Determining response probability density of nonlinear stochastic systems by modifying analytical result of degenerated systems
Tài liệu tham khảo
Caughery, 1971, Nonlinear theory of random vibration, Adv Appl Mech, 11, 209, 10.1016/S0065-2156(08)70343-0
Lin, 1995
Caughey, 1967, On the response of a class of self excited oscillators to stochastic excitation, Int J Non-Linear Mech, 2, 125, 10.1016/0020-7462(67)90010-8
Caughey, 1982, The steady-state response of a class of dynamical systems to stochastic excitation, ASME J Appl Mech, 49, 629, 10.1115/1.3162538
Dimentberg, 1982, An exact solution to a certain nonlinear random vibration problem, Int J Non-Linear Mech, 17, 231, 10.1016/0020-7462(82)90023-3
Lin, 1988, Exact stationary response solution for second order nonlinear systems under parametric and external white noise excitations: part II, ASME J Appl Mech, 55, 702, 10.1115/1.3125852
Fuller, 1969, Analysis of nonlinear stochastic systems by means of the Fokker–Planck equations, Int J Control, 9, 603, 10.1080/00207176908905786
Soize, 1994
Zhu, 1996, Exact stationary solutions of stochastically excited and dissipated integrable Hamiltonian systems, ASME J Appl Mech, 63, 493, 10.1115/1.2788895
Zhu, 2001, Exact stationary solutions of stochastically excited and dissipated partially integrable Hamiltonian systems, Int J Non-Linear Mech, 36, 39, 10.1016/S0020-7462(99)00086-4
Wang, 2000, A generalized analysis technique of the stationary FPK equation in nonlinear systems under Gaussian white noise excitations, Int J Eng Sci, 38, 1315, 10.1016/S0020-7225(99)00081-6
To, 2000
Huang, 2008, Construction of the stationary probability density for a family of SDOF strongly non-linear stochastic second-order dynamical systems, Int J Non-Linear Mech, 43, 563, 10.1016/j.ijnonlinmec.2008.02.001
Shinozuka, 1972, Monte Carlo solution of structural dynamics, Comput Struct, 2, 855, 10.1016/0045-7949(72)90043-0
Spanos, 1981, Monte-Carlo Simulations of response of non-symmetric dynamics system to random excitations, Comput Struct, 13, 371, 10.1016/0045-7949(81)90146-2
Zhu, 2006, Nonlinear stochastic dynamics and control in Hamiltonian formulation, Appl Mech Rev, 59, 230, 10.1115/1.2193137
Caughey, 1963, Equivalent linearization techniques, J Acoust Soc Am, 35, 1706, 10.1121/1.1918794
Crandall, 1980, On statistical linearization for nonlinear oscillations, 2
Proppe, 2003, Equivalent linearization and Monte Carlo simulation in stochastic dynamics, Probab Eng Mech, 18, 1, 10.1016/S0266-8920(02)00037-1
Roberts, 1986, Stochastic averaging-an approximate method of solving random vibration problems, Int J Non-Linear Mech, 21, 111, 10.1016/0020-7462(86)90025-9
Zhu, 1991, Stochastic averaging of energy envelope, ASCE J Eng Mech, 117, 1890, 10.1061/(ASCE)0733-9399(1991)117:8(1890)
Spencer, 1993, On the numerical solution of the Fokker–Planck equation for nonlinear stochastic systems, Nonlinear Dyn, 4, 357, 10.1007/BF00120671
Sun, 1990, The generalized cell mapping method in nonlinear random vibration based upon short-time Gaussian approximation, ASME J Appl Mech, 57, 1018, 10.1115/1.2897620
Kougioumtzoglou, 2013, Response and first-passage statistics of nonlinear oscillators via a numerical path integral approach, ASCE J Eng Mech, 139, 1207, 10.1061/(ASCE)EM.1943-7889.0000564
Crandall, 1963, Perturbation techniques for random vibration of nonlinear systems, J Acoust Soc Am, 35, 1700, 10.1121/1.1918792
Kougioumtzoglou, 2009, An approximate approach for nonlinear system response determination under evolutionary stochastic excitation, Curr Sci, 97, 1203
Iyengar, 1978, Study of the random vibration of nonlinear systems by the Gaussian closure technique, ASME J Appl Mech, 45, 393, 10.1115/1.3424308
Hampl, 1989, Probability densities of the response of nonlinear substitutes under stochastic dynamic excitation, Probab Eng Mech, 4, 2, 10.1016/0266-8920(89)90002-7
Er, 1998, Multi-Gaussian closure method for randomly excited non-linear systems, Int J Non-Linear Mech, 33, 201, 10.1016/S0020-7462(97)00018-8
Er, 2000, Exponential closure method for some randomly excited non-linear systems, Int J Non-Linear Mech, 35, 69, 10.1016/S0020-7462(98)00088-2
Chen, 2017, Stationary response probability distribution of SDOF nonlinear stochastic system, ASME J Appl Mech, 84, 10.1115/1.4036307
Jaynes, 1957, Information theory and statistical mechanics, Phys Rev, 106, 620, 10.1103/PhysRev.106.620
Sobczyk, 1999, Approximate probability distributions for stochastic systems: maximum entropy method, Comput Meth Appl Mech Eng, 168, 91, 10.1016/S0045-7825(98)00135-2
Ricciardi, 2002, A novel local stochastic linearization method via two extremum entropy principles, Int J Non-Linear Mech, 37, 785, 10.1016/S0020-7462(01)00099-3