RESPONSE ANALYSIS OF CLAMPED-CLAMPED BEAM UNDER CONCENTRATED LOAD

Abstract

This paper studies the static and dynamic behavior of a clamped-clamped Euler Bernoulli beam subjected to a transverse point load applied at an arbitrary location x = a. Exact expressions for the deflection and stiffness are derived using Hermite basis functions, allowing the behavior of the beam to be evaluated for off-center loading. In the dynamic case, Krylov eigenfunction expansions and lumped mass models are used to study the resonance. The resulting modal solutions are verified using finite difference modeling. The proposed Galerkin-based approximations achieve an error of less than 4%, while simplifying the computational process and making them well suited for MEMS applications where the load position may vary.