Advanced theory of vibration: nonlinear vibration and one dimensional structures
The Theory Of Vibration - Particularly Advanced Theory - Is Scattered Over A Large Number Of Publications Relating To Different Disciplines. What Has Been Attempted In The Present Book Is A Comprehensive Consolidation Of Them And Its Presentation In A Concise Manner For The Benefit Of Those Aspiring To Specialise In Vibration Studies At Postgraduate And Doctoral Level. The Contents Of This Book Have Got Crystallised Over A Period Of 25 Years While Teaching And Guiding Doctoral Level Research. The Emphasis In This Book Is On Analysis Of Continuous Rather Than Discrete System Models. A Concise Treatment Of Variational Principles And Their Application To Vibration Problems Is Given Next. Vibration Theories Of Viscoelastic Materials In Longitudinal Vibration And Lateral Vibration Are Also Considered At Length.Solutions To Problems Of Free And Forced Vibrations Are Presented. The Book Seeks To Explain To Students A Large Variety Of Problems Of One-Dimensional Structures.
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Forced Oscillations of Nonlinear Systems
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amplitudes of vibration analysis angle approximate assume axis becomes behaviour bending body boundary conditions coefficients coordinate corresponding cosh damping defined deflection deformation derivatives determine differential equation displacement field Duffing dynamic Effects of shear eigen value problem elastic elementary theory equation of motion Euler Euler-Lagrangian equation excitation force external force fixed-free forced vibration free vibration Frequency equation frequency ratio Galerkin method generalised gives Hamilton's principle Hence initial conditions integral curves kinetic energy Lagrange method Lagrangian Laplace transform lateral inertia layer Let us consider longitudinal vibration Mode shape modulus natural frequencies nondimensional nonlinear system obtained oscillator phase plane pre-twist Rayleigh Reissner method response Ritz method roots shape functions shear stiffness shown in Fig singular point stability strain energy stress field Substituting taper tensor Timoshenko beam torsional rigidity torsional vibration traction forces trajectory unstable variable varied paths velocity virtual displacement viscoelastic viscoelastic bar zero