Shock Analysis of an Antenna Structure Subjected to Underwater Explosions

Transcription

1 Shock Aalysis of a Atea Structure Subjected to Uderwater Explosios Mehmet Emre Demir, Mehmet Caliska Departmet of Mechaical Egieerig Middle East Techical Uiversity, Akara, Turkey ASELSAN Ic., Radar ad Electroic Warfare Systems Busiess Sector Atea Techologies Departmet, Akara, Turkey Abstract Atea structures costitute vital parts of electroic warfare systems. Mechaical desig is as crucial as electromagetic desig of atea structures for proper fuctioig ad meetig high system performace demads. Failure of mechaical ad electroic structures operatig uder shock loadig is a commo occurrece i aval electroic warfare applicatios. A complete shock aalysis of a dipole atea structure subjected to uderwater explosios is performed to foresee adverse effects of mechaical shock pheomea o the atea structure. Theoretical models of the atea structure; amely, mathematical model ad fiite elemet model, are built o multi-degree-of-freedom approach. Modal properties are derived from Classical Beam Theory ad trasiet resposes to iput shock loadig are obtaied by Recursive Filterig Relatioship (RFR) Method for the mathematical model. Iput shock loadig is sythesized from assessed shock specificatio to classical shock iput. Trasiet resposes exerted from RFR method are also approximated by simplified ad SDOF models. Fiite elemet aalysis of the aalytical model is performed o ANSYS platform. Comparisos of aalytical results are preseted for iterchageable use of proposed models. Numerical results are verified with both modal ad trasiet results collected from experimetal aalysis. Experimetal aalysis is performed for exact dimesios of atea structure subjected to sythesized shock iput criteria. Thus, the complete shock aalysis of the atea structure is performed for typical atea desig to withstad uderwater shock explosios. Keywords Uderwater Explosios (UNDEX), Shock Profile Sythesis, Trasiet Respose Aalysis, Experimetal Shock Aalysis, Ramp Ivariat Recursive Filterig Relatioship Method. I. INTRODUCTION Desig specificatios of aval electroic warfare applicatios for customers cotai harsh aval shock survival criterio. Mechaical structures of such systems should withstad ad pass laboratory tests for aval shock. Prelimiary desig cosideratios should be take ad further actios should be carried with the shock aalysis ad tests beforehad. Thus, uderwater explosio shock (UNDEX) should be studied aalytically ad should be qualified with fiite elemet models ad experimets. Most of the customers for those C- ESM systems are iteratioal. As stadards o military testig methods like MIL-STD-810F/G [1] do ot iclude uderwater shock iputs ad testig methods, proper atioal stadards such as BV043 [2] ca be take as referece. Therefore, shock iputs ad testig methods are determied by shock profile sythesis i these stadards ito possible frequetly used sigals ad methods. A mathematical model of atea structure is built from both SDOF ad MDOF poit of view. For these models, solutio techiques ad faster solutio algorithms are provided. Pre-defied ad sythesized shock pulses are used as iput sigals to solve resultig equatios. Fiite elemet model that describes the pheomeo is developed for the problems solved aalytically before. These fiite elemet model verificatios ca serve as a guide for complex geometries for which complete aalytical models are very hard to build. Further, those aalytical ad mathematical models are validated with experimets. Aalytical ad fiite elemet models ca be exploited for ease of experimetally difficult verificatios, as experimets of shock cases with high amplitudes over a short time duratio for big ad bulk mechaical parts are very hard. Similarly, experimetal aalysis ca be used istead of aalytical or FE models whe the system cosists of elemets that are hard to model like composite structures, isolators or other o-liear elemets. Therefore, this study aims to provide all possible ways for uderwater shock aalysis ad desig that ca serve guidace for desigers from prelimiary desigs to postfailure isolatio problems. II. SHOCK PROFILE SYNTHESIS BV043 stadard [2] is the buildig specificatio for ships of the Germa Federal Armed Forces. MIL-S-901D [3] stadard is a military specificatio for High Impact mechaical shock to be applied to equipmet attached o aval platforms. I this stadard, shock qualificatio criteria of the structure are defied with shock testig procedures like full-scale ship/submarie tests ad floatig barge test. Sice MIL-STD- 810F/G does ot cover ay aval shock or uderwater explosio testig stadard, ad i Turkey o facility to perform

2 MIL-S-901D testig stadard requiremets exists, the equivalet, eve more strict to perform BV043 stadard is typically take as a referece for aval projects by demads of customers. I BV043 stadard, the shock loadigs o the equipmet attached o stadard surface ship ad submarie are defied briefly. It is possible to calculate stadard time equivalece of the shock sigal whose spectrum value is already kow by meas of BV043. Geerally, half-sie or saw-tooth shock forms are used i stadards because such types of forms are easy to be geerated i laboratory coditios, as double half-sie form is used to i BV043 stadard. I the followig part, double half-sie shock time sigal determiatio process is preseted. I order to defie time iput, 2, 4, 1, 2 V values should be calculated usig tabulated a a t t ad 1 a0, V0 ad d 0 values from the stadard [4]. miimum amplitude ad time spa that displays the shock profiles i -1.5dB tolerace (amplitude x ) iterval are derived. For shock respose profile sythesis, MATLAB code is used i order to solve followig SDOF SRS equatio [5]. x 2exp t cos t x exp 2 t x 2 ty... i d i1 i2 i 2 t exp t 1 2 si t 2 cos ty d d i1 d For SRS calculatios, Q=10 is take as recommeded i MIL- STD-810G. For axis determiatio, the followig defiitio is used as illustrated i Figure 2. (1) Figure 2 Axis Defiitios for Submarie From the tabulated double half-sie acceleratio-time sigals, the correspodig half-sie profiles are sythesized as illustrated i Table 2. Table 2 Calculated ad Sythesized Shock Profiles Figure 1 Geeral Form of Double Half-Sie Shock Acceleratio-Time Sigal Acceleratio-time sigal for the equipmet istalled o a submarie of class >2000t ca be straightforwardly calculated from the equatios exerted from the double half-sie profile show i Figure 1 ad the tabulated values give i stadard. Hece, the acceleratio-time sigals are tabulated i Table 1. Table 1 Calculated Acceleratio-Time Sigals From mechaical ad electromagetic poit-of-view, vertical acceleratio-time iput is foud to be the most critical. Therefore, 250g-8ms half sie iput will be used for aalyses. I order to illustrate sythesis process, sythesized vertical shock iput is preseted i Figure 3. Acceleratio-time iput sigal is determied from the aforemetioed aval shock respose spectrum approach. However, double-sie shock iput is hard to geerate i laboratory coditios. Therefore, double-sie sigals extracted from BV043 stadard should be sythesized to half-sie form. Upo performig this, testig procedure of the atea will be so easy as the half-sie form ca be geerated experimetally by meas of a drop table. I MIL-STD-810G Method 516.5, for shock profiles used i the form of shock respose spectrum iside the 90% of Hz frequecy iterval, -1.5/+3 db tolerace is specified. Therefore, half-sie shock profiles with Figure 3 Shock Profile Shock Respose Spectrum for Z Axis: Defied by BV043 (blue) ad Sythesized (red)

3 III. TRANSIENT RESPONSE ANALYSIS OF ANTENNA STRUCTURE Mathematical model of the atea structure is built o the basis of modal aalysis by meas of cotiuous modelig with classical approach (Euler-Beroulli Beam Theory) ad MDOF modal trasiet aalysis with Recursive Filterig Relatioship Method [6, 7]. Apart from this model, SDOF trasiet model ad simplified models are also preseted for completeess. Followig the roadmap of aalysis procedure, first, MDOF trasiet respose aalysis which is the mai purpose of the study is performed by RFR method. Modal aalysis outputs such as atural frequecies, mode shapes ad participatio factors are used as iputs to RFR trasiet aalysis. Therefore, this aalysis ca also be called as Modal Trasiet Aalysis because of the use of modal matrices built i cotiuous modelig. Shock profiles simulatig uderwater explosios are also used as acceleratio iputs. The output of aalysis icludes displacemet, acceleratio ad velocity shock resposes obtaied at ay poit o the atea structure. Critical displacemet ad acceleratio respose rages ca be ivestigated with Phase Portrait plots. Histograms ca also represet the reluctace of atea structure to failure or electromagetic malfuctios. For the MDOF RFR trasiet respose aalysis, time step ca be calculated as follows. dyamic respose of the atea structure ca be approximated by a catilever beam sice atea structure displays similar boudary coditios ad geometrical properties as catilevered beams. For cotiuous modelig of the atea structure, Euler-Beroulli beam model is used. Upo calculatio of atural frequecies ad mode shapes, this data is iput ito multi-degree-of-freedom trasiet aalysis. Trasiet resposes i terms of acceleratio, relative velocity ad relative displacemet of the atea structure are obtaied exactly ad umerically by differet methods for MDOF models, ad approximated; SDOF models. The major poit of iterest is the tip poit respose of the atea, because electrical compoets are placed i the viciity of the tip of the atea. Atea model used for aalysis is preseted i Figure 5. t dt t T 2exp t cos t cos t T exp 2 t T..., i d d, i 1, i2 2 exp( )cos( ) 1 exp( ) wi m t 2 1si( dt) t d 2t exp( t)cos( dt) 2 1 exp( 2t) wi m t exp( t)si( d t) d (2 t)exp( 2 t) exp( t) wi 2 m t 2 1si( dt) 2 cos( dt) d From time step calculatio, resposes ca be calculated by Equatio (3) where T is the time costat ad eigevector for the correspodig mode. r 1 Y (2) is the y( x, t) Y ( x) T ( t) (3) C-ESM/COMINT atea system is located o submaries ad special types of avy ships. The locatio of the platform is just upper side of the periscope support. The dipole COMINT atea is located vertically or horizotally i regards to the polarizatio eeds. Attachmet of atea oto the platform ca be basically described as fixig its base to the platform with bolted joits as illustrated i Figure 4. The other ed of the atea is free. Therefore, for atea structure, shock iput ca be categorized as base acceleratio type iput. Half-sie base acceleratio shock iput is determied for modelig as the shock profile uder cosideratio. Moreover, Figure 4 Atea Structure Attached to the Platform Figure 5 Three-Dimesioal Model of Atea Structure Geometrical ad mechaical properties of the atea structure are preseted o Table 3 ad 4. Table 3 Geometrical Properties of Atea Structure Table 4 Mechaical Properties of Atea Structure

4 From the modal aalysis performed aalytically, modal properties of atea structure are foud as follows. Table 5 Modal Properties of the Atea Structure Usig MDOF RFR Method, trasiet acceleratio-time respose of the atea tip is foud for the specified shock iput. Acceleratio (G) Acceleratio Respose of Atea Tip Acceleratio Respose 200g 8ms Half-sie Iput Time (sec) Figure 6 MDOF Absolute Acceleratio Respose of the Atea Tip Maximum absolute acceleratio ad relative displacemets ca also be estimated by meas of simplified methods. A comparative evaluatio of results is carried to uderstad the efficiecy of these simplified models i predictig the atea respose to shock iput as described. Fially SDOF trasiet aalysis is preseted. For SDOF trasiet aalysis, three differet methods are used. Results of these methods are compared with each other ad also compared with MDOF results. Sice SDOF trasiet aalysis methods are based o very primitive ad geometry-idepedet model, it is expected that resposes are ot very close to MDOF models aturally. For all aalysis procedures, MATLAB scripts are built ad results are obtaied by meas of these scripts. Complete results for mathematical modelig of the trasiet respose aalysis are preseted i Table 6. Table 6 Mathematical Model Resposes at the Atea Tip It has bee observed that MDOF modelig of atea structure by RFR Method is more tha capable to predict almost exact results whe the outcomes are compared. Therefore, validatio of the MDOF mathematical model is achieved. This is very importat to perform further aalysis studies for isolatio ad compoet fatigue. Exact solutio is obtaied from the toolbox by Yag [8] as the excitatio is classical pulse. The atea geometry ca be modeled as a catilever beam with iitial coditios all kept zero. However, for differet types of excitatio ad/or for differet boudary coditios, it is ot possible to fid a exact solutio. O the other had, MATLAB script writte for MDOF RFR Aalysis is capable to perform the aalysis with various shock iputs (e.g. square, sie, saw-tooth) ad boudary coditios like fixed-fixed or simply supported. Arbitrary shock iputs ca eve be aalyzed by MATLAB script with some modificatios o samplig ad discretizatio. Simplified methods estimate the trasiet respose of atea structure with mode-superpositio method. Modal iformatio of atea structure ad correspodig SRS value of mode iterested is used i this process. Therefore, it is better approximatio tha SDOF aalysis. Simplified methods yield very close results to MDOF aalysis for relative displacemet while the acceleratio respose cotais certai amout of error. Amog these methods, Square-Root-of- Sumof-Squares (SRSS) method gives acceptable results for the atea structure. Therefore, this method ca be used as a alterative for further studies like isolatio ad compoet fatigue. Other two methods are more successful while differeces betwee atural frequecies are higher. Naval Research Laboratories (NRL) method, for example is the basis of Direct Dyamic Aalysis Method (DDAM). I this method, differet methodology is followed for modal aalysis [9]. Sigle-degree-of freedom solutio is the most erroeous model amog these models because it is idepedet from geometrical ad modal properties of the structure cosidered. I this study, SDOF model is utilized for determiatio of SRS ad buildig the MDOF model from SDOF basics of RFR Method. IV. FINITE ELEMENT ANALYSIS FOR TRANSIENT RESPONSE OF ANTENNA STRUCTURE Trasiet respose aalysis of the atea structure subjected to uderwater shock explosios is performed by meas of Fiite Elemet Aalysis (FEA). I the scope of the study, modal ad trasiet aalyses are performed by meas of fiite elemet software package ANSYS R15.0. Atea geometry created o computer aided drawig software program (NX ) is imported to ANSYS Workbech. Material properties of AA6061-T6 are itroduced to the egieerig data library. Workbech-Modal ad Trasiet commads are employed for complete aalysis alog with Eforced Motio Extesio. APDL code is also writte to itroduce boudary coditios, shock iputs, base acceleratio iput case ad shock duratio determiatio ad to obtai meaigful shock outputs like absolute acceleratio, relative displacemet

5 ad relative velocity. Modal aalysis is performed to validate the atea FEA model with MDOF mathematical model results. The, trasiet aalysis follows with validated model ad shock resposes are compared to MDOF model results. As a outcome of this study, FEA modelig optio is to be proposed as a alterative to mathematical model i order to perform shock aalysis from simple to complex atea structures. For modal aalysis, ANSYS results ad theoretical results are ot differet more tha 1.3% for the first four modes. Thus the ANSYS results match quite well with Euler-Beroulli beam theory. Trasiet aalysis ca be performed based o the evidece that the model is validated. Table 7 Natural Frequecies of the Atea Structure Foud by FEA Trasiet resposes are obtaied ad compared to MDOF aalysis by RFR Method. Shock iput is the same as before, that is, 200g 8ms half-sie base acceleratio is applied to the structure. Absolute acceleratio respose of the atea tip is preseted i Figure 7. Table 8 Compariso of Maximum Trasiet Resposes Comparig, a slight differece is observed whe the results from mathematical modelig ad fiite elemet aalysis are compared. There are several reasos behid this slight differece although the atea structure is aalyzed with full modal-trasiet method o ANSYS. ANSYS model uses Newmark algorithm for the solutio methodology while the mathematical model oly uses recursive algorithm to solve covolutio itegrals. Therefore, the solutio formulatio for the mathematical model is almost exact. Moreover, i the mathematical model the beam elemet is modeled as 1-D for forcig directios. Thus, oly trasverse forces are cosidered i the model. However, fiite elemet aalysis software uses beam elemets o which three-directioal forcig is applied. This causes additioal effects that chage the dyamic respose of the beam elemet. Cosequetly, fiite elemet modelig may preset closer results to real-life cases. Sice both methods preset very close resposes, they ca be used iterchageably for differet cases i regard to the ease of use. Figure 7 ANSYS Absolute Acceleratio Respose of the Atea Tip As see from Table 8, fiite elemet aalysis results ca be termed satisfactory withi the 4.5-percet error rage compared to the exact result. Therefore, for complex geometries ad for the cases whose mathematical model is hard to obtai, fiite elemet aalysis ca be the alterative feasible way of solutio. As a importat remark, durig desig process, 5 to 6-percet error margi ca be defied i order to be o the safe side by fiite elemet aalysis for trasiet aalysis. V. EXPERIMENTAL VERIFICATION Theoretical models preseted are tried to be verified by meas of both modal ad trasiet experimetal aalyses. Experimetal aalysis for modal verificatio is performed by impact hammer tests. The atea structure is clamped i catilever beam cofiguratio to the experimetal setup base. A impact hammer is triggered to excite atea modes ad moitor the respose measured from the atea tip by meas of a micro-accelerometer. The tip respose is collected as a frequecy respose fuctio. Excitatio is take as the forcig by hammer ad the respose is measured by the accelerometer o the atea tip i the form of acceleratio per uit force. Therefore, atural frequecies ad modal dampig values are calculated via acquired data. Figure 8 Hammer Test of Atea Structure

6 Natural frequecies of atea structure obtaied from experimetal data due to impact hammer testig are preseted i Table 9. For this case, results are compared with mathematical model results with tip mass cosiderig the accelerometer mass additio to the model. Acceleratio respose measured from the atea tip is compared to results of the theoretical model i Figures 10 ad 11. Table 9 Natural Frequecies of Atea Structure with Tip Mass Table 10 Modal Dampig Ratios of Atea Structure Figure 10 Mathematical Model ad Experimet Compariso Shock testig is performed after modal verificatio. Shock testig is executed by meas of a drop table. Desired acceleratio iput values i desired time iterval is oly possible with high impact shock machies or drop table as a simple shock machies. Shock profile sythesis is performed i order to be able to perform shock testig with drop table test set-up istead of high impact shock machies because of the iadequacy of such experimetal ifrastructure. Therefore, it has become possible to perform drop tests for verificatio of models or qualificatio of structures istead of complex test procedures. Shock tests are performed usig drop table ad data acquisitio system. Data is acquired by meas of high acceleratio (up to 1000g) durable shock accelerometers. Figure 11 FEA Model ad Experimet Compariso Absolute acceleratio respose results are tabulated i Table 11 i order to compare results from theoretical models ad experimetal results. The experimetal results are take as the referece ad errors associated with modelig are evaluated with respect to the experimetal results. Figure 9 Drop Test Experimet

7 Table 11 Maximum Absolute Acceleratio Results of All Aalyses After the experimetal aalysis is performed for atea structure, it ca be cocluded that mathematical model ad FEA models are satisfactory eough for use i desig, qualificatio ad isolatio stages. I the lights of these verificatios, these models ca be readily employed for shock severity cosideratios at shock survival stage of electromechaical desig. VI. CONCLUSIONS Proposed shock aalysis for atea structure subjected for uderwater explosios is verified with both experimetal ad fiite elemet aalysis tools. By meas of the proposed methodology throughout the study, multi-degree-of-freedom trasiet respose aalysis of the atea structure is accurately performed usig four modes (90% of the effective modal mass) of the structure. Trasiet respose aalysis of the similar (beam type) atea structures with differet dimesios ad differet field of applicatios ca be readily applied. I the process of performig the shock profile sythesis i order to obtai meaigful shock iput data, it is observed that differet types of shock iputs ca be sythesized for reproducibility. Sythesized profiles are more coservative tha the origial oes due to the fact that shock respose spectrum coverage is higher tha origial pulses at low frequecies. For trasiet aalysis of the atea structure, RFR method is used for the solutio algorithm. This method is very easy to apply to the shock respose aalysis formulatio ad it is very fast. Elapsed time for respose obtaied from this method is almost oe secod for both modal ad trasiet aalysis. ANSYS solutio takes almost te secods for complete solutio. Therefore, the method developed for trasiet solutio ca be cosidered as very fast ad accurate. Moreover, the flexibility of the model is such that differet boudary coditio selectio, material selectio, icluded umber of modes selectio, modal dampig selectio, ad desired respose locatios, differet shock iput type selectios are readily possible to apply. REFERENCES [1] MIL-STD-810G, Evirometal Egieerig Cosideratios ad Laboratory Tests, Departmet of Defese Test Method Stadard, USA, [2] Buildig Specificatio for Ships of the Federal Armed Forces, 043, Shock Resistace Experimetal ad Mathematical Proof, March [3] "MIL-S-901D (Navy), Military Specificatio: Shock Tests. H.I. (High- Impact) Shipboard Machiery, Equipmet, ad Systems, Requiremets For". Uited States, Departmet of Defese. March 17, [4] Demir, M.E., Shock Aalysis of a Atea Structure Subjected to Uderwater Shock Explosios, M.Sc. Thesis, Middle East Techical Uiversity, Akara,Turkey, September [5] Irvie, T., A Itroductio to the Shock Respose Spectrum, Vibratio Data, July [6] Smallwood, D. O., A Improved Recursive Formula for Calculatig Shock Respose Spectra, 51 st Shock ad Vibratio Bulleti, Sadia Natioal Laboratories, Albuquerque, New Mexico, [7] Irvie, T., Modal Trasiet Aalysis of a System Subjected to a Applied Force via a Ramp Ivariat Digital Recursive Filterig Relatioship, Revisio K, Vibratio Data, [8] Yag, Bige. Stress, Strai, ad Structural Dyamics: A Iteractive Hadbook of Formulas, Solutios, ad MATLAB Toolboxes, Elsevier Ic., Sa Diego, [9] Irvie, T., Shock ad Vibratio Stress As a Fuctio of Velocity, Vibratio Data, April 2013.