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acceleration aluminum cantilever aluminum simply supported amplitude assumed axis calculated cantilever beam cantilever plate circular plate clamped clamped edge critical damping cross section degree of freedom diameter dimensions displacement Dunkerley's equation elastic body Example Find the frequencies free vibration frequency constants frequency factor frequency formula fundamental frequency given in Table gives frequencies higher modes inches inertia infinite number kilogram kinetic energy lateral vibration length linear spring constant longitudinal magnesium mass attached massless material correction factor maximum metre modes of lateral modes of vibration modulus natural frequency nodal lines nodal pattern percent plate clamped Poisson's ratio potential energy quency radial radius of gyration rectangular plate second mode frequency shear simple harmonic motion simply supported beam single degree solid circular cross-section Solution sound velocity square plate static deflection stiffness thickness third mode frequencies three modes tion torsional U.S. Customary units undamped vibratory system consists wave width