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CONTINUOUS SYSTEMS Heavy Shafts and Beams
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a.sin acceleration amplitude angle angular displacement Appendix applied force arbitrary constants axis beam calculated Chapter complementary function corresponding cosh cot+<f critical damping critical value cross-section curve cycle damping coefficient damping forces dashpot degrees of freedom determined dynamic magnifier dynamic stiffness effective inertia energy engineering equation of motion example expression formula Fourier Fourier analysis Fourier series frequency equation frequency p/2n given harmonic Hence inertia excitation initial conditions Ker Wilson lbs./in lbs.ins.secs.2 linear mass maximum mcot method modulus natural frequency node obtained operator P0 sin pt pendulum phase-angle polar inertia poundals practical proportional quantities quency radians ratio resonant frequency result shear shown in Fig simple harmonic motion sinh sinpt sinusoidal slugs solution spring static deflection static position steady rotation substitution swinging form system of Fig termed torque torsional system torsional vibration unit vector vibration problems vibration study Young's modulus zero damping