Dynamic response of beams with passive tuned mass dampers

Passive tuned mass damper (TMD) is a stand-alone vibrating system attached to a primary structure and designed to reduce vibration of the structure at selected frequency. This study focuses on the application of single or multiple TMDs on Euler-Bernoulli beams and examines their effectiveness based on free and forced vibration characteristics of the beams, i.e., the primary structures. There is a gap in the existing literature in terms of free and forced vibration analysis of beams carrying any number of concentrated elements. There are methods developed for the free vibration analysis but they are not practical due to the complex mathematical expressions. Numerical assembly method (Wu and Chou, 1999) is used to determine free vibration characteristics of beams in order to get over the drawbacks of other approaches in the literature and forced vibration response is obtained based on modal analysis approach and orthogonality condition. The free-vibration formulations for uniform, non-uniform single-span and multi-span continuous beams carrying any number of elastically mounted masses are derived for various boundary conditions. Numerical solutions for dynamic responses of these beams subjected to impulsive, harmonic, moving and moving pulsating loads are presented. A numerical eigenvalue solution is used to obtain the modal properties of the entire beam at its fundamental and lower normal modes. The modal analysis approach allows calculatin displacement, velocity, acceleration and jerk responses at any point on the beam. The resultant dynamic responses of beams with and without TMDs are compared with each other in order to observe the performance of TMDs. Numerical examples are given to confirm the validity and efficiency of the proposed method. Natural frequencies and mode shapes of several structures studied in literature are calculated and compared with those in existing literature to verify the accuracy of the developed algorithm. The illustrative forcing functions are considered as human-induced dynamic loads for uniform single and multiple span beams. The results demonstrate that passive TMDs are efficient in reducing the dynamic responses of beams subjected to harmonic excitations. However, passive TMDs do not show the same level of performance under non-harmonic loads. Additionally, wind load analysis is performed for a sample high mast lighting tower (HMLT) represented as a cantilever non-uniform beam in this study and the efficiency of attached TMD is analyzed. Experimental wind velocity data is used to generate the wind induced dynamic load on the HMLT. Results indicate that properly tuned passive TMDs may be an option to reduce dynamic response in wind-excited HMLTs