S7-1 SECTION 7 FREQUENCY RESPONSE ANALYSIS

S7-2 INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS n Frequency response analysis is a method used to compute structural response to steady-state oscillatory excitation. u Examples of oscillatory excitation include rotating machinery, unbalanced tires, and helicopter blades. n In frequency response analysis the excitation is explicitly defined in the frequency domain. u All of the applied forces are known at each forcing frequency. u Forces can be in the form of applied forces and/or enforced motions (displacements, velocities, or accelerations).

S7-3 INTRODUCTION TO FREQUENCY RESPONSE ANALYSIS (Cont.) n Oscillatory loading is sinusoidal in nature. u In its simplest case, this loading is defined as having an amplitude at a specific frequency. u The steady-state oscillatory response occurs at the same frequency as the loading. l The response may be shifted in time due to damping in the system. The shift in response is called a phase shift because the peak loading and peak response no longer occur at the same time.

S7-4 n For the cantilever beam shown here (figure at top), and a cosine (Harmonic) forcing function presented as a tip load, the Frequency Response procedure finds a solution that matches the theory. The first natural frequency is 325 Hz n Plotting the tip displacement magnitude as a function of the frequency of the harmonic excitation (figure at bottom) one can clearly see the static solution and the resonance when the first natural frequency is reached. Resonance Static solution  = 0 FREQUENCY RESPONSE

S7-5 TYPICAL FREQUENCY RESPONSE

S7-6 FREQUENCY RESPONSE n Frequency based dynamics should have the following characteristics: u The system should be linear. (but could have nonlinear preloading) l Linearized material behavior l No change in contact conditions l No nonlinear geometric effects other than those resulting from preloading. n The important results obtained from a frequency response analysis usually include the displacements, velocities, and accelerations of grid points as well as the forces and stresses of elements

S7-7 FREQUENCY RESPONSE n The important results obtained from a frequency response analysis usually include the displacements, velocities, and accelerations of grid points as well as the forces and stresses of elements. n The computed responses are complex numbers defined as magnitude and phase (with respect to the applied force) or as real and imaginary components, which are vector components of the response in the real/imaginary plane.

S7-8 FREQUENCY RESPONSE

S7-9 FREQUENCY RESPONSE

S7-10 Solution Parameters

S7-11 Loadings and Boundary conditions n Nodal u Displacement u Force n Elemental u Pressure u Inertia load Load case Job parameters MSC.Marc doesn’t support it until 2005r2

S7-12 Mentat Interface