The method of bonding a first object (1) to a second object (2) uses a connector, the connector having a first sheet portion and a second sheet portion (32). The first sheet portion has at least one outwardly protruding first attachment portion (33), and the second sheet portion has at least one outwardly protruding second attachment portion (34). The connector (3) further has a spacer between the first and second sheet portions. For bonding, the first and second objects (1, 2) and the connector (3) are positioned relative to each other so that the connector is placed between the first and second objects. Then the first and second objects (1, 2) are pressed against each other while mechanical vibration energy impinges on the first and/or second object until a first flow portion of thermoplastic material of the first object in contact with the first attachment portion(s) and a second flow portion of thermoplastic material in contact with the second attachment portion(s) become flowable allowing the respective attachment portions (33, 34) to be pressed into material of the first and second object, respectively. After re-solidification of the flow portions, a positive-fit connection between the first and second objects via the connector results. The spacer defines a width (w) of a gap between the first and second objects (1, 2) after bonding.