Estimating the Dynamic Behavior of Printed Circuit Boards

REFERENCES

• Avalos , D. R. , Larrondo , H. and Laura , A. A. 1993 . Vibrations of a simply supported plate carrying an elastically mounted concentrated mass . Ocean Engineering , 20 : 195 – 205 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Xiang , Y. , Liew , K. M. and Kitipornchai , S. 1997 . “Vibration analysis of rectangular mindlin plates resting on elastic edge supports” . Journal of Sound and Vibration , 204 : 1 – 16 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Laura , P. A. A. and Grossi , R. O. 1978 . Transverse vibration of a rectangular plate elastically restrained against rotation along three edges and free on the fourth edge . Journal of Sound and Vibration , 59 : 355 – 368 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Laura , P. A. A. and Grossi , R. O. 1981 . Transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation . Journal of Sound and Vibration , 75 : 101 – 107 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Wu , J. S. and Luo , S. S. 1997 . Use of the analytical-and-numerical-combined method in the free vibration analysis of a rectangular plate with any number of point masses and translational springs . Journal of Sound and Vibration , 200 : 179 – 194 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Grossi , R. O. and Nallim , L. G. 1997 . A note on the strain energy stored in rotational springs at the plate edges of non-uniform thickness . Journal of Sound and Vibration , 206 : 448 – 452 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Nicholson , J. W. and Bergman , L. A. 1986 . Vibration of damped plate-oscillator systems . Journal of Engineering Mechanic , 112 : 14 – 30 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Gorman , D. J. 1997 . Accurate free vibration analysis of shear-deformable plates with torsional elastic edge support . Journal of Sound and Vibration , 203 : 209 – 218 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Reddy , J. N. 2004 . Mechanics of Laminated Composite Plates and Shells. Theory and Analysis, , 2nd ed. , Boca Raton, FL : CRC Press .
   Google Scholar
• Reddy , J. N. 1999 . Theory and Analysis of Elastic Plates , Philadelphia, PA : Taylor and Francis .
   Google Scholar
• Lim , C. W. and Liew , K. M. 1995 . “Vibrations of perforated plates with rounded corners” . Journal of Engineering Mechanics , 121 ( 2 ) : 203 – 213 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. and Liu , F. L. 1997 . “Differential cubature method: a solution technique for Kirchhoff plates of arbitrary shape” . Computer methods in Applied Mechanics and Engineering , 145 ( 1–2 ) : 1 – 10 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. , Kitipornchai , S. , Leung , A. Y. T. and Lim , C. W. 2003 . “Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method” . International Journal of Mechanical Sciences , 45 ( 5 ) : 941 – 959 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Huang , K. C. , Lim , M. K. and Liew , K. M. 1993 . “Boundary beam characteristics orthonormal polynomials in energy approach for vibration of symmetric laminates—II: elastically restrained boundaries” . Composite Structures , 26 ( 3–4 ) : 185 – 209 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. , Hung , K. C. and Lim , M. K. 1993 . “Method of domain decomposition in vibrations of mixed edge anisotropic plates” . International Journal of Solids and Structures , 30 ( 18 ) : 3281 – 3301 . [CSA] [CSA]
   Google Scholar
• Xiang , Y. , Liew , K. M. and Kitipornchai , S. 1997 . “Vibration analysis of rectangular mindlin plates resting on elastic edge supports” . Journal of Sound and Vibration , 204 ( 3 ) : 1 – 16 . [CSA] [CSA]
   Google Scholar
• Liew , K. M. , Hung , K. C. and Lam , K. Y. 1993 . “On the use of the substructure method for vibrations analysis of rectangular plates with discontinuous boundary conditions” . Journal of Sound and Vibration , 163 ( 3 ) : 451 – 462 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. , Hung , K. C. and Lim , M. K. 1993 . “Roles of domain decomposition method in plate vibrations; Treatment of mixed discontinuous periphery boundaries” . International Journal of Mechanical Sciences , 35 ( 7 ) : 615 – 632 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. , Hung , K. C. and Lim , M. K. 1994 . “On the use of the domain decomposition method for vibration of symmetric laminates having discontinuities at the same edge” . Journal of Sound and Vibration , 178 ( 2 ) : 243 – 264 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liew , K. M. , Huang , Y. Q. and Reddy , J. N. 2004 . Analysis of general shaped thin plates by the moving least-squares differential quadrature method . Finite Element in Analysis and Design , 40 : 1453 – 1474 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Liu , F. L. and Liew , K. M. 1999 . Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method . Journal of Sound and Vibration , 255 : 915 – 934 . [CSA] [CSA]
   Google Scholar
• Liew , K. M. , Huang , Y. Q. and Reddy , J. N. 2002 . “A hybrid moving least squares and differential quadrature (MLSDQ) meshfree method” . Int. J. Comp. Meth. Engn. Sci. Mech. (formerly Int. J. Comp. Engng. Sci.) , 3 ( 1 ) : 1 – 12 . [CSA] [CSA]
   Google Scholar
• Liu , F. L. and Liew , K. M. 1999 . “Vibration analysis of discontinuous Mindlin plates by differential quadrature element method” . Journal of Vibration and Acoustics , 121 ( 2 ) : 204 – 208 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Bellman , R. E. , Kashef , B. G. and Casti , J. 1972 . Differential quadrature: a technique for rapid solution of nonlinear partial differential equations . Journal Computational Physics , 10 : 40 – 52 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Civan , F. and Sliepcevich , C. M. 1983 . Application of differential quadrature to transport processes . Journal of Mathematical Analysis and Applications , 93 : 206 – 221 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Civan , F. 1994 . Solving multivariable mathematical models by the quadrature and cubature methods . Numerical Methods for Partial Differential Equations , 10 : 545 – 567 . [CSA] [CSA]
   Google Scholar
• Han , J. B. and Liew , K. M. 1999 . Axisymmetric free vibration of thick annular plates . International Journal of Mechanical Science , 41 : 1089 – 1109 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Chen , W. and Zhong , T. 1997 . The study on the nonlinear computations of the DQ and DC methods . Numerical Methods for Partial Differential Equations , 13 : 57 – 75 . [CSA] [CSA]
   Google Scholar
• Bert , C. W. , Wang , X. and Striz , A. G. 1994 . Convergence of the DQ method in the analysis of anisotropic plates . Journal of Sound and Vibration , 170 : 140 – 144 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Bert , C. W. , Wang , X. and Striz , A. G. 1993 . Differential quadrature for static and free vibration analysis of anisotropic plates . International Journal of Solids and Structures , 30 : 1737 – 1744 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Bert , C. W. , Wang , X. and Striz , A. G. 1994 . Static and free vibration analysis of beams and plates by differential quadrature method . Acta Mechanica , 102 : 11 – 24 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Malik , M. and Bert , C. W. 1996 . “Implementing multiple boundary conditions in the DQ solution of higher-order PDE's: application to free vibration of plates” . International Journal for Numerical Methods in Engineering , 39 : 1237 – 1258 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Chon , C. T. 1984 . Design sensitivity analysis strain energy via distribution . AIAA Journal , 22 : 559 – 561 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Tielking , J. T. 1980 . Asymmetric bending of annular plates . International Journal of Solids and Structures , 16 : 361 – 373 . [CSA] [CSA]
   Web of Science ®Google Scholar
• Lin , S. 1997 . Vibration Analysis of Printed Circuit Boards , Master's Thesis National Sun Yat-Sen University .
   Google Scholar