Nonlinear Dynamics Analysis of a Printed Wiring Board With Simple and Clamped Boundary Conditions

2001 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Resonance ◽  
Failure Criteria ◽  
Dynamics Analysis ◽  
Printed Wiring Board ◽  
Resonance Behavior ◽  
Condition Effect ◽  
Wiring Board

Abstract Dynamic response of a printed wiring board (PWB) is analyzed in nonlinear dynamics approach. Equations of motion for the simply supported PWB and the clamped PWB are obtained by the Galerkin’s method. A 2-layer plastic PWB made of isotropic laminates is studied for its boundary condition effect on the vibratory behavior in deflection and stresses. Failure due to plane stress interaction is estimated based on the composite failure criteria. It is found that nonlinear resonance occurs almost periodically in both frequency and temporal domain. Load frequency and magnitude affect the deflection response under different boundary conditions. Resonance behavior is critical in PWB failure prediction based on the stress analysis. The analytical results can be extended to the nonlinear dynamics analysis of the thin laminated plate.

Nonlinear Dynamics Analysis of a Laminated Printed Wiring Board

2002 ◽  
Vol 124 (2) ◽  
pp. 77-84 ◽  
Author(s):  
Xiaoling He ◽  
Robert E. Fulton
Keyword(s):  
Dynamic Response ◽  
Large Deflection ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Printed Wiring Board ◽  
High Acceleration ◽  
Dynamic Stress Field ◽  
Laminate Theory ◽  
Wiring Board ◽  
Nonlinear Elastic

Nonlinear laminate theory is applied for the printed wiring board (PWB) dynamic response analysis. Equations of motion for the nonlinear elastic deformation of the isotropic laminates are derived for the dynamic response of a simply supported PWB. Numerical results are generated for the nonlinear response characterization of the PWB deformation. Comparisons are made between the response of linear and nonlinear systems. Results show that PWB is in large deflection under high acceleration or certain pressure load. Nonlinear theory gives more accurate results for the large deflection than the linear theory does. Besides, lamina stresses are analyzed and illustrated from finite difference computation. The analytical derivation in modal approach and the stress analysis provide the basis for PWB reliability studies, especially the defect and failure induced by the dynamic stress field.

Dynamic Behavior of Electronic Module Spring Clips, Retention Bar, and Backplane Connector: Modeling and Testing

2009 ◽  
Author(s):  
Kenneth P. Vandevoordt ◽  
Michael Feng
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Element Model ◽  
Guidance System ◽  
Printed Wiring Board ◽  
Wiring Board ◽  
Electrical Components ◽  
Hardware Test ◽  
The Finite Element Model

Electronic modules for a guidance system are mounted in a rack with spring clips resisting motion normal to the printed wiring board (PWB) and an aluminum bar with an elastomer pad keeping the module connected to a backplane. The elastomer pad also resists motion normal to the board. The proper boundary conditions for the spring clips, retention bar, and connector are needed in a finite element model in order to evaluate the shock and vibration transmitted to the module’s electrical components. The finite element model of the module was assembled, and an actual module was tested under random vibration and a 1g sine sweep. The printed wiring board elastic modulus was artificially set higher in the FEM than a measured value to account for the stiffening effect of board components which were omitted from the model. By also choosing the proper boundary conditions to represent the spring clips, retention bars, and backplane connection, the finite element model was able to match the first and second mode frequencies from the hardware test results.

Nonlinear Shell Dynamics—Intrinsic and Semi-Intrinsic Approaches

1983 ◽  
Vol 50 (3) ◽  
pp. 531-536 ◽  
Author(s):  
A. Libai
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Field Equations ◽  
Nonlinear Shell ◽  
Initial And Boundary Conditions ◽  
Shell Dynamics

The intrinsic approach to the nonlinear dynamics of shells, which was introduced in [6], is reviewed and extended by the addition of appropriate initial and boundary conditions of the dynamic and kinematic types to the field equations. The alternative semi-intrinsic velocity approaches (where the velocity components supply the connection between the equations of motion and the time rates of the metric and curvature) are also presented. Both linear and rotational velocity forms are included. The relative merits of these approaches to shell dynamics are discussed and compared with extrinsic approaches.

Nonlinear Dynamics of Stockbridge Dampers

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
O. Barry ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Nonlinear Frequency ◽  
Modulation Equations ◽  
Proposed Model ◽  
Cantilevered Beams ◽  
Stockbridge Damper

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

Nonlinear Thermal and Mechanical Analysis in the Vibration of a Printed Wiring Board

2000 ◽  
Author(s):  
Xiaoling He ◽  
Robert Fulton
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Temperature Variation ◽  
Equations Of Motion ◽  
Mechanical Analysis ◽  
Response Analysis ◽  
Printed Wiring Board ◽  
Simply Supported ◽  
Laminate Theory ◽  
Wiring Board

Abstract Nonlinear laminate theory is applied and extended for the printed wiring board dynamic analysis. Equations of motion for the isotropic laminates are derived for vibration response analysis of the simply supported printed wiring board under mechanical and thermal loads. Temperature variation in spatial domain is taken into consideration. The effect of the temperature variation on the response character is analyzed and demonstrated by means of numerical results. Modal analysis is made to predict the vibration behavior in terms of deflection and stresses. Lamina stresses are used for failure prediction.

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