirms the accuracy of the developed scaling model. The exactness of the dimensionless numbers is also confirmed through analytical solutions. The model allows for the scaling of strain rate and, for the first time, the scaling of the strain state between the full-scale structure and its scaled replica.

Yao X., Huang R., Zhao K., Yin Y.

Xiong Q., Zhang P., Liu C., Li M., Liu X., Ma H.

Zhou J., Luo Z., Li L., Tang R., Ma T., Yang D.

Zhang H., Sun W., Zhang Y., Ma H., Luo H., Liu F., Xu K.

Wang L., Yin Y., Qi L., Qu C., Yu Y., Liu B., Xia X.

Ji W., Yu Z., Ma H., Sun W., Yang T.

Zhou J., Luo Z., Li L., Ma T., Li H.

Luo Z., Sun X., Yu B., Zhang C.

Thin-walled carbon fiber tubes can be used as support structures for satellite antennas but low-energy impacts may produce invisible damage. In this paper, a finite element model (FEM) of thin-walled carbon fiber tube is proposed for predicting low-energy transverse impact damage. Impact damage sensitivity studies have also been carried out. Low-energy transverse impact damage experiments at energies of 2 J, 4 J, 6 J, 8 J and 10 J were performed to validate the FEM. The maximum error of peak load between experimental and FEM is 7.8%. Both experiments and finite element modelling show that the peak load and damage time increase with increasing impact energy, and that the energy absorbed by the tube also increases. The direction of cracking from impact is similar to the direction of the outermost lamination. For the modulus of elasticity and the outermost layup angle, the layup angle has the greatest degree of damage sensitivity, with a dimensionless damage sensitivity parameter of 4.72.

Sun Y., Zhang G., Lee H.P., Zheng H., Luo Z., Li F.

To enhance the low-frequency sound insulation performance of conventional double panels, this work proposes a truss-based X-shape inertial amplification (TXIA) metamaterial double panel. A semi-analytical method is developed for computing the sound transmission loss (STL) of the TXIA metamaterial double panel, with numerical and experimental validations confirming the convergence and accuracy of this method. To further investigate the low-frequency acoustic wave attenuation of the proposed structure, four configurations are analyzed and discussed. Numerical results indicate that, compared to conventional and equivalent mass double panels, the TXIA metamaterial double panel effectively shifts the STL peaks to lower frequencies, exhibiting higher STL amplitudes and a reduced low-STL region. Configurations incorporating different springs enhance the STL performance without altering mass or other parameters. The STL dips of the metamaterial double panel coincide with odd-odd modes of the double panel, which have higher radiation efficiencies. Parametric studies reveal that changes in the IA angle shift the dips induced by in-phase modes to lower frequencies, while increased stiffness shifts these in-phase dips to higher frequencies. The depth of the cavity between the two panels only affects the first-order anti-phase dip. Additionally, increased stiffness enhances the STL performance and introduces a new peak in the stiffness-controlled region. Due to its flexibility, the TXIA metamaterial double panel holds significant potential for industrial applications.

Chen R., Lv J., Tian J., Ai Y., Zhang F., Yao Y.

There is a complex dynamic interaction between the aero-engine bearing and the rotor, and the resulting time-varying system parameters have an impact on the nonlinear dynamic characteristics of the rolling bearing-flexible rotor system. In this study, the interaction between the time-varying stiffness of the rolling bearing and the transient response of the flexible rotor is considered. The Newmark-β integral method is used to solve the dynamic equation, and the relationship between the time-varying characteristics of bearing stiffness and load and the dynamic characteristics of the rotor is studied. The relationship between bearing stiffness and vibration strength is analyzed, and the influence of damage size on the time domain signal energy of the disc is analyzed. The results show that the model established in this paper can accurately reflect the dynamic interaction between the bearing and the rotor. With the extension of the bearing damage, the dynamic stiffness of the bearing attenuates, the intensity of the excitation force increases, and the vibration is transmitted to the disc, which affects the motion stability and vibration response of the disc.

Luo Z., Liang B., Sun K., Li L., Hao H., Wu X.

Elastic ring squeeze film damper (ERSFD) has been extensively utilized in aero-engines due to its superior ability to suppress vibrations. However, during the operation of aero-engines, misalignment faults can occur owing to manufacturing and installation inaccuracies, rotor flexibility, thermal instability, and other factors. There is currently no research on the dynamic characteristics of ERSFD-rotor systems affected by coupling angular misalignment. This paper establishes the mathematical model of the ERSFD-rotor system with coupling angular misalignment using the lumped mass method and analyzes the misalignment's impact on the system. Additionally, the study explores the impact of the elastic ring's structural parameters on the nonlinear vibration of the ERSFD-rotor system with coupling angular misalignment. Ultimately, the model's accuracy and the reliability of certain simulation results are confirmed through experiments conducted on the ERSFD rotor test bench.

Dou J., Yao H., Li H., Wu Y., Yang J.

In response to the issue of broadband torsional vibrations generated by high power density powertrain systems, a multi-stable nonlinear energy sink (MSNES) is proposed. The basic principles and structure of the MSNES are introduced. The installation position of the MSNES is determined by studying the results of sensitivity analysis and the vibration mode, thereby establishing the dynamic model of the powertrain-MSNES system. The response surface optimization method is employed to ascertain the optimal parameter combination for the MSNES. Furthermore, the vibration suppression performance of the MSNES is compared to that of the traditional linear dynamic vibration absorber (LDVA). For the feasibility of the experiment, a scale model of the powertrain system is established. The reliability of the scaled model and the effectiveness of the MSNES on the scaled model are verified. Finally, experimental verification is conducted. The results indicate that the MSNES can efficiently diminish multi-modal transient vibrations across a wide frequency band by employing resonance capture cascade (RCC). Furthermore, multiple strongly modulated response (SMR) regions are presented, effectively mitigating steady-state vibrations. The displacement attenuation speed in transient responses can reach 89.66 %. Meanwhile, the MSNES demonstrates impressive vibration suppression rates, reaching 81.22 % in simulations and 74 % in experiments for steady-state responses.

Liu P., Yang D., Wang X., Zhang X., Wang Y.

Du Y., Fan G., Zhang Y., Wang D.

Adopting traditional similitude theory to analyze the similarity characteristics of large-scale concentrator unit in space solar power station, the thickness distortion problem exists in the scaled model, leading to the failure of the complete similarity criterion established by similarity analysis. Taking SSPS-OMEGA concept as an example, this paper proposed a strategy named the separated part similarity method based on the dimensional analysis to address the above problem. Firstly, the preliminary similarity criteria are obtained without considering distortion based on dimensional analysis. Secondly, the scaled model is established considering thickness distortion through two sub-models: complete similarity and partial similarity. Then the natural frequency prediction equation is established considering the thickness distortion of large-scale concentrator unit. Finally, the finite element models of protype and scale model are established to verify the method proposed in this paper. Results indicate the natural frequency predicted value of the large-scale prototype by this method is 28.34 Hz, and the theoretical value is 28.32 Hz. The error of the first four order natural frequencies between the predicted value and the theoretical value of the prototype is kept within 0.4%.

Du Y., Fan G., Chen G., Zhang Y., Wang D., Li X.

The distortion model may arise due to the inability to isometrically scale the thickness dimensions when utilizing similitude theory to develop scaling laws for large-scale concentrator units in the Space Solar Power Satellite. Previous works to address the distortion model neglect its negative impacts and persistent limits, resulting in insufficient prediction accuracy for prototype. To obtain scaling laws of the distortion model, this paper introduces a novel strategy called the performance-dominated separate similitude analysis, which significantly reduces the distortion model's negative impacts and persistent limits on similitude prediction. Firstly, performance parameters sensitive to the distortion model are generated by dimensional analysis and the governing equation method. Secondly, the distortion model is separated into two scaled models: complete and partial similitude, based on the sensitive performance parameters. Subsequently, the scaling laws of complete and partial similitude models are derived, respectively. Finally, the scaling laws of the distortion model are derived by combining the complete and partial similitude laws. The proposed method is validated through finite element model simulation for both the concentrator unit prototype and the distortion model. Results indicate that in the best case, the prediction error doesn't exceed 0.2%, and the prediction accuracy can be improved by up to 87.34% compared to the existing methods.