Dept of Structural Engineering Earthquake Engg and Structural control (EESC) Tutorial 5 Course coordinators: Prof. Giorgio Serino (serino@unina.it) and Prof. Chandrasekaran Answer all questions. (chandrasekaran.srinivasan@unina.it) You are encouraged to use Matlab 1. For the given branched system, formulate the Equation of motion in free undamped vibrations. Assume k = 1 kN/m and m = 100 kg. Using Matlab, compute the natural frequencies and mode shapes of the spring-mass system. 1.5k ww x,(t) x(t) x(t) x(t) WWW 1.5m www m www 3m www2.5m wwwww 2m 3 k 2k 4k 2k 1.5k wwwwww wwwww 2k 2k x(t) 2. Define natural frequency of vibrating systems & its importance in design. What is classical damping, why it is useful in design? 3. Write the equations of motion for the one-story, one-bay frames shown below. The mass lumped at the beam is m. Assume the frames to be massless and neglect damping. 4. El = h El L m EI 12 p(t) El h El m L = 2h - p(t) El A system that is composed of two rigid beams is given below. (mL = m) (a) Determine the equations of motion. Use lumped-mass assumption. (b) Determine the eigenvalues and eigenvectors. L/2 P(1) m no mass m k L/2 L/2 L/2