978-1-4244-2118-3/08/$25.00 ©2008 IEEE 1 2008 10 th Electronics Packaging Technology Conference Vibration Analysis of a Simply Supported PCB with a Component– An Analytical Approach Banu Aytekin † , H. Nevzat Özgüven* † The Scientific and Technological Research Council of Turkey - Defence Industries Research and Development Institute TUBITAK-SAGE, P.K. 16 Mamak, 06261 Ankara, Turkey Phone: + 90 312 590 9233 Fax: +90 312 590 9148 Email: banu.aytekin@sage.tubitak.gov.tr *Mechanical Engineering Department, Middle East Technical University, 06531 Ankara, Turkey Phone: + 90 312 210 2549 Fax: +90 312 210 2536 Email: ozguven@metu.edu.tr Abstract It is a well known fact that vibration is one of the most important loading condition in electronic systems. This study deals with dynamic analysis of a printed circuit board (PCB) with a component on it under vibratory loading. The objective of the study is to develop an analytical model for common PCB configurations and electronic components on them in order to predict dynamics of the assembly under vibratory loading, and thus to study the effects of component location. As an application, in this paper an analytical model of a simply supported PCB with a component is presented. The validity of the two degree of freedom analytical model is demonstrated by comparing numerical results for random vibration input with those of a finite element model. Introduction Electronic devices used in control, guidance and communication systems are one of the most important parts of modern avionic systems. Common aim in the aerospace industry is to design and produce systems which have a life of at least 20 years with high reliability levels. The complex and fragile structure of electronic systems requires special attention in order to meet the expectations of the aerospace industry. Since vibratory loading is very critical for electronic systems, several studies are performed to analyze and isolate vibration in electronic systems. Steinberg [1] presented analytical and empirical methods for analyzing vibration of electronic assemblies. Veprik [2] used a 2 degree of freedom mass, spring and damper system for solving vibration isolation problems in electronic boxes. Suhir [3] studied component vibrations in electronic equipments. He derived a formula which gives the natural frequency of a heavy electronic component mounted on a circuit board with a plated through- hole. Perkins and Sitaraman [4] investigated the effect of an electronic component on the vibration characteristics of an electronic system. Esser and Huston [5] used dynamic vibration absorber to control the vibration of printed circuit boards. Jung et al. [6] studied the structural vibrations of an electronic equipment by using analytical modeling, finite element modeling and testing. Cifuentes and Kalbag [7] studied optimization of support locations of a PCB. They employed finite element modeling in their study. Cifuentes [8] also carried out studies to identify factors that affect the dynamic behavior of PCB. Salvatore and Followell [9] studied the fatigue in solder joints due to vibration. They investigated the effect of component location, component size and component type. Schaller [10] added the effects of components by increasing the board’s modulus of elasticity and density in regions where components are located. He analyzed the wedge locks and connectors and modeled them as torsional springs and springs, respectively. Veilleux [11] dealt with controlling the destructive resonant amplitude of PCBs in electronic systems. He compared isolation, extensional damping and shear damping techniques for decreasing resonant amplitude value. Zampino [12] studied finite element model of a rectangular electronic box containing a PCB. Pitarresi [13] used different finite element modeling approaches for PCB vibrations and compared the results obtained with experimental outcomes. Lau and Keely [14] investigated the lead dynamics with and without solder joints. They employed finite element analysis to obtain natural frequencies, and verified their results by vibration tests using a Laser Doppler Vibrometer. Ham and Lee [15] also investigated the effect of vibration on lead wire fatigue life. There are various studies in which vibratory behaviors of an electronic system are obtained by performing experiments or by using finite element modeling. However, these approaches are generally time consuming. In this paper a simple analytical model is suggested in order to avoid expensive finite element modeling and experimental approaches in preliminary design stage of PCBs. The model suggested makes it possible to study the vibratory responses of critical elements on a PCB for different design alternatives in the preliminary design stage. As a specific application, 100 mm x 70 mm x 1.6 mm printed circuit FR4 board with simply supported boundary conditions is considered and a four leaded electronic component is added at the center of the PCB. The two degree of freedom spring mass model suggested for PCB-component system is used to obtain the response of the system to a random vibration profile. Acceleration spectral density and root mean square value of acceleration are calculated for the electronic component. They are compared with those obtained with a detailed finite element model in order to demonstrate the validity of the model proposed. Discrete Model The discrete model suggested (Fig. 1) represents the first mode of the printed circuit board and the vibration of a component on the PCB. Equivalent mass and spring constants representing the first mode of the PCB are calculated, and combined with the discrete model of the component on it. Printed circuit board modeling is performed by applying a unit force to the point which vibrates the most at the first mode. Amount of static displacement is calculated for simply supported PCB. The displacement is used for calculating