Date This is to certify that the thesis entitled EVALUATION OF A VIBRATION TEST METHOD FOR CUSHIONING MATERIALS presented by GEORGE WALTER YOUNG has been accepted towards fulfillment of the requirements for M.S. degree in Packaging 2 >4» 4/ ' W Dr. James W. Goff Major professor May S. 1978 0-7639 EVALUATION OF A VIBRATION TEST METHOD FOR CUSHIONING MATERIALS By George Walter Young A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1978 ABSTRACT EVALUATION OF A VIBRATION TEST METHOD FOR CUSHIONING MATERIALS BY — George W. Young Vibration cushion curves are used to define the natural frequency of materials and are used as tools in package design. The generally accepted test method for developing the data implies that static stress alone affects the natural frequency of a given materia}. This research was undertaken to determine whether other variables affect the natural frequency. The test method was evaluated by individually determining the effect of six test variables using one material. The variables were; sample size, input acceleration, sweep rate, sweep direction, applied deflection and static stress. The response of the cushioning material :0 vibration was recorded on an X-Y recorder. The results conclusively indicate that natural frequency andv transmissibility are affected by a number of variables. Therefore, cushion curves cannot accurately define the natural frequency or transmissibility of a material based on changes in static stress alone and should be used cautiously in package development. To THERESA M. DeLUCA my wife to be, whose patience during preparation of this document was necessary for its completion. ii ACKNOWLEDGMENTS The author wishes to extend his gratitude to those who worked diligently to obtain an optimum operating vibration system and performed the tests, Randall Bush, Roxanne Chatman, Lynn Flygar, and Steve Siakel, and to Nancy Kocinski for her assistance with the fixture diagram. Thanks is extended to Mr. Robert Kuhn of Dow Chemical Company for providing the material samples and to Dr. James Goff for his assistance in planning the research and to Theresa DeLuca for her assistance in preparing this document. iii TABLE OF CONTENTS PAGE LIST OF TABLES ....................................... V LIST OF FIGURES ...................................... Vi INTRODUCTION ......................................... I 1 DEFINITION OF TEST VARIABLES ......................... 7 TEST PROCEDURE ....................................... 9 TEST RESULTS ......................................... 11 DISCUSSION OF RESULTS ................................ 13 CONCLUSIONS AND RECOMMENDATIONS ...................... 23 APPENDIX A TEST FIXTURE AND VIBRATION SYSTEM DIAGRAM .......... 25 APPENDIX B PRESENTATION OF RESPONSE CURVES .................... 30 REFERENCES ........................................... 49 iv LIST OF TABLES Table l — Detail of Parameters of Test Variables ..... Table 2 - Test Results Figure 9b - A1 - A2 - Bl - BZ - B3 - B4 - B6 — B8 - LIST OF FIGURES Typical Loaded Cushion Response to Vibration Pre-test Recording of Acceleration ............ Post-test Recording of Acceleration ........... Effect of Changing Sample Size ................ Effect of Changing Input Acceleration ......... Effect of Changing Sweep Rate ................. Effect of Changing Sweep Direction ............ Effect of Changing Applied Deflection ......... Effect of Changing Static Stress, Natural Frequency ................................... Effect of Changing Static Stress, Trans- missibility ................................. Test Fixture .................................. Vibration System Diagram ...................... Control Test # l .............................. Test # 1-1 .................................... Test Test Test Test Test # 6—1 .................................... Test # 7-1 .................................... vi 31 32 Figure B9 810 Bll 812 813 B14 B15 816 81? B18 Test Test Test Test Test Test Test Test Test Test Ethnthqtitqtqtqtlt Page 8-1 ................................... 39 9-1 ................................... 40 10-1 .................................. 41 11-1 .................................. 42 12-1 .................................. 43 13-1 .................................. 44 14-1 .................................. 45 15-1 .................................. 46 15-1 .................................. 47 17-1 .................................. 48 vii INTRODUCTION An important function of packaging is one of protection to prevent damage to the product during physical distri- bution. A universal hazard found in all modes of transportation is vibration. Vibration is a significant factor contributing to the damage of many products, and all products transported are subjected to vibrational forces. Due to the unavoidable and potentially damaging forces of carrier vibration, the package or product must be designed to avoid damage. Generally, the most economical approach is to design the product such that it will not be damaged by vibration. However, products are often not so designed and packaging is employed to provide the necessary protection. For fragile items the package design will include cushioning. All cushioning materials under load respond similarly to vibration. The forcing vibration will cause an amplified response of the mass supported by the cushion. The fre- quency at which maximum acceleration response occurs is the natural frequency of the system comprised of the cushion and the load. Figure 1 shows the typical response 1 2 of a system using a cushioning material when subjected to a frequency sweep at constant acceleration input. The natural frequency of the system and the peak re— sponse acceleration are identified by the upper-most peak of the curve. 10 - g 1.0- Acceleration, on I '1 .4 1 1 I 1 10 100 200 Frequency, Hz Figure 1 - Typical Loaded Cushion Response to Vibration The peak acceleration is often quantified as the ratio of response acceleration to input acceleration which is defined as the transmissibility. Although transmissibility refers to response-input ratio across the entire frequency sweep, the term in this paper implies peak transmissibility. Peak transmissibility occurs at the natural frequency of the system and this is where damage from vibration is most likely to occur. If incorrectly used, cushioning materials can damage the product rather than provide protection against vibration. 3 This type of damage is generally a result of application of cushioning materials to package design without adequate consideration of the effect of variable frequency vibra- tion on the system. To aid users of cushioning materials, many suppliers provide information on the natural frequencies of their specific materials. Cushion curves present the natural frequency versus static stress for a given material and thickness. There is a potentially large risk involved in directly applying the values from cushion curves to package design. One reason is due to the many factors other than static stress that affect the natural fre- quency. This research was conducted to evaluate the reliability of a generally accepted test method used to determine natural frequency. This was done by evaluating the effects of a number of test variables on the repeatability of the results. The testing was performed using one material, Ethafoam 220 (Dow Chemical Co.). The material was cut into samples of uniform thickness and conditioned at standard temperature and humidity prior to testing. The thickness was approximately two inches. The six variables listed below were evaluated. 1. Sample size 2. Input acceleration Sweep rate Sweep direction Applied deflection 030190.) Static stress There are a number of other variables that were assumed to be constant throughout the testing. These variables were not specifically monitored and include: recorder accuracy (overshoot), input acceleration waveform, material consistency, temperature, and operator con- sistency. Another potentially significant variable in interlaboratory testing is the fixture design and con— struction. The response of the test block in the fixture was re— corded to document the accuracy of the input acceleration across the frequency sweep.' Figures 2 and 3 are X-Y recorder graphs of the input acceleration. Figure 2 is the pre-test recording and Figure 3 is the post-teSt recording taken at the completion of the final tests. The graphs are a copy of the original X-Y recorder graphs made using a felt pen. The objective of the testing was to evaluate the repeat- ability of the test method. The hypothesis is that the results, natural frequency and transmissibility, are sig- nificantly affected by test variables other than static stress. y! .1. ”OQKO V) V M N ~GQNO ‘0 V M N s-b—v-».-. , . -..-_-. t-....,.-. $--. IJJJ 111 l . _._ u—n—c— "too-o- '9'4—.~ --_- .,, ‘ tié‘.+—..-H -A.i».~f.nua—o-o4_ “fijf‘f‘f? m-$m - ».'u—..1.-o¢“¢§. .A“ ‘uotieaataoov Tie ' ,o. 'Io. , . I | o . H-.-...5, -..—- .p........... . Cowpwhmaooo< “o mcwcuooom vmmvnpmom I m mhswfim 71:33.: 14.4 .41.? u: .hocosvonm V O O a T. a J 2 1. T: O u on DEFINITION OF TEST VARIABLES To evaluate the changes caused by the different test variables, a set of control test parameters were established. A test series consisted of three iden- tical tests. Each test series was a discrete alter- ation of one of the control test parameters. An expection to the above rule was required during the static stress tests where the sample size was also changed to maintain the test block at a manageable weight. The six test variables are defined below, followed by Table 1 which details the values of the six variables for each test series. The underline indicates the change made to the control test parameters. 1. Sample size: length and width, in inches, of the square cushioning material sample. 2. Input acceleration: acceleration amplitude of the vibration table, measured in g's zero to peak, maintained at a constant value during a frequency sweep. 3. Sweep rate: logarithmic rate, measured in decades per minute, at which the frequency of the vibration table is changed during the frequency sweep. 4. Sweep direction: direction of a single frequency sweep, either up or down, between the frequency limits which were held constant at 3 Hz and 200 Hz. 8 Applied deflection: distance, in inches, that the cushion samples are deflected by the fixture (in addition to the deflection caused by the test block resting on the bottom cushion sample) prior to the frequency sweep. Static stress: weight of the test block divided by the area of the top surface of the bottom cushion sample, measured in pounds per square inch (psi). Table 1 - Detail of Parameters of the Test Variables Input Applied Sample Acceler- Sweep Deflec- Static Test Size ation Rate Sweep ‘tion Stress Series inches g's dec./min. Direction inch psi 1 4x4 .5 .5 Down 0.10 0.5 2 §§§_ .5 .5 Down 0.10 0.5 3 4x4 .5 .5 Down 9;Q_ 0.5 4 4x4 .5 .5 Down 0.15 0.5 5 4x4 412. .5 Down 0.20 0.5 6 4x4 ,2;_ .5 Down 0 10 0.5 7 4x4 5 ;32_ Down 0.10 0.5 8 4x4 .5 .5 Ep_ 0.10 0.5 9 4x4 .5 .5 Down/Up 0.10 0.5 10 §§§ .5 .5 Down 0.10 9;; 11 §§§ .5 .5 Down 0.10 Q_._2_ 12 _8_)_c_8_ .5 .5 Down 0.10 9;; 13 §§§_ .5 .5 Down 0.10 ‘QLZ 14 4x4 .5 .5 Down 0.10 1;9_ 15 4x4 .5 .5 Down 0.10 .ILQ 16 4x4 .5 .5 Down 0.10 ‘ILQ 17 4x4 .5 .5 Down 0.10 2 0 TEST PROCEDURE The testing was performed by students at the School of Packaging according to instructions provided by the author. The following basic procedure was used through- out the testing: 1. Allow the vibration system electronics and hydraulics to warm-up prior to testing. 2. Perform standard calibration checks on tracking filters, X-Y recorder, and response accelerometer. 3. Select the control test parameters on vibration system and switch to standby mode. 4. Place test block between two untested cushion samples. 5. Securely fasten the fixture, over the cushion system, onto the vibration table. 6. Apply the deflection. 7. Check test block to assure that vertical movement is not restructed. 8. Connect accelerometer cable to response accelerometer. 9. Initiate table vibration. 10. While system comes up to selected acceleration level, place graph paper into X-Y recorder and switch to record. - ll. Initiate the frequency sweep. 12. At completion of sweep, switch recorder to standby mode and remove graph paper. 13. Switch vibration system to standby mode. 14. Disconnect response accelerometer cable and remove cushion samples. 10 15. Repeat steps 4 - 14 for two additional tests. 16. Select next set of test parameters as indicated and repeat steps 4 - 15. The results are presented in Table 2 by TEST RESULTS which consists of three identical tests. For each test, the natural frequency and peak response acceleration are determined from the X—Y recorder graphs. The data is presented using the following symbols: Fn frequency of maximum acceleration response (natural frequency) mean natural frequency of test series maximum or peak response acceleration (acceleration at Fn) mean peak response acceleration of test series transmissibility of mean peak response acceleration test series The low standard deviations indicate that the test method repeatable in each test series. Although the accuracy of results could be challenged, permitting an accurate comparison of the effect of the variables. The test variables that were not precisely monitored were held constant during the testing as shown by the consistency of the results of each series. 11 test series number of was the each series was very consistent 12 Table 2 ~ Test Results Test Param- Series ___ Series eter Number Fn Pa 3 E T C 1 54 2.45 2 54 2.45 2.45 3 53 53.7 2.45 4.9 1 8x8 1 53 2.35 2 53 2.4 3 53 53 2.35 2 37 4.74 2 0.0" 1 35 1.6 2’ 44 1.85 3 37 38.7 1.75 l 73 3.46 3 0.15" 1 52 2.4 2 51 2.4 3 52 51.3 2.35 2.38 4.76 4 0.20" 1 52 2.35 2 53 2.4 3 52 52.3 2.4 2.38 4.76 S .753 1 55 3.5 2 52 3.4 3 53 53.3 3.5 3.47 4.63 6 .253 1 54 1.35 2 53 1.35 3 54 53.7 1.35 1.35 5.4 7 .25 1 68 3.1 dec./min. 2 69 3.4 3 70 69 3.4 3.3 6.6 8 up 1 137 2 2 139 2.2 3 139 138.3 2.25 2.15 4.3 9 down/ 1 up 133 2.15 up 1 d 53 2.5 2 up 132 2.2 2 d 52 2.5 3 up 133 up 132.7 2.2 up 2.18 up 4.36 3 d 53 d 52.7 2.5 d 2.5 d 5.0 10 0.1 psi 1 125 2.95 2 130 3.2 3 133 129.3 3.5 3.22 6.44 '11 0.2 psi 1 82 2.4 2 82 2.35 3 78 80.7 2.35 2.37 4.74 12 0 3 psi 1 68 2.3 2 72 2.35 3 70 70 2.35 2.33 4.66 13 0 7 psi 1 45 2.4 2 46 2.25 3 46 45.7 2.25 2.3 4.6 14 1.0 psi 1 47 2.45 2 48 2.4 3 48 47.7 2.4 2.42 4.84 15 1.3 psi 1 28 2.0 2 29 2.15 3 29 28.7 2.2 2.12 4.24 16 1 6 psi 1 35 2.15 2 35 2.25 3 33 34.3 2.05 2.15 4.3 17 2 0 psi 1 27 2.2 2 29 2.1 3 30 28.7 2.1 2 13 4.26 DISCUSSION OF RESULTS The results of the previous section are summarized here by test variable. The mean natural frequency and trans- missibility of each parameter of the six variables are combined with those of the control test. The results are organized similarly for all six variables; test series number, test parameter, mean natural frequency, and transmissibility. In addition, the static stress summary includes two test parameters due to the required sample size change. Following the summarized listing for each variable, the results are presented graphically. All natural frequency graphs and likewiZe all transmissibility graphs, are presented on the same scale to aid in the comparison of the relative changes caused by the six variables. 1. Change in sample size TC 4x4 53.7 Hz 4.9 T1 8x8 53 Hz 4.74 13 14 u N u :1: "-4 H A .H 3 a CD (I) a 2 2: ‘ ‘ m n- C: m 50 a 1 1 54 r; E-* H 4x4 8x8 fi inches 63 Z 5. 0 4x4 8x8 inches Figure 4 - Effect of Changing Sample Size The purpose of this test series was to provide an indication of the effect of sample size. The test served to justify the required change in sample size for the static stress tests. The results are considered to be within recording accuracy which is affected by placement of the paper into the X—Y recorder and interpretation of the graphs. Changes in both the natural frequency and transmissibility are very small indicating that sample size does not affect repeatability. 2. Change in input acceleration T6 .25g 53.7 Hz 5.4 TC .5g 53.7 Hz 4.9 T5 .75g 53.3 Hz 4.63 15 3 >. g 3: 5.4 L :5 H g 60 E a ~§ 5.0 - 2:. ”7"“ 2 50- E 1, l L g 4 6 ' 1 _1 I and 25 .5 75 H 25 .5 .75 ZS: g's E‘ g's Figure 5 - Effect of Changing Input Acceleration The results indicate that a change in input acceleration has a negligible effect on repeatability of the natural frequency and a slight effect on the repeatability of transmissibility. A possible cause for the difference in transmissibility, results from the bottoming-out phenomenon characteristic of cushions. At the low input acceleration, the test block moves within the effective cushioning range of the material resulting in a high transmissibility value. Whereas, at high input acceleration the test block is displaced a greater actual distance and begins to bottom—out the cushion. This results in an attenuation of the response acceleration and a lower transmissibility value. 3. Change in sweep rate T7 .25 decade/minute 69 Hz 6.6 TC .5 decate/minute 53.7 Hz 4.9 16 6.8 - O N >= 6.4 b m 70 - . 3:: - H > a g g 6.0 ~ a) 60 " CD a m g ' '2 5 6 :2 50 r 33 . 1 1 d H H 2 .25 .5 F 5'2 ' 3 dec./min. Cd 0 2 4.8 h 1 1 .25 .5 dec./min. Figure 6 - Effect of Changing Sweep Rate In comparison to the effect of sample size and input acceler- ation, the effect of sweep rate was more significant. The results indicate an unquestionable change in both natural frequency and transmissibility. Due to the slower rate of change in the frequency during the sweep, the cushion system has more time to react to the forcing vibration resulting in a shift in the natural frequency. Similarly, the amplification of the acceleration at the natural frequency is allowed to respond for a longer duration resulting in an increase in response acceleration and transmissibility. Hz Natural Frequency, 17 Change in sweep direction TC down 53.7 Hz 4.9 T8 up 138.3 Hz 4.3 T9 down 52.7 Hz 5.0 T9 up 132.7 Hz 4.36 ' > 4.) 5 5.0 h z 125 P m m 'E 46" m . :1 0 CG 0 g: 42h.. up down 100 b 75 r : 50 b 1 1 up down Figure 7 - Effect of Changing Sweep Direction 18 The change in sweep direction had a slight effect on trans- missibility and a very significant effect on natural frequency. The natural frequency of the up sweep is approximately 2% times the value of the down sweep. Test series 9 is a complete cycle sweep from and returning to 200 Hz. The results for each direction are consistent with the results of the single sweep tests. As the frequency is swept from the lower limit, the natural frequency is shifted toward the upper limit and as the frequency is swept from the upper limit the natural fre- quency is shifted toward the lower limit. Sweep rate is likely to have a significant effect on the differences caused by the change in sweep direction. At a lower sweep rate, the natural frequency should be more consistent as the sweep direction is changed. 5. Change in applied deflection T2 0.0 inch 38.7 Hz 3.46 TC 0.10 inch 53.7 Hz 4.9 T3 0.15 inch 51.3 Hz 4.76 T4 0.20 inch 52.3 Hz 4.76 19 5.0 F > +3 N :3 4.6 '- m E .. -r-I E; 55 — 3 4 2 p a -H (D E a m 8‘ 45 — 5 3.8 +- a a m B .3 35 _ 3.4 _ S 1 I .L 1 I l l J g 0.0 .1 .15 .2 0.0 .1 .15 .2 2 inch inch Figure 8 - Effect of Changing Applied Deflection The effect of applied deflection on both the natural fre- quency and transmissibility was characterized by'a sharp increase followed by a leveling off of the results. Applied deflection has a significant effect on the repeatability of the test results. There is no significant difference in the results of the three tests which include an applied deflection. The dif— ferences at zero applied deflection versus applied deflection is due to the loss of contact of the test block with the cushion samples. At zero deflection, the top cushion rests on the test block in a fully expanded condition (free height). At the natural frequency, the displacement of the test block causes a compression of one cushion sample resulting in loss of contact with the other cushion. With the application of 20 the applied deflection the test block remains in contact with both cushion samples throughout the frequency sweep. The natural frequency and transmissibility increase upon introduction of applied deflection. 6. Change in static stress T10 8x8 0.1psi 129.3 Hz 6.44 Tll 8x8 0.2psi 80.7 Hz 4.74 T12 8x8 0.3psi 70.0 Hz 4.66 TC,Tl 4x4/8x8 0.5psi 53.3 Hz* 4.81* T13 4x4 0.7psi 45.7 Hz 4.6 T14 4x4 1.0psi 47.7 Hz 4.84 T15 4x4 1.3psi 28.7 Hz 4.24 T16 4x4 1.6psi 34.3 Hz 4.3 T17 4x4 2.0psi 28.7 Hz 4.26 *calculated from six tests of TC and T1 Natural Frequency, Hz 21 125 P 100 _ 75 ~ 50 P 25 _ l 1 I 1 J 1 1 .1 .2 .3 .5 .7 1.0 1.3 1.6 2.0 psi Figure 9a - Effect of Changing Static Stress, Natural Frequency 22 6.5 P 6.0 b >5 +3 ".4 53 55- g . "-4 m m °H 55.0” f: o S 0 Ed . v 4.5 ” ___ O . C 114 J L l l l _L .1 .2 .3 .5 .7 1.0 1.3 1.6 2.0 psi Figure 9b - Effect of Changing Static Stress, Transmissibility As the static stress is increased, the initial effect on the natural frequency and transmissibility is very significant. The natural frequency gradually decreases in rate of change and approaches the shape of an exponential curve. Other than the initial sharp decline, the transmissibility results remain relatively consistent and are comparable to the effeCts caused by changing sweep direction and sweep rate. Ethafoam is characteristically a highly damped cushion material, and the results indicate a non-linear spring rate. There is a sig- nificant effect on the repeatability of the results as the static stress is changed. CONCLUSIONS AND RECOMMENDATIONS The reliability of the vibration test method for cushioning materials is sensitive to test variables other than static stress. Static stress had the most significant effect, however, other variables have been identified that also significantly effect the repeatability of the test results. The six test variables are ranked below based on the results of this research, in order of descending relative effect on natural frequency and transmissibility. Natural Frequency Transmissibility static stress static stress sweep direction sweep rate sweep rate applied deflection applied deflection input acceleration sample size sweep direction input acceleration sample size Due to the limited range of parameters evaluated for some variables, such as sample size, the results may understate the effect that these variables have on the results. On the other hand, the limited range of parameters tested for variables such as sweep rate was sufficient to determine that the results were significantly affected. It is important to identify and control all variables of the test method. Vibration cushion curves can be misleading. One should not interpret information presented on the natural frequency and 23 24 transmissibility of a material as the true values for that material in use. As shown, the test method can have an effect on the results obtained. Also, material density can change and the package design will not generally reproduce the test configuration and therefore, result in a change in cushioning performation. It is recommended that cushion curves be used as guidelines for design and that the final packaging system be qualified by laboratory performance testing. In conclusion, the generally accepted test method for evaluating cushioning materials and developing vibration cushion curves can easily produce different natural frequency and transmis- sibility results for a given material. . APPENDICES 26 monitor and control the oscillation (displacement) of the actuator. 3. Kistler, Model 818 Pieztron Accelerometers with 581A Coupler. The accelerometer signals pass, individually, through the coupler and are input into the appropriate tracking filter. The response accelerometer measures the acceleration of the test block and the control accelerometer measures the table or input acceleration. 4. Unholtz-Dickie, Model TFll-LFZ, Tracking Filters. The tracking filters follow the frequency of the vibra- tion system and filter the noise from the acceleration signals. The control filter signal is input into the acceleration signal to a DC signal proportional to peak acceleration for input into the X-Y recorder. 5. Spectral Dynamics, Model SD104A-l Sweep Oscillator. The frequency generator provides control of: sweep rate, fre- quency limits, waveform and table frequency. The unit pro- vides DC output proportional to frequency for input into the X-Y recorder and tuning frequency for input into the tracking filters and acceleration controller. 6. Spectral Dynamics, Model SD105C-l Amplitude Servo/ Monitor. The acceleration amplitude controller monitors the control acceleration signal and adjusts the vibration 27 system primary control signal, to maintain a constant input acceleration. 7. Hewlett Packard, Model 5327B Timer, Counter, DVM. Monitors the period of the frequency signal to aid in setting the frequency limits and calibration of the frequency genera— tor. 8. Krohn-Hite, Model 3750 Filter. Filters the DC signal (low pass at 2 Hz) of the response tracking filter to add stability to the X—Y recorder. 9. Hewlett Packard, Model 7034A X-Y Recorder. Plots test block (cushion system) response, acceleration vs frequency. 10. Tektronix, Type 502 Oscilloscope. Monitors the acceler- ation signal, filtered or unfiltered. top nuts .28 [1771] washers T\\\S\ 9 «<4 spacer placement 2 ‘1 bottom nut hold-down [[1112] r11 2‘ M device cushion | cw /// 7 nylon rollers / . _ - response mpg; accelerometer - e K , ' o jZ/T test block ‘ cushion \\\\\\\“i\\\\\N ‘5\\_control accelerometer v I Figure A1 - Test Fixture '29 response accelerometer @. I control couplerf] r""1 I_§$FJ acceIErometerr 1 CD ____. ‘%___ I response tracking filter syStem * 1 controller <:) I <:) control A ' requency .- enerator @ 1 track' filter acceleration [counter] loontrdller <:)' -<:> 09H: I— ® ‘ ' . , ‘1 f I log DCN peak g's A¥ low pass * Lfilter .' scepe l . .____> X-Y recorder 10g DC~Hz @ Figure A1 - Vibration System Diagram APPENDIX B PRESENTATION OF RESPONSE CURVES An X—Y recorder was used to plot the response of each test. Presented here is the first graph of each test series. Due to the light tracing made by the recorder, it was necessary to reproduce the graphs to gain effective copyability. The graphs were traced over the original onto a second sheet of graph paper with a felt pen. The curves represent very closely the original tracing, but are somewhat thicker. The graphs are in order by test number, beginning with the control test which identifies the six test variables. Each subsequent graph identifies the test number and alteration of the control test parameters. The frequency sweep is from 3 to 200 Hz on a logarithmic scale. Acceleration is recorded from .1 to 10 g's on logarithmic scale. 30 H %.Pmoa Houpnoo 1 an casmfim .~,... _~ n: .zocesvonm . O "QQN .9 ‘uOrieaaIaoov mmmhpm owpdam fimn m.o 53383 8393 :9: 36 :owpomhwv Qmwzm £306 mama nomsm mpzcfis\mumOmu m. soapmnmamoom pans“ m m. mafia mHQEMm ax: I—OQ TH .4 Ema .. mm 48mg a 73:3. - a: .zocmnvmnm F-OQ N V 0 O 9 TL 9 J E 1. I: O u an exam mamsmm mam "QQN v n « _o-onv n N .oosvmw n a Hum 4 name 1 mm spawns a: . hocmzdmnm V. O” O a T. a J B 1.. I. O u an nonpomflcoe 6644554 son“ o.o Hum 4 same - 4m spawns u: . zocosvoum :onpomamoe ewnaagm Sosa mfi.o V 0 C 9 I a J B 1. T: O u I_ 3.. v 74 4 «was . mm 9:63 _ a: .aocmsuonm I-QQ N V 3 0 a I a J B 1. .L. O u an. n compomahou omfiannm non“ om.o 7m 4 $2. - om 25»; 2:32:23... I N: .AOCmsumum "OQ N V O O a T. 9 I B 01*- T: O u 6 ad Compmnmamoom Psgzw m mm. ”fink Te 4 puma r mm 9:68 v O O a _.L 9 J v... n... t- O .u an Goapwnoamoom 959.3 m mm. _00 N TN. 1.. $8. . mm 8%: aw—A um .hocoswmhb ~66 N V O O 3 TL 9 J 2 ,1. To 0 u . an span mmmzm .cfls\.omu mm. 9 ~9Qk 7m 4 $2. I am 8:63 a: .hoCoswmum V O O 3 _..L 8 J B a... T: O u an Soapomnflc nomsm a: Ta 4 3.39 - 3m 2.62 u: .zocmsconm V O 0 9 _.L a J B 1. I. O u S :oweomhfio mmmzm m=\:306 73 4 $3. . in 48mg 2:232:17. L _.., N: .hocmsvmhm mmohpm caveam “mm H.o 8 ‘uotisaataoov P-QQ ”O. N T: s. 5.5.8. .1 NE 9.33 um .zocmsdmnm mmonpm afipmpm Hmm m.o WV 0 O a T. 3 ,1 B 1. I. O u as TN; 4 $2. . 9m 8:52 212444 a: .zoCcsvmnm V O a a I a J B 1. T: o u an m mmmnpm owpmpm Hma m.Q I-Dfik 73 4 $2. - 3m 2&3 :3E:... a _ 1 ED, N: .hocmsuoum V O O 3 .L 8 J B 1. I. O u an mmoppm aflpmpm and 5.0 #11:.“ * Paw—H. I Mam mH—JNHW. a: .hozmswmum V o o a I a J B .+ The o u I on mwmppm oasdpm Hmm o.H HumH % pmme I mam musmfim 2:2: u: .zocosuonm V o o a T. a J B .+, r... o u an mmmupm oapmwm Ham m.H 73 .4 pace I. Sm 63mg :erCLLL. u: .zocmswohm v V O O 9 T. 9 J E "T T- O U 3 mmmhpm aflpmpm Hmn w.H TE 4 58.. . 3m 2:62 um .zosmzumnh v; a 0,. a I a I e 1. to o u a: mmmhpm oaempm awn o.N REFERENCES REFERENCES Godshall, W.D., ”Effects of Vertical Dynamic Loading on Corrugated Fibreboard Containers”, Forest Products Laboratory. U.S. Department of Agriculture, July 1978. Pierce, S.R. and Wambaugh, J., Vibration Transmissibility of Resilient Package Cushioning Materials, Technical Report No. 21, Multi—Sponsor Research Program, School of Packaging, Michigan State University, January 1973. Young, G., "Development of a Method to Measure the Effects of Pre-applied Deflection on Transmissibility of Cushions” Research Paper, School of Packaging, Michigan State University, Sept. 1976. 49 HICHIGRN STATE UNIV. LIBRARIES IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 31293000802763