Formulas for Structural Dynamics

Formulas for Structural Dynamics 

Olga Lebed,

Preference :

Deformable systems with distributed parameters are widely used in modern engineering. Among these systems, planar systems such as beams, arches, and frames, are some of the most commonly used systems in practice. These systems find wide applications in civil and transport engineering (supported structures, framing elements for airplanes, ships, and rockets), in mechanical engineering, robotics and radio-engineering (load-bearing members, electric drives for robotics and mechanisms, boards of radio-electronic apparatus, etc). With the development of ‘high technologies’, the purpose of deformable systems (DS) and their functional peculiarities as part of an engineering system is changed. Elastic elements become objects of active control. Elastic beam elements are used as mechanical filters in electronics. Elastic DS is used in control and measurement systems, which include elements of different natures, such as electrical, acoustical, optical, magnetic elements. Beam systems are widely used as resonant strain gauges in micro-mechanical systems for the measurement of forces, accelerations, displacements, and pressure.

Content :
  • Transverse vibration equations
  • Analysis methods
  • Fundamental equations of classical beam theory
  • Special functions for the dynamical calculation of beams and frames
  • Bernoulli–euler uniform beams with classical boundary conditions
  • Bernoulli–euler uniform one-span beams with elastic supports
  • Bernoulli–euler beams with lumped and rotational masses
  • Bernoulli–euler beams on elastic linear foundation
  • Bernoulli–euler multispan beams
  • Prismatic beams under compressive and tensile axial loads
  • Bress–timoshenko uniform prismatic beams
  • Non-uniform one-span beams
  • Optimal designed beams
  • Nonlinear transvers vibrations
  • Arches
  • Frames

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