Modeling an Electrodynamic Shaker Using Experimental Substructuring

A comprehensive modal survey test based on multi-input multi-output experimental modal analysis techniques was conducted on the CASSIOPE spacecraft. This paper describes the details of the methodology used to perform the successful experimental modal test to efficiently extract the critical modes of the spacecraft. Results from the modal test have been used to validate the analytical finite element model and to provide confidence in the structural integrity of the spacecraft design. The test was performed on the flight model of the CASSIOPE spacecraft in the final stages of integration, which included all of the payload and bus instruments and electronics boxes. The multiple-input excitation for the spacecraft was generated using two portable electrodynamic modal shakers installed on the top and bottom of the spacecraft to distribute the excitation energy and the response was measured using 81 miniature accelerometers. A digital multi-channel data acquisition system was used to record the time domain data and calculate the frequency domain spectra. Advanced modal analysis software was used to extract modal parameters from the measured data and critical modes were compared with predictions from the finite element model. Most modes identified through the experimental data compared favorably with the predictions. Nevertheless, some differences were large enough to require iterative update of the finite elelement model. The structural dynamics information from the updated finite element model was used to plan the mechanical vibration qualification test and predict the response of the spacecraft to the launch vehicle environmental loads through coupled loads analysis.

EXTRACTION OF RITZ VECTORS FROM VIBRATION TEST DATA

The Shanghai Tower is a newly built 127-story and 632 m high super tall building. As of April 2017, it was ranked as the second tallest building in the world. Its main structural system is a mega-frame-tube-outrigger system with six outrigger trusses along the height. Due to its unique structural configuration, a series of field and laboratory model tests have been conducted to better understand its dynamic characteristics. Before its construction, a scaled model of the tower was tested on a shake table, and the results were used to refine the design of the tower. At the completion of the construction, full-scale ambient vibration tests were performed. A Bayesian method was used to perform operational modal analysis from the shake table and full-scale ambient vibration tests. The most probable value of the modal parameters and the associated posterior uncertainties were calculated using this method. The first eight modes were identified, including three translational modes in each principal direction and two torsional modes. Using these results, the dynamic characteristics and associated uncertainties obtained from the two tests were investigated and compared in this paper. Due to the scaling of the model, there are some discrepancies between the natural frequencies obtained from two different tests, but the identified mode shapes matched very well. Although the structure was designed in a very innovative manner, its dynamic characteristics are similar to regular tall buildings. The results from this investigation provide valuable information for an ongoing condition assessment of this super tall building.

A comparison is made of the two different types of vibration testing: modal and environmental. Their application to the determination of the flight-safety characteristics of a flight vehicle is discussed. A brief history is included of the development of the equipment and techniques for modal or resonance vibration testing, which is so important before first flight. An example is given of a modal vibration test on an unusually complex aircraft structure, the Lockheed WV-2E, that shows the problems of separation of modes closely spaced in frequency and the difficulties in obtaining all of the modes, clean. The significance of mode shapes, location of mode lines, and mode-frequency ratios are discussed as to how they affect dynamic responses and flutter susceptibilities.

In this paper, the abnormal vibration of the bogie brake test stand during its operation is tested and analyzed. The vibration test and modal test were carried out for the test stand, and the radial runout test was carried out for the wheels of the bogie and the rollers of the test stand. By analyzing the results of the stability test, modal test, and Fourier transform method, the time-frequency spectrum of the bearing pedestal is obtained. The degree of the wheel polygon is obtained by analyzing the wheel out of roundness through the radial runout test results. The comprehensive comparison test results show that the coupling between the polygonal frequency of the wheel and the modal frequency of the bearing pedestal of the test stand leads to vibration amplification, which is also the main reason for abnormal vibration. Finally, some suggestions are put forward to improve the abnormal vibration.

The vibration testing program including excitation location, control location and hanging location has important influence in the slender body two-point excitation vibration test. The modal test results will be referenced when selecting the testing program before the two-point excitation vibration test. Based on the principle of testing program and the modal test theory, a calculation formula will be established when select the testing program using the modal test results. Through the calculation results, we can know that the two testing programs can be intuitively comparison.

Advancements in hybrid dynamic models combining experimental and finite element substructures

The paper considers an issue of updating a turbine blade finite element model. The turbine blade is fixed in the special rig and the unknown contact conditions strongly influences on the blade dynamics. Hence, there is a difference between the real blade dynamic characteristics and the results of the finite element simulation. The task is to update the blade FE model on the basis of the modal test data to obtain fine dynamic model of the structure. The experimental modal parameters are known with some scatter, which is the result of measurement errors, and some differences from blade to blade within the kit of parts. The proposed algorithm is capable to update the turbine blade finite element model by variation of elasticity modulus in contact areas taking into account the experimental modal parameters scatter. It is worth noting that elasticity modulus of finite elements near the contact area should be considered as unknown contact stiffness parameters. The stochastic updating algorithm based on the sensitivity analysis is proposed. The paper presents equations to define sensitivity coefficients and provides the special recurrence relations, on which the proposed algorithm is based. The eigenvalue problem is resolved repeatedly with system parameters changing during the algorithm implementation. The system parameters (elasticity modulus in the contact areas) are recalculated according to the recurrence relations, mentioned above. To implement the proposed algorithm, a special software in C++ language has been developed. The proposed algorithm has demonstrated its efficiency for updating the finite element model of the complex structure. Thus, the differences between the calculated eigenfrequencies and those of identified from modal testing have been reduced from 13% to 3%. The updated model of the turbine blade could be used for accurate simulation of the blade dynamic behavior under different operating conditions.

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.

Interior permanent magnet synchronous motors (IPMSMs) have been widely used in a variety of applications. The IPMSM will generate vibration as well as functioning like other traditional motors, which will affect the performance and the durability of the motor itself. The modal and vibration characteristics of the IPMSM and an optimization design to reduce vibration are researched in this paper. The formulas of electromagnetic force are deduced and analyzed, and a finite element model is established. The model is used for modal calculation, and the low order natural frequency is obtained. Then, the modal test is carried out by the hammering method, and the resonance frequency is found by analyzing the results. Eventually, the electromagnetic vibration is analyzed by taking the electromagnetic force as the load condition, the vibration displacement waveform is obtained, and the correctness of the dynamic calculation is verified by vibration tests. In addition, an eccentric tooth edge design is proposed to weaken the dominant radial electromagnetic force and the vibration displacement is compared with the designed prototype. This design method, which could help to reduce the vibration and noise of the IPMSM, has great potential in future applications.

In this study the structural deployment dynamics of a rollable micro air vehicle wing are investigated. The wing is composed of a single layer of woven, carbon-fiber composite and behaves like a tape-spring, remaining stiff in one direction (lift) while rolling easily in the other for storage. A finite element model is developed and evaluated for its comparison to an experimental model. A vacuum chamber is used to eliminate fluid effects on the structural deployment dynamics, which are recorded using a high-speed video camera. Modal testing and finite element updating are used to estimate unknown composite material properties for the analysis. A laser vibrometer is used to record wing mode shapes, and they are found to agree well with fitted mode shapes and their frequencies from the updated Abaqus finite element model. A wing deployment is simulated in Abaqus and compared with experimental deployments, and the time history displacements matched well. The deployment is found to be sensitive to the wing mount as well as to material properties, particularly damping.

Sensor set expansion for modal vibration testing

The fundamental issue confronting a vibration test engineer is how to obtain the best representation for the natural frequencies and corresponding mode shapes of a mechanical system. In the case of a structure such as a vehicle that has rigid body degrees of freedom, a vibration test requires some sort of artificial support system. The purpose of this work is to quantify the influence of this support system using two example structures: a one-degree-of-freedom oscillator, and a uniform beam on two types of supports. In all cases, the actual influence of the supports on the modal test results is greater than one would estimate a priori. It is hoped that these results, which have been derived from exact solutions, will provide insight for designing test supports for more complex structures.

In this paper, the vibration durability of both SAC305 & eutectic SnPb interconnects is investigated with narrow-band harmonic vibration tests and finite element simulation. The tests are conducted at the first natural frequency of the test board using constant amplitude excitation. Compared to broad-band vibration durability test, the advantage of harmonic test is less complexity, hence, less uncertainty in the desired fatigue constant. A time-domain approach, reported in the literature 0, was adapted in this study for the fatigue analysis. The test board consists of daisy-chained components, to facilitate real-time failure monitoring. The tests are conducted at different loading amplitude to obtain the durability data points located at both low cycle fatigue and high cycle fatigue region. The SAC305 solder was found to have lower fatigue durability than the SnPb solder, under narrow-band harmonic excitation, which is consistent with results from broad-band vibration test 0, as well as with results of mechanical cycling studies and repetitive mechanical shock studies conducted earlier 0. The test board was first characterized before the vibration durability test. A modal test was conducted to determine the mode shape and natural frequency, which were used to decide the excitation frequency of durability test. Flexure strain amplitudes at critical locations on the PWB were first characterized with strain gages at each level used in the test excitation. Detailed local finite element analysis was then conducted to estimate the strain transfer function between the PWB flexure strain and the strain in the critical solder joints for selected components (BGA256, LCR1210 and LCR2512). Then the strain history in the critical solder joint was estimated from the measured PWB strain, using the strain transfer function. Finally the solder strain and the measured time-to-failure data were used to estimate durability model constants for a generalized strain-life fatigue model 0 for both SAC305 and eutectic SnPb solder. Destructive failure analysis (cross-sectioning, polishing and microscopy) was used to confirm that the failure was by solder fatigue.

The Electrodynamic Vibration Exciter (shakers) has been one of the most employed excitation sources in modal tests. The shaker is an electromechanical device that provides a mechanical motion due to the input signal sent to its coil. Despite being widely used, it is well known that the shaker interacts with the structure under test. In particular, when the structure passes through a given resonance, the force delivered by the shaker abruptly decreases, causing the so called drop off phenomenon. This paper aims to study this force drop off phenomenon in the single shaker modal testing. Analytical models are developed to help in understanding the physical principles involved in the interaction between the shaker and the structure under test. Experimental analyses are performed using different shakers as well as excitation signals, in order to evaluate the effects of the input signal, as well as the power amplifier operational modes, on the structure dynamics. Preliminary tests revealed that significant distortions might occur during vibration tests using shakers and these distortions significantly affect the determination of the structure response.