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By N. Shanmugam, C. Wang

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1957), Vibration design charts. Transactions, ASME, 79, 1459–1475. H. B. (1964), Transverse vibrations of tapered cantilever beams with end loads. Journal of the Acoustical Society of America, 36, 463–469. H. B. (1968), Transverse vibrations of tapered cantilever beams with end support. Journal of the Acoustical Society of America, 44, 1739–1741. H. B. (1972), Transverse vibrations of double-tapered cantilever beams. Journal of the Acoustical Society of America, 51, 1771–1774. H. B. (1974), Transverse vibrations of double-tapered cantilever beams with end support and with end mass.

Engineering Structures, 22(9), 1180–1188. Sato, K. (1980), Transverse vibrations of linearly tapered beams with ends restrained elastically against rotation subjected to an axial force. International Journal of Mechanical Sciences, 22, 109–115. N. and Isakson, G. (1951), Approximate analytical methods for determining natural modes and frequencies of vibration, Massachusetts Institute of Technology Report ONR Proj. NR-035-259, 141–146. W. J. (1956), Free lateral vibration of beams of variable crosssection.

Z7〉 {q1 q2 ... 86 L This allows the septimal interpolation function to be written as w = 〈N1 N2 ... 88 Appropriate differentiation of Eqs. 88) and substitution of Eq. 87) into Eqs. 11) and then into Eq. 92 The stiffness and mass matrices for each element ( )e may be assembled into the global counterpart matrices K and M using equilibrium and compatibility in the usual way. When the energy function Π remains stationary with respect to the vector of structural or global deformations Q, dΠ/dQ = 0, so that in Eq.

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Analysis and Design of Plated Structs. [V. 2 - Dynamics] by N. Shanmugam, C. Wang


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