Practice on Gravity-1 Rocket Dynamic Characteristics Design

Since the Dongfeng-2 missile, full-vehicle modal testing has been established as an indispensable part of the development and testing of rocket and missile models. However, as rockets have been developed larger, the cost and duration of such tests have significantly increased, magnifying their impact on model development. This article follows the process of the modal testing practice of the Gravity-1 rocket, reviewing and summarizing the design process of the rocket's dynamic characteristics. Initially, the article introduces common modeling techniques for launch rockets, including the mass-beam model and the hybrid element model. It then discusses the relationship between the structural dynamics model of the launch rocket and modal testing, aiming to reduce testing costs through refined structural dynamics modeling methods. Subsequently, the article describes the dynamic characteristics design process of the Gravity-1 carrier rocket, categorizes structural parameters, and studies how the selection of structural parameters affects the predicted dynamic characteristics of the rocket. Finally, it elaborates on the design of the modal testing scheme and the dynamic characteristics design based on the test data.

Modal Strain Energy Based Structural Damage Localization for Offshore Platform using Simulated and Measured Data

Modal strain energy based methods for damage detection have received much attention. However, most of published articles use numerical methods and some studies conduct modal tests with simple 1D or 2D structures to verify the damage detection algorithms. Only a few studies utilize modal testing data from 3D frame structures. Few studies conduct performance comparisons between two different modal strain energy based methods. The objective of this paper is to investigate and compare the effectiveness of a traditional modal strain energy method(Stubbs index) and a recently developed modal strain energy decomposition(MSED) method for damage localization, for such a purpose both simulated and measured data from an offshore platform model being used. Particularly, the mode shapes used in the damage localization are identified and synthesized from only two measurements of one damage scenario because of the limited number of sensors. The two methods were first briefly reviewed. Next, using a 3D offshore platform model, the damage detection algorithms were implemented with different levels of damage severities for both single damage and multiple damage cases. Finally, a physical model of an offshore steel platform was constructed for modal testing and for validating the applicability. Results indicate that the MSED method outperforms the Stubbs index method for structural damage detection.

Influence of Trailing-Edge Wear on the Vibrational Behavior of Wind Turbine Blades

To study the impact of the trailing-edge wear on the vibrational behavior of wind-turbine blades,unworn blades and trailing-edge worn blades have been assessed through relevant modal tests.According to these experiments,the natural frequencies of trailing-edge worn blades-1,-2,and-3 increase the most in the second to fourth order,thefifth order increases in the middle,and thefirst order increases the least.The damping ratio data indi-cate that,in general,thefirstfive-order damping ratios of trailing-edge worn blades-1 and trailing-edge worn blades-2 are reduced,and thefirstfive-order damping ratios of trailing-edge worn blades-3 are slightly improved.The mode shape diagram shows that the trailing-edge worn blades-1 and-2 have a large swing in the tip and the blade,whereas the second-and third-order vibration shapes of the trailing edge-worn blade-3 tend to be improved.Overall,all these results reveal that the blade’s mass and the wear area are the main fac-tors affecting the vibration characteristics of wind turbine blades.

Dynamic analysis and modal test of long-span cable-stayed bridge based on ambient excitation

To study the stiffness distribution of girder and the method to identify modal parameters of cable-stayed bridge, a simplified dynamical finite element method model named three beams model was established for the girder with double ribs. Based on the simplified model four stiffness formulae were deduced according to Hamilton principle. These formulae reflect well the contribution of the flexural, shearing, free torsion and restricted torsion deformation, respectively. An identification method about modal parameters was put forward by combining method of peak value and power spectral density according to modal test under ambient excitation. The dynamic finite element method analysis and modal test were carried out in a long-span concrete cable-stayed bridge. The results show that the errors of frequencies between theoretical analysis and test results are less than 10% mostly, and the most important modal parameters for cable-stayed bridge are determined to be the longitudinal floating mode, the first vertical flexural mode and the first torsional mode, which demonstrate that the method of stiffness distribution for three beams model is accurate and method to identify modal parameters is effective under ambient excitation modal test.

Effect of Tire Repeated Root Modal on Tire Modelling with Experimental Modal

The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial tire,a multiple reference frequency domain method based on a least squares（LMS PolyMAX）algorithm is used to identify modal parameters.Then,modal stability diagram（MSD）,modal indication function（MIF）and modal assurance criteria（Auto-MAC）matrix are utilized to induce multiple inputs multiple outputs（MIMO）frequency response function（FRF）matrixes.The tests reveal that notable repeated roots exist in both radial and tangential response modes.Their modal frequencies and damping factors are approximately the same,the amplitudes of modal vectors are in the same order of magnitude,and the mode shapes are orthogonal.Based on the works mentioned,the method of trigonometric series modal shapes fitting is adopted,the effects of RRM model on tire modeling with a vertical experimental modal are discussed.The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire’s different exciting points during tire modeling,and since considering the RRM,the tire mode shapes can be unified and fixed during tire modeling.

DAMAGE DETECTION IN BUILDINGS USING A TWO-STAGE SENSITIVITY-BASED METHOD FROM MODAL TEST DATA

Many multi-story or highrise buildings consisting of a number of identical stories are usually considered as periodic spring-mass systems. The general expressions of natural frequencies, mode shapes, slopes and curvatures of mode shapes of the periodic spring-mass system by utilizing the periodic structure theory are derived in this paper. The sensitivities of these mode parameters with respect to structural damages, which do not depend on the physical parameters of the original structures, are obtained. Based on the sensitivity analysis of these mode parameters, a two-stage method is proposed to localize and quantify damages of multi-story or highrise buildings. The slopes and curvatures of mode shapes, which are highly sensitive to local damages, are used to localize the damages. Subsequently, the limited measured natural frequencies, which have a better accuracy than the other mode parameters, are used to quantify the extent of damages within the potential damaged locations. The experimental results of a 3-story experimental building demonstrate that the single or multiple damages of buildings, either slight or severe, can be correctly localized by using only the slope or curvature of mode shape in one of the lower modes, in which the change of natural frequency is the largest, and can be accurately quantified by the limited measured natural frequencies with noise pollution.

Research on Modal Test Technology of LM-6A Solid-Liquid Strap-On Launch Vehicle

The LM-6 A new generation solid-liquid strap-on launch vehicle has the structural dynamic characteristics of lower frequencies,denser modes and coupling modes in longitudinal,bending and torsion modal space.During the development phase of LM-6 A,modal tests of partial stacks and the full vehicle were designed to obtain the structural dynamic properties.The structural dynamic models using the finite element method(FEM)have been verified and calibrated based on the modal test data.This paper describes the pre-test predictions and test execution,and details the comparison between the pre-test predictions and the test data.The successful maiden flight of LM-6 A further confirmed the effectiveness of structural dynamic modeling and modal test for LM-6 A.

一级入轨大型液体捆绑火箭全箭模态特性研究

Structural vibration modes of large clustered liquid launch vehicles are important criteria for attitude stability design,POGO stability design and structural dynamic load calculation.As the first large one-stage-to-orbit clustered liquid launch vehicle of China,LM-5B has unique structural modal properties which are different from other launch vehicles at home and abroad because of its special structural scheme.Hence,it was necessary to study the structural modal properties for LM-5B.In this paper,ground modal tests for the whole vehicle were conducted to verify and modify the finite-element model of LM-5B,then the structural modal properties were obtained via simulation during flight time,providing significant input for the development of the vehicle.

SYSTEM IDENTIFICATION OF ADAPTIVE TRUSS STRUCTURES USING PIEZOELECTRIC ACTIVE MEMBERS

Adaptive truss structures are a new kind of structures with integrated active members,whose dynamic characteristies can be beneficially modified to meet mission requirements.Active members containing actuating and sensing units are the major components of adaptive truss structures.Modeling of adaptive truss structures is a key step to analyze the structural dynamic characteristics.A new experimental modal analysis approach,in which active members are used as excitatiDn sources for modal test,has been proposed in this paper.The excitation forces generated by the active members, which are different from the excitation forces exerted on structures in the conventional modal test,are internal forces for the truss structures.The relation between internal excitation forces and external forces is revealed such that the traditional identification method can be adopted to obtain modal parameters of adaptive structures.Placement problem of the active member in adaptive truss structures is also discussed in this work. Modal test and analysis are conducted with a planar adaptive truss structure by using piezoelectric active members in order to verify the feasibility and effectiveness of the proposed method.

Modeling and Measurement of a Tunable Acoustoelastic System

Acoustoelastic coupling occurs when a hollow structure’s in-vacuo mode aligns with an acoustic mode of the internal cavity.The impact of this coupling on the total dynamic response of the structure can be quite severe depending on the similarity of the modal frequencies and shapes.Typically,acoustoelastic coupling is not a design feature,but rather an unintended result that must be remedied as modal tests of structures are often used to correlate or validate finite element models of the uncoupled structure.Here,however,a test structure is intentionally designed such that multiple structural and acoustic modes are well-aligned,resulting in a coupled system that allows for an experimental investigation.First,coupling in the system is identified using a measure termed the magnification factor.Next,the structural-acoustic interaction is measured.Modifications to the system demonstrate the dependency of the coupling on changes in the mode shape and frequency proximity.This includes an investigation of several practical techniques used to decouple the system by altering the internal acoustic cavity,as well as the structure itself.These results show that acoustic absorption material effectively decoupled the structure while structural modifications,in their current form,proved unsuccessful.Readily available acoustic absorptive material was effective in reducing the coupled effects while presumably adding negligible mass or stiffness to the structure.

A Robust Damage Detection Method Developed for Offshore Jacket Platforms Using Modified Artificial Immune System Algorithm

Steel jacket-type platforms are the common kind of the offshore structures and health monitoring is an important issue in their safety assessment. In the present study, a new damage detection method is adopted for this kind of structures and inspected experimentally by use of a laboratory model. The method is investigated for developing the robust damage detection technique which is less sensitive to both measurement and analytical model uncertainties. For this purpose, incorporation of the artificial immune system with weighted attributes （AISWA） method into finite element （FE） model updating is proposed and compared with other methods for exploring its effectiveness in damage identification. Based on mimicking immune recognition, noise simulation and attributes weighting, the method offers important advantages and has high success rates. Therefore, it is proposed as a suitable method for the detection of the failures in the large civil engineering structures with complicated structural geometry, such as the considered case study.

A review of welding residual stress test methods

Due to local uneven heating during the welding process,the residual stress of the structure after welding affects the reliability of it.In order to ensure the reliability,it is of great significance to test the residual stress distribution of the welded joint.It has always been the focus to find a simple and feasible method for residual stress testing to quickly and accurately obtain the residual stress distribution of welded joints.The mechanical measurement method has high measurement accuracy,convenient and easy operation,but it will cause certain damage to the components.Physical measurement method can avoid damage to components,but its test cost is usually high,and its measurement accuracy can also be affected by the material microstructure characteristics of welded components.Based on the advantages and disadvantages of these two residual stress test methods,a modal test method is proposed.This method is a non-destructive measurement method.Based on the mathematical relationship between the residual stress of the welded structure and the natural frequency(mathematical model),the natural frequency is measured through the modal test to calculate the residual stress quickly.However,it is difficult to establish a mathematical model with this method,and it is not suitable for realization.

Acquisition of Launch Vehicle Dynamic Characteristics Based on Numerical Simulation

and then in the absence of test data to establish the dynamic model.The issue was,how to accurately obtain the mode data of LM-8 with numerical simulations which directly affects the control reliability of flight.In this paper,various approaches to obtain the dynamic characteristics of LM-8 are described from the perspective of refined dynamic modeling and simulating,mode slope prediction,vertical modal test,etc.The numerical simulations were found to be in good agreement with the experimental data,and satisfied the requirements for the engineering application,which effectively supported the successful maiden flight mission of LM-8.

Modal analysis of AC quadrupole magnet system for CSNS/RCS

The quadrupole magnet of the China Spallation Neutron Source （CSNS） Rapid-cycling Synchrotron （RCS） is operated at a 25 Hz sinusoidal alternating current which causes severe vibration. The vibration will influence the long-term safety and reliable operation of the quadrupole magnet. By taking the quadrupole magnet and girder as specific model system, a method for analyzing and studying the dynamic characteristic of the system is put forward by combining theoretical calculation with experimental testing. The theoretical modal analysis results coincide with the experimental testing results. It shows that the dynamic characteristic parameters of the structure can be obtained by modal analysis which will provide a theoretical basis for the further study and the magnet girder optimal design of CSNS/PtCS.

Vibration analysis and topology optimization of the header of full-feeding rice combine harvester

The header frame of full-feeding rice combine harvester was characterized by severe vibration due to the excitation force generated by the movement of each working part.In order to solve the problem,the parametric model of the header frame was established,and the accuracy of the finite element model was verified by comparison of the results of the free modal analysis and free vibration modal test based on Eigensystem Realization Algorithm(ERA).Then the constrained modal frequencies were calculated and compared with the external excitation source frequencies,the results showed that the first and eighth order modal natural frequencies were coupled with the excitation frequencies of the threshing cylinder and the engine respectively,which were apt to resonate.To avoid resonance and achieve lightweight design,topology optimization,and finite element analysis were carried out.The optimization results showed that the strength and rigidity meet the requirements and the weight was 14.17%lower than before.The first and eighth order modal natural frequencies were far away from the excitation frequencies range of the threshing cylinder and engine,and the frequencies were far away from the range of each excitation frequency,which effectively avoided the occurrence of resonance.Field experiments showed that the peak value of the vibration acceleration in the three directions of the 8 measuring points of the optimized header frame was significantly reduced,which effectively reduced the vibration of the header frame during harvest.This study provides a method for obtaining the vibration characteristics of key components of agricultural machinery and provides a reference for the weight and vibration reduction of header frames of rice,wheat,rape,and other crop combine harvesters.

Theoretic analysis and experiment on aeroelasticity of very flexible wing

A high-altitude long-endurance aircraft with high-aspect-ratio wing usually generates large deformation,which brings the geometric nonlinear aeroelastic problems.In recent decades,it has become a key focus of the international researchers of aeroelasticity.But some critical technologies are not developed systematically,such as aerodynamic calculation methods of the curved wing with deformation,moreover,there are few experimental validations of these technologies.In this paper,we established the steady aerodynamic calculating method of the curved wing with quite large deformation based on the extended lifting line method,and calculated the unsteady aerodynamics using the strip theory considering curved surface effects.Combining the structure geometrical nonlinear finite element method,we constructed a systematic analytic approach for the static aeroelasticity and flutter of very flexible wing,and further designed the ground vibration and wind tunnel test to verify this approach.Through the test and the theoretic results comparison,we concluded that the extended lifting line method has adaptable precision for the static aeroealsticity and the strip theory considering curved surface effects for flutter analysis can give exact critical speed and flutter mode when the dynamic stall does not happen.The work in this paper shows that the geometric nonlinear aeroelastic analytic approach for very flexible wing has very high efficiency and adaptable precision.It can be used in the engineering applications,especially the iterated design in preliminary stage.

Experimental and numerical investigations on dynamic and acoustic responses of a thermal post-buckled plate

Experiments were carried out for a clamped rectangular aluminum plate to study the dynamic and acoustic behaviors in both pre-and post-buckling ranges under thermal loads.Plate temperature was elevated from ambient value to the level above the theoretical critical buckling temperature of the plate.In the whole test temperature range,the measured frequencies decreased to the minimum values in sequence,and then turned to increase as temperature rose.The softening effect of thermal stresses played the leading role in the decreasing stage and the stiffening effect of thermal buckling deflection became the major influence factor in the increasing stage.The later one could drive the temperature equilibrium point of the heated plate to move towards lower temperature range.All the frequencies would not drop to zero due to the inherent initial deflection which provides additional stiffness to the plate.Dynamic responses state two variation trends in different temperature ranges,shifting toward the lower frequency range and closing up in the mid-frequency range.The characters of spectrum responses changed gradually as the temperature was elevated.Numerical simulations gave predictions with same variation trend as the test results.

Vibration research of the AC dipole-girder system for CSNS/RCS

The China Spallation Neutron Source （CSNS） is a high intensity proton accelerator based facility. Its accelerator complex includes two main parts： an H- linac and a rapid cycling synchrotron （RCS）. The RCS accumulates the 80 MeV proton beam and accelerates it to 1.6 GeV, with a repetition rate of 25 Hz. The AC dipole of the CSNS/RCS is operated at a 25 Hz sinusoidal alternating current which causes severe vibration. The vibration will influence the long-term safety and reliable operation of the magnet. The dipole magnet of CSNS/RCS is an active vibration equipment, which is different from the ground vibration accelerator. It is very important to design and study the dynamic characteristics of the dipole-girder system. This paper takes the AC dipole and girder as a specific model system. A method for studying the dynamic characteristics of the system is put forward by combining theoretical calculation with experimental testing. The ANSYS simulation method plays a very important role in the girder structure design stage. With this method, the mechanical resonance phenomenon was avoided in the girder design time. At the same time the dipole vibratory force will influence the other equipment through the girder. Since it is necessary to isolate and decrease the dipole vibration, a new isolator was designed to isolate the vibratory force and decrease the vibration amplitude of the magnet.