Dynamic response of a one-degree-of-freedom linear system to a shock load during drop tests: Effect of viscous damping

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Linear System ◽  
Dynamic Response ◽  
Degree Of Freedom ◽  
Shock Load ◽  
Viscous Damping ◽  
Drop Tests

A Resonance Chart for Damped Vibration

1955 ◽  
Vol 59 (540) ◽  
pp. 850-852 ◽  
Author(s):  
R. E. D. Bishop
Keyword(s):  
Linear System ◽  
Convenient Method ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Viscous Damping ◽  
Similar Form ◽  
Hysteretic Damping ◽  
Resonance Curves ◽  
Phase Angles

A convenient method is pointed out for calculating the response of a damped linear system with one degree of freedom to harmonic excitation. Results of such calculations are usually represented by the familiar “ resonance curves ”—one curve being plotted for each intensity of damping. These curves are not particularly convenient to use and Yates has overcome several of their defects by throwing them into a nomographic form. Yates' nomogram is based upon the concept of viscous damping and it does not give the information of a conventional set of resonance curves in that it relates to the velocity of vibration. By changing over to hysteretic damping, a nomogram of somewhat similar form may be constructed such that it gives amplitudes and phase angles of displacements while retaining the advantages, over resonance curves, of this form of representation.

Could Shock Tests Adequately Mimic Drop Test Conditions?

2002 ◽  
Vol 124 (3) ◽  
pp. 170-177 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Dynamic Response ◽  
Impact Load ◽  
Probabilistic Approach ◽  
Drop Test ◽  
Shock Load ◽  
Structural Element ◽  
Test Conditions ◽  
Maximum Value ◽  
Drop Tests ◽  
External Acceleration

Drop tests are often substituted in qualification or life testing of microelectronic and optoelectronic products by shock tests. The existing (e.g., Telcordia) qualification specifications require that a short term load of the given magnitude and duration (say, an “external” acceleration with the maximum value of 500 g, acting for 0.001 s) is applied to the support structure of the product under test. The natural frequencies of vibration are not taken into account. The objective of our study is to develop simple analytical (“mathematical”) predictive models for the evaluation of the dynamic response of a structural element in a microelectronic or an optoelectronic product/package to an impact load occurring as a result of drop or shock tests. We use the developed models to find out if a shock tester could be “tuned” in such a way that the shock tests adequately mimic drop test conditions. We suggest that the maximum induced curvature and the maximum induced acceleration be used as suitable characteristics of the dynamic response of a structural element to an impact load. Indeed, the maximum curvatures determine the level of the bending stresses, and the maximum accelerations are supposedly responsible for the functional (electronic or photonic) performance of the product. We use the case of an elongated rectangular simply supported plate as an illustration of the suggested concept. We show that in order to adequately mimic drop test conditions, the shock test loading should be as close as possible to an instantaneous impulse, and that the duration of the shock load should be established based on the lowest (fundamental) natural frequency of vibrations. We show also that, for practical purposes, it is sufficient to consider the fundamental mode of vibrations only, and that the shock load does not have to be shorter than, say, half the quarter of the fundamental period. We demonstrate that, if the loading is not short enough, the induced curvatures and accelerations can exceed significantly the curvatures and accelerations in drop test conditions. Certainly, the results of such shock tests will be misleading. After the appropriate duration of the shock impulse is established, the time dependence and the maximum value of the imposed (“external”) acceleration in shock tests should be determined, depending on the most likely drop height, in order to adequately mimic drop test conditions. We demonstrate that the application of a probabilistic approach can be helpful in understanding the mechanical behavior and to ensure high short- and long-term reliability of an electronic or photonic device that might be or will be subjected to an accidental or expected impact loading. We conclude that although it is possible to “tune” the shock tester, so that the drop test conditions are adequately reproduced, actual drop tests should be conducted, whenever possible. The results of the analysis can be helpful in physical design and qualification testing of microelectronic and photonic products, experiencing dynamic loads of short duration.

scholarly journals Investigation of X and Y Configuration Modal and Dynamic Response to Velocity Excitation of the Nanometer Resolution Linear Servo Motor Stage with Quasi-Industrial Guiding System in Quasi-Stable State

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 951
Author(s):  
Artur Piščalov ◽  
Edgaras Urbonas ◽  
Darius Vainorius ◽  
Jonas Matijošius ◽  
Artūras Kilikevičius
Keyword(s):  
Dynamic Response ◽  
System Analysis ◽  
Operating Time ◽  
Stable State ◽  
Degree Of Freedom ◽  
Diagnostic Tools ◽  
Nanometer Scale ◽  
Positioning Systems ◽  
Industrial Enterprises ◽  
Guiding System

Research institutions and industrial enterprises demand high accuracy and precision positioning systems to fulfil cutting edge requirements of up-to-date technological processes in the field of metrology and optical fabrication. Linear motor system design with high performance mechanical guiding system and optical encoder ensures nanometer scale precision and constant static error, which can be calibrated by optical instruments. Mechanical guiding systems has its benefits in case of control theory and its stability; unfortunately, on the other hand, there exists high influence of structure geometry and tribological effects such as friction and modal response. The aforementioned effect cannot be straightforwardly identified during the assembly process. Degradation of dynamic units can be detected only after certain operating time. Single degree of freedom systems are well investigated and the effect of degradation can be predicted, but there exists a gap in the analysis of nanometer scale multi degree of freedom dynamic systems; therefore, novel diagnostic tools need to be proposed. In this particular paper, dual axes dynamic system analysis will be presented. The main idea is to decouple standard stacked XY stage and analyse X and Y configuration as two different configurations of the same object, while imitators of corresponding axes are absolutely solid and stationary. As storage and analysis of time domain data is not efficient, main attention will be concentrated on frequency domain data, while, of course, statistical and graphical representation of dynamic response will be presented. Transfer function, dynamic response, spectral analysis of dynamic response, and modal analysis will be presented and discussed. Based on the collected data and its analysis, comparison of X and Y responses to different velocity excitation will be presented. Finally, conclusions and recommendations of novel diagnostic way will be presented.

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

Accelerometer correction for the dynamic analysis of damped multi-degree of freedom systems

1969 ◽  
Vol 59 (4) ◽  
pp. 1591-1598
Author(s):  
G. A. McLennan
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Exact Method ◽  
Three Degrees Of Freedom

Abstract An exact method is developed to eliminate the accelerometer error in dynamic response calculations for damped multi-degree of freedom systems. It is shown that the exact responses of a system can be obtained from the approximate responses which are conventionally calculated from an accelerogram. Response calculations were performed for two typical systems with three degrees of freedom for an assumed pseudo-earthquake. The results showed that the approximate responses may contain large errors, and that the correction developed effectively eliminates these errors.

Dynamic response of a two degree of freedom spherical system in a fluid

1967 ◽  
Vol 35 (6) ◽  
pp. 351-361 ◽  
Author(s):  
J. F. Carney ◽  
L. F. Mockros ◽  
S. L. Lee
Keyword(s):  
Dynamic Response ◽  
Degree Of Freedom ◽  
Spherical System ◽  
Two Degree Of Freedom
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