Dynamic behaviour of thin walled bars of open cross section

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Trends towards more slender structures and increased awareness of the potentially disastrous consequences of major forms of dynamic loading, such as induced by earthquakes, blasts and severe impacts, has resulted in continued interest in the dynamic response of structures and structural components. a first step towards understanding the response of structures to dynamic loading is to study their natural frequencies and corresponding modes of vibration. this information can be incorporated in analyses, based on mode superposition, to give the complete linear response to prescribed dynamic loading (timoshenko et a. clough and penzienl in mathematical terms, the natural frequencies are the eigenvalues of the governing undamped equations of motion, while the modes of vibration are the corresponding eigenvectors. in practical terms, if an undamped mechanical system is excited at a frequency close to one of its natural frequencies, the amplitude of the corresponding mode of vibration increases rapidly, and is limited only by nonlinear effects, a condition referred to as resonance.